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Bouncing cosmologies: progress and problems. (English) Zbl 1372.83002

Summary: We review the status of bouncing cosmologies as alternatives to cosmological inflation for providing a description of the very early universe, and a source for the cosmological perturbations which are observed today. We focus on the motivation for considering bouncing cosmologies, the origin of fluctuations in these models, and the challenges which various implementations face.

MSC:

83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83F05 Relativistic cosmology
83C75 Space-time singularities, cosmic censorship, etc.
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
85A40 Astrophysical cosmology
83E30 String and superstring theories in gravitational theory

References:

[1] Guth, A.H.: The Inflationary Universe: A Possible Solution To The Horizon And Flatness Problems. Phys. Rev. D 23, 347 (1981) · Zbl 1371.83202 · doi:10.1103/PhysRevD.23.347
[2] Brout, R., Englert, F., Gunzig, E.: The creation of the universe as a quantum phenomenon. Ann. Phys. 115, 78 (1978) · doi:10.1016/0003-4916(78)90176-8
[3] Starobinsky, A.A.: A new type of isotropic cosmological models without singularity. Phys. Lett. B 91, 99 (1980) · Zbl 1371.83222 · doi:10.1016/0370-2693(80)90670-X
[4] Sato, K.: First order phase transition of a vacuum and expansion of the universe. Mon. Not. R. Astron. Soc. 195, 467 (1981) · doi:10.1093/mnras/195.3.467
[5] Fang, L.Z.: Entropy generation in the early universe by dissipative processes near the Higgs’ phase transitions. Phys. Lett. B 95, 154 (1980) · doi:10.1016/0370-2693(80)90421-9
[6] Vachaspati, T., Trodden, M.: Causality and cosmic inflation. Phys. Rev. D 61, 023502 (1999). doi:10.1103/PhysRevD.61.023502 · doi:10.1103/PhysRevD.61.023502
[7] Berezhiani, L., Trodden, M.: How Likely are Constituent Quanta to Initiate Inflation? Phys. Lett. B 749, 425 (2015). doi:10.1016/j.physletb.2015.08.007. arXiv:1504.01730 · Zbl 1364.83064 · doi:10.1016/j.physletb.2015.08.007
[8] Penrose, R.: Difficulties with inflationary cosmology. Ann. N. Y. Acad. Sci. 571, 249 (1989) · doi:10.1111/j.1749-6632.1989.tb50513.x
[9] Gibbons, G.W., Turok, N.: The measure problem in cosmology. Phys. Rev. D 77, 063516 (2008). doi:10.1103/PhysRevD.77.063516 · doi:10.1103/PhysRevD.77.063516
[10] Carroll, S.M., Tam, H.: Unitary Evolution and Cosmological Fine-Tuning, arXiv:1007.1417 · Zbl 0939.83054
[11] Mukhanov, V., Chibisov, G.: Quantum fluctuation and nonsingular universe. JETP Lett. 33, 532 (1981). In Russian Pisma Zh. Eksp. Teor. Fiz. 33, 549 (1981)
[12] Press, W.H.: Spontaneous production of the Zel’dovich spectrum of cosmological fluctuations. Phys. Scripta 21, 702 (1980). doi:10.1088/0031-8949/21/5/021 · doi:10.1088/0031-8949/21/5/021
[13] Sato, K.: First order phase transition of a vacuum and expansion of the universe. Mon. Not. R. Astron. Soc. 195, 467 (1981) · doi:10.1093/mnras/195.3.467
[14] Brandenberger, R.H.: Inflationary cosmology: progress and problems. arXiv:hep-ph/9910410 · Zbl 1228.83120
[15] Mukhanov, V.F., Feldman, H.A., Brandenberger, R.H.: Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions. Phys. Rep. 215, 203 (1992) · doi:10.1016/0370-1573(92)90044-Z
[16] Brandenberger, R.H.: Lectures on the theory of cosmological perturbations. Lect. Notes Phys. 646, 127 (2004). arXiv:hep-th/0306071 · Zbl 1207.83075 · doi:10.1007/978-3-540-40918-2_5
[17] Hawking, S.W., Penrose, R.: The Singularities of gravitational collapse and cosmology. Proc. R. Soc. Lond. A 314, 529 (1970). doi:10.1098/rspa.1970.0021 · Zbl 0954.83012 · doi:10.1098/rspa.1970.0021
[18] Borde, A., Vilenkin, A.: Eternal inflation and the initial singularity. Phys. Rev. Lett. 72, 3305 (1994). doi:10.1103/PhysRevLett.72.3305. arXiv:gr-qc/9312022 · doi:10.1103/PhysRevLett.72.3305
[19] Martin, J., Brandenberger, R.H.: The TransPlanckian problem of inflationary cosmology. Phys. Rev. D 63, 123501 (2001). doi:10.1103/PhysRevD.63.123501 · doi:10.1103/PhysRevD.63.123501
[20] Brandenberger, R.H., Martin, J.: The Robustness of inflation to changes in superPlanck scale physics. Mod. Phys. Lett. A 16, 999 (2001). doi:10.1142/S0217732301004170. arXiv:astro-ph/0005432 · Zbl 1138.83379 · doi:10.1142/S0217732301004170
[21] Niemeyer, J.C.: Inflation with a Planck scale frequency cutoff. Phys. Rev. D 63, 123502 (2001). doi:10.1103/PhysRevD.63.123502. arXiv:astro-ph/0005533 · doi:10.1103/PhysRevD.63.123502
[22] Niemeyer, J.C., Parentani, R.: Transplanckian dispersion and scale invariance of inflationary perturbations. Phys. Rev. D 64, 101301 (2001). doi:10.1103/PhysRevD.64.101301. arXiv:astro-ph/0101451 · doi:10.1103/PhysRevD.64.101301
[23] Kempf, A., Niemeyer, J.C.: Perturbation spectrum in inflation with cutoff. Phys. Rev. D 64, 103501 (2001). doi:10.1103/PhysRevD.64.103501. arXiv:astro-ph/0103225 · doi:10.1103/PhysRevD.64.103501
[24] Starobinsky, A.A.: Robustness of the inflationary perturbation spectrum to transPlanckian physics. JETP Lett. 73, 371 (2001). doi:10.1134/1.1381588. Pisma Zh. Eksp. Teor. Fiz. 73, 415 (2001). arXiv:astro-ph/0104043 · doi:10.1134/1.1381588
[25] Easther, R., Greene, B.R., Kinney, W.H., Shiu, G.: Inflation as a probe of short distance physics. Phys. Rev. D 64, 103502 (2001). doi:10.1103/PhysRevD.64.103502. arXiv:hep-th/0104102 · doi:10.1103/PhysRevD.64.103502
[26] Kaloper, N., Kleban, M., Lawrence, A.E., Shenker, S.: Signatures of short distance physics in the cosmic microwave background. Phys. Rev. D 66, 123510 (2002). doi:10.1103/PhysRevD.66.123510. arXiv:hep-th/0201158 · doi:10.1103/PhysRevD.66.123510
[27] Brandenberger, R.H., Martin, J.: On signatures of short distance physics in the cosmic microwave background. Int. J. Mod. Phys. A 17, 3663 (2002). doi:10.1142/S0217751X02010765. arXiv:hep-th/0202142 · Zbl 1012.83026
[28] Brandenberger, R., Ho, P.M.: Noncommutative space-time, stringy space-time uncertainty principle, and density fluctuations, Phys. Rev. D 66, 023517 (2002) [AAPPS Bull. 12(1), 10 (2002)] doi:10.1103/PhysRevD.66.023517. arXiv:hep-th/0203119
[29] Danielsson, U.H.: A Note on inflation and transPlanckian physics. Phys. Rev. D 66, 023511 (2002). doi:10.1103/PhysRevD.66.023511. arXiv:hep-th/0203198 · doi:10.1103/PhysRevD.66.023511
[30] Danielsson, U.H.: Inflation, holography, and the choice of vacuum in de Sitter space. JHEP 0207, 040 (2002). doi:10.1088/1126-6708/2002/07/040. arXiv:hep-th/0205227 · doi:10.1088/1126-6708/2002/07/040
[31] Starobinsky, A.A., Tkachev, I.I.: Trans-Planckian particle creation in cosmology and ultra-high energy cosmic rays, JETP Lett. 76, 235 (2002) [Pisma Zh. Eksp. Teor. Fiz. 76, 291 (2002)] doi:10.1134/1.1520612. arXiv:astro-ph/0207572 · Zbl 1342.83236
[32] Goldstein, K., Lowe, D.A.: A Note on alpha vacua and interacting field theory in de Sitter space. Nucl. Phys. B 669, 325 (2003). doi:10.1016/j.nuclphysb.2003.07.014. arXiv:hep-th/0302050 · Zbl 1031.81037 · doi:10.1016/j.nuclphysb.2003.07.014
[33] Martin, J., Brandenberger, R.: On the dependence of the spectra of fluctuations in inflationary cosmology on transPlanckian physics. Phys. Rev. D 68, 063513 (2003). doi:10.1103/PhysRevD.68.063513. arXiv:hep-th/0305161 · doi:10.1103/PhysRevD.68.063513
[34] Alberghi, G.L., Goldstein, K., Lowe, D.A.: Ultrahigh energy cosmic rays and de sitter vacua. Phys. Lett. B 578, 247 (2004). doi:10.1016/j.physletb.2003.10.088. arXiv:astro-ph/0307413 · doi:10.1016/j.physletb.2003.10.088
[35] Easther, R., Greene, B.R., Kinney, W.H., Shiu, G.: Imprints of short distance physics on inflationary cosmology. Phys. Rev. D 67, 063508 (2003). doi:10.1103/PhysRevD.67.063508. arXiv:hep-th/0110226 · Zbl 1222.83194 · doi:10.1103/PhysRevD.67.063508
[36] Niemeyer, J.C., Parentani, R., Campo, D.: Minimal modifications of the primordial power spectrum from an adiabatic short distance cutoff. Phys. Rev. D 66, 083510 (2002). doi:10.1103/PhysRevD.66.083510. arXiv:hep-th/0206149 · doi:10.1103/PhysRevD.66.083510
[37] Bozza, V., Giovannini, M., Veneziano, G.: Cosmological perturbations from a new physics hypersurface. JCAP 0305, 001 (2003). doi:10.1088/1475-7516/2003/05/001. arXiv:hep-th/0302184 · Zbl 1029.83011 · doi:10.1088/1475-7516/2003/05/001
[38] Brandenberger, R.H., Martin, J.: Trans-Planckian issues for inflationary cosmology. Class. Quant. Grav. 30, 113001 (2013). doi:10.1088/0264-9381/30/11/113001. arXiv:1211.6753 · Zbl 1271.83002 · doi:10.1088/0264-9381/30/11/113001
[39] Finelli, F., Brandenberger, R.: On the generation of a scale-invariant spectrum of adiabatic fluctuations in cosmological models with a contracting phase. Phys. Rev. D 65, 103522 (2002). arXiv:hep-th/0112249 · doi:10.1103/PhysRevD.65.103522
[40] Brandenberger R.H.: The matter bounce alternative to inflationary cosmology. arXiv:1206.4196
[41] Gasperini, M., Veneziano, G.: Pre-big bang in string cosmology. Astropart. Phys. 1, 317 (1992). doi:10.1016/0927-6505(93)90017-8. arXiv:hep-th/9211021 · Zbl 0939.83054 · doi:10.1016/0927-6505(93)90017-8
[42] Khoury, J., Ovrut, B.A., Steinhardt, P.J., Turok, N.: The Ekpyrotic universe: colliding branes and the origin of the hot big bang. Phys. Rev. D 64, 123522 (2001). arXiv:hep-th/0103239 · doi:10.1103/PhysRevD.64.123522
[43] Brandenberger, R.H., Vafa, C.: Superstrings in the early universe. Nucl. Phys. B 316, 391 (1989) · doi:10.1016/0550-3213(89)90037-0
[44] Nayeri, A., Brandenberger, R.H., Vafa, C.: Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology. Phys. Rev. Lett. 97, 021302 (2006). arXiv:hep-th/0511140 · doi:10.1103/PhysRevLett.97.021302
[45] Martin, J.: Everything you always wanted to know about the cosmological constant problem (but were afraid to ask). C. R. Phys. 13, 566 (2012). arXiv:1205.3365 · doi:10.1016/j.crhy.2012.04.008
[46] Arkani-Hamed, N., Dimopoulos, S., Dvali, G., Gabadadze, G.: Nonlocal modification of gravity and the cosmological constant problem, arXiv:hep-th/0209227 · Zbl 1355.81103
[47] Dvali, G., Hofmann, S., Khoury, J.: Degravitation of the cosmological constant and graviton width. Phys. Rev. D 76, 084006 (2007). doi:10.1103/PhysRevD.76.084006. arXiv:hep-th/0703027 · doi:10.1103/PhysRevD.76.084006
[48] Patil, S.P.: Degravitation, inflation and the cosmological constant as an afterglow. JCAP 0901, 017 (2009). doi:10.1088/1475-7516/2009/01/017. arXiv:0801.2151 · doi:10.1088/1475-7516/2009/01/017
[49] Patil, S.P.: On Semi-classical degravitation and the cosmological constant problems, arXiv:1003.3010
[50] Sunyaev, R.A., Zeldovich, Y.B.: Small scale fluctuations of relic radiation. Astrophys. Space Sci. 7, 3 (1970)
[51] Peebles, P.J.E., Yu, J.T.: Primeval adiabatic perturbation in an expanding universe. Astrophys. J. 162, 815 (1970). doi:10.1086/150713 · doi:10.1086/150713
[52] Ijjas, A., Steinhardt, P.J., Loeb, A.: Inflationary paradigm in trouble after Planck2013. Phys. Lett. B 723, 261 (2013). doi:10.1016/j.physletb.2013.05.023. arXiv:1304.2785 · doi:10.1016/j.physletb.2013.05.023
[53] Mukhanov, V.: Inflation without Selfreproduction. Fortsch. Phys. 63, 36 (2015). doi:10.1002/prop.201400074. arXiv:1409.2335 · Zbl 1338.83223 · doi:10.1002/prop.201400074
[54] Brandenberger, R.H.: Is the spectrum of gravitational waves the ’Holy Grail’ of inflation? arXiv:1104.3581
[55] Brandenberger, R.H., Nayeri, A., Patil, S.P., Vafa, C.: String gas cosmology and structure formation. Int. J. Mod. Phys. A 22, 3621 (2007). arXiv:hep-th/0608121 · Zbl 1141.83310 · doi:10.1142/S0217751X07037159
[56] Novello, M., Bergliaffa, S.E.P.: Bouncing cosmologies. Phys. Rep. 463, 127 (2008). doi:10.1016/j.physrep.2008.04.006. arXiv:0802.1634 · doi:10.1016/j.physrep.2008.04.006
[57] Battefeld, D., Peter, P.: A critical review of classical bouncing colmologies. Phys. Rep. 571, 1 (2015). doi:10.1016/j.physrep.2014.12.004. arXiv:1406.2790 · Zbl 1370.83107 · doi:10.1016/j.physrep.2014.12.004
[58] Lilley, M., Peter, P.: Bouncing alternatives to inflation. Comptes Rendus Phys. 16, 1038 (2015). doi:10.1016/j.crhy.2015.08.009. arXiv:1503.06578 · doi:10.1016/j.crhy.2015.08.009
[59] Peter, P., Uzan, J.P.: Primordial cosmology, Oxford University Press, Oxford (2013) ISBN: 978-0199665150
[60] Battefeld, T.J., Brandenberger, R.: Vector perturbations in a contracting universe. Phys. Rev. D 70, 121302 (2004). doi:10.1103/PhysRevD.70.121302. arXiv:hep-th/0406180 · doi:10.1103/PhysRevD.70.121302
[61] Sasaki, M.: Large scale quantum fluctuations in the inflationary universe. Prog. Theor. Phys. 76, 1036 (1986). doi:10.1143/PTP.76.1036 · doi:10.1143/PTP.76.1036
[62] Mukhanov, V.F.: Quantum theory of gauge invariant cosmological perturbations. Sov. Phys. JETP 67, 1297 (1988). Zh. Eksp. Teor. Fiz. 94N7, 1 (1988)
[63] Wands, D.: Duality invariance of cosmological perturbation spectra. Phys. Rev. D 60, 023507 (1999). arXiv:gr-qc/9809062 · Zbl 1161.83475 · doi:10.1103/PhysRevD.60.023507
[64] Gordon, C., Wands, D., Bassett, B.A., Maartens, R.: Adiabatic and entropy perturbations from inflation. Phys. Rev. D 63, 023506 (2001). doi:10.1103/PhysRevD.63.023506. arXiv:astro-ph/0009131 · doi:10.1103/PhysRevD.63.023506
[65] Malik, K.A., Wands, D.: Adiabatic and entropy perturbations with interacting fluids and fields. JCAP 0502, 007 (2005). doi:10.1088/1475-7516/2005/02/007. arXiv:astro-ph/0411703 · doi:10.1088/1475-7516/2005/02/007
[66] Li, C., Cheung, Y.K.E.: Dualities between scale invariant and magnitude invariant perturbation spectra in inflationary/bouncing cosmos, arXiv:1211.1610
[67] Cai, Y.F., Wilson-Ewing, E.: A \[\Lambda\] ΛCDM bounce scenario. JCAP 1503(03), 006 (2015). doi:10.1088/1475-7516/2015/03/006. arXiv:1412.2914 · doi:10.1088/1475-7516/2015/03/006
[68] Cai, Y.F., Duplessis, F., Easson, D.A., Wang, D.G.: Searching for a matter bounce cosmology with low redshift observations. Phys. Rev. D 93(4), 043546 (2016). doi:10.1103/PhysRevD.93.043546. arXiv:1512.08979 · doi:10.1103/PhysRevD.93.043546
[69] Cai, Y.F., Xue, W., Brandenberger, R., Zhang, X.M.: Thermal fluctuations and bouncing cosmologies. JCAP 0906, 037 (2009). doi:10.1088/1475-7516/2009/06/037. arXiv:0903.4938 · doi:10.1088/1475-7516/2009/06/037
[70] Gasperini, M., Veneziano, G.: The Pre - big bang scenario in string cosmology. Phys. Rep. 373, 1 (2003). doi:10.1016/S0370-1573(02)00389-7. arXiv:hep-th/0207130 · doi:10.1016/S0370-1573(02)00389-7
[71] Copeland, E.J., Easther, R., Wands, D.: Vacuum fluctuations in axion—dilaton cosmologies. Phys. Rev. D 56, 874 (1997). doi:10.1103/PhysRevD.56.874. arXiv:hep-th/9701082 · doi:10.1103/PhysRevD.56.874
[72] Copeland, E.J., Lidsey, J.E., Wands, D.: S duality invariant perturbations in string cosmology. Nucl. Phys. B 506, 407 (1997). doi:10.1016/S0550-3213(97)00538-5. arXiv:hep-th/9705050 · Zbl 0925.83093 · doi:10.1016/S0550-3213(97)00538-5
[73] Horava, P., Witten, E.: Eleven-dimensional supergravity on a manifold with boundary. Nucl. Phys. B 475, 94 (1996). doi:10.1016/0550-3213(96)00308-2. arXiv:hep-th/9603142 · Zbl 0925.81180 · doi:10.1016/0550-3213(96)00308-2
[74] Horava, P., Witten, E.: Heterotic and type I string dynamics from eleven-dimensions. Nucl. Phys. B 460, 506 (1996). doi:10.1016/0550-3213(95)00621-4. arXiv:hep-th/9510209 · Zbl 1004.81525 · doi:10.1016/0550-3213(95)00621-4
[75] Notari, A., Riotto, A.: Isocurvature perturbations in the ekpyrotic universe. Nucl. Phys. B 644, 371 (2002). doi:10.1016/S0550-3213(02)00765-4. arXiv:hep-th/0205019 · Zbl 0999.83066 · doi:10.1016/S0550-3213(02)00765-4
[76] Finelli, E.: Assisted contraction. Phys. Lett. B 545, 1 (2002). doi:10.1016/S0370-2693(02)02554-6. arXiv:hep-th/0206112 · Zbl 0998.83066 · doi:10.1016/S0370-2693(02)02554-6
[77] Di Marco, F., Finelli, F., Brandenberger, R.: Adiabatic and isocurvature perturbations for multifield generalized Einstein models. Phys. Rev. D 67, 063512 (2003). doi:10.1103/PhysRevD.67.063512. arXiv:astro-ph/0211276 · doi:10.1103/PhysRevD.67.063512
[78] Lehners, J.L., McFadden, P., Turok, N., Steinhardt, P.J.: Generating ekpyrotic curvature perturbations before the big bang. Phys. Rev. D 76, 103501 (2007). doi:10.1103/PhysRevD.76.103501. arXiv:hep-th/0702153 · doi:10.1103/PhysRevD.76.103501
[79] Buchbinder, E.I., Khoury, J., Ovrut, B.A.: New Ekpyrotic cosmology. Phys. Rev. D 76, 123503 (2007). doi:10.1103/PhysRevD.76.123503. arXiv:hep-th/0702154 · Zbl 1245.83084 · doi:10.1103/PhysRevD.76.123503
[80] Creminelli, P., Senatore, L.: A Smooth bouncing cosmology with scale invariant spectrum. JCAP 0711, 010 (2007). doi:10.1088/1475-7516/2007/11/010. arXiv:hep-th/0702165 · doi:10.1088/1475-7516/2007/11/010
[81] Israel, W.: Singular hypersurfaces and thin shells in general relativity, Nuovo Cim. B 44S10, 1 (1966) [Nuovo Cim. B 48, 463 (1967)] [Nuovo Cim. B 44, 1 (1966)]. doi:10.1007/BF02710419, 10.1007/BF02712210 · Zbl 1344.83065
[82] Hwang, J.C., Vishniac, E.T.: Gauge-invariant joining conditions for cosmological perturbations. Astrophys. J. 382, 363 (1991). doi:10.1086/170726 · doi:10.1086/170726
[83] Deruelle, N., Mukhanov, V.F.: On matching conditions for cosmological perturbations. Phys. Rev. D 52, 5549 (1995). doi:10.1103/PhysRevD.52.5549. arXiv:gr-qc/9503050 · doi:10.1103/PhysRevD.52.5549
[84] Martin, J., Peter, P., Pinto Neto, N., Schwarz, D.J.: Passing through the bounce in the ekpyrotic models. Phys. Rev. D 65, 123513 (2002). doi:10.1103/PhysRevD.65.123513. arXiv:hep-th/0112128 · doi:10.1103/PhysRevD.65.123513
[85] Martin, J., Peter, P., Pinto-Neto, N., Schwarz, D.J.: Comment on’Density perturbations in the ekpyrotic scenario. Phys. Rev. D 67, 028301 (2003). doi:10.1103/PhysRevD.67.028301. arXiv:hep-th/0204222 · doi:10.1103/PhysRevD.67.028301
[86] Martin, J., Peter, P.: Parametric amplification of metric fluctuations through a bouncing phase. Phys. Rev. D 68, 103517 (2003). doi:10.1103/PhysRevD.68.103517. arXiv:hep-th/0307077 · doi:10.1103/PhysRevD.68.103517
[87] Martin, J., Peter, P.: On the properties of the transition matrix in bouncing cosmologies. Phys. Rev. D 69, 107301 (2004). doi:10.1103/PhysRevD.69.107301. arXiv:hep-th/0403173 · doi:10.1103/PhysRevD.69.107301
[88] Falciano, F.T., Lilley, M., Peter, P.: A classical bounce: constraints and consequences. Phys. Rev. D 77, 083513 (2008). doi:10.1103/PhysRevD.77.083513. arXiv:0802.1196 · doi:10.1103/PhysRevD.77.083513
[89] Durrer, R., Vernizzi, E.: Adiabatic perturbations in pre-big bang models: matching conditions and scale invariance. Phys. Rev. D 66, 083503 (2002). doi:10.1103/PhysRevD.66.083503. arXiv:hep-ph/0203275 · doi:10.1103/PhysRevD.66.083503
[90] Cartier, C., Durrer, R., Copeland, E.J.: Cosmological perturbations and the transition from contraction to expansion. Phys. Rev. D 67, 103517 (2003). doi:10.1103/PhysRevD.67.103517. arXiv:hep-th/0301198 · doi:10.1103/PhysRevD.67.103517
[91] Tsujikawa, S., Brandenberger, R., Finelli, F.: On the construction of nonsingular pre-big bang and ekpyrotic cosmologies and the resulting density perturbations. Phys. Rev. D 66, 083513 (2002). doi:10.1103/PhysRevD.66.083513. arXiv:hep-th/0207228 · doi:10.1103/PhysRevD.66.083513
[92] Gordon, C., Turok, N.: Cosmological perturbations through a general relativistic bounce. Phys. Rev. D 67, 123508 (2003). doi:10.1103/PhysRevD.67.123508. arXiv:hep-th/0206138 · doi:10.1103/PhysRevD.67.123508
[93] Tolley, A.J., Turok, N.: Quantum fields in a big crunch / big bang space-time. Phys. Rev. D 66, 106005 (2002). doi:10.1103/PhysRevD.66.106005. arXiv:hep-th/0204091 · Zbl 1405.83086 · doi:10.1103/PhysRevD.66.106005
[94] Hwang, J.C., Noh, H.: Nonsingular big bounces and evolution of linear fluctuations. Phys. Rev. D 65, 124010 (2002). doi:10.1103/PhysRevD.65.124010. arXiv:astro-ph/0112079 · doi:10.1103/PhysRevD.65.124010
[95] Lyth, D.H.: The Primordial curvature perturbation in the ekpyrotic universe. Phys. Lett. B 524, 1 (2002). doi:10.1016/S0370-2693(01)01374-0. arXiv:hep-ph/0106153 · Zbl 0981.83065 · doi:10.1016/S0370-2693(01)01374-0
[96] Brandenberger, R., Finelli, F.: On the spectrum of fluctuations in an effective field theory of the Ekpyrotic universe. JHEP 0111, 056 (2001). doi:10.1088/1126-6708/2001/11/056. arXiv:hep-th/0109004 · doi:10.1088/1126-6708/2001/11/056
[97] Khoury, J., Ovrut, B.A., Steinhardt, P.J., Turok, N.: Density perturbations in the ekpyrotic scenario. Phys. Rev. D 66, 046005 (2002). doi:10.1103/PhysRevD.66.046005. arXiv:hep-th/0109050 · doi:10.1103/PhysRevD.66.046005
[98] Battefeld, T.J., Patil, S.P., Brandenberger, R.H.: On the transfer of metric fluctuations when extra dimensions bounce or stabilize. Phys. Rev. D 73, 086002 (2006). doi:10.1103/PhysRevD.73.086002. arXiv:hep-th/0509043 · doi:10.1103/PhysRevD.73.086002
[99] Khoury, J., Steinhardt, P.J.: Adiabatic ekpyrosis: scale-invariant curvature perturbations from a single scalar field in a contracting universe. Phys. Rev. Lett. 104, 091301 (2010). doi:10.1103/PhysRevLett.104.091301. arXiv:0910.2230 · doi:10.1103/PhysRevLett.104.091301
[100] Khoury, J., Steinhardt, P.J.: Generating scale-invariant perturbations from rapidly-evolving equation of state. Phys. Rev. D 83, 123502 (2011). doi:10.1103/PhysRevD.83.123502. arXiv:1101.3548 · doi:10.1103/PhysRevD.83.123502
[101] Ijjas, A., Lehners, J.L., Steinhardt, P.J.: General mechanism for producing scale-invariant perturbations and small non-Gaussianity in ekpyrotic models. Phys. Rev. D 89(12), 123520 (2014). doi:10.1103/PhysRevD.89.123520. arXiv:1404.1265 · doi:10.1103/PhysRevD.89.123520
[102] Levy, A.M., Ijjas, A., Steinhardt, P.J.: Scale-invariant perturbations in ekpyrotic cosmologies without fine-tuning of initial conditions. Phys. Rev. D 92(6), 063524 (2015). doi:10.1103/PhysRevD.92.063524. arXiv:1506.01011 · doi:10.1103/PhysRevD.92.063524
[103] Ijjas, A., Steinhardt, P.J.: The anamorphic universe. JCAP 1510(10), 001 (2015). doi:10.1088/1475-7516/2015/10/001. arXiv:1507.03875 · doi:10.1088/1475-7516/2015/10/001
[104] Moffat, J.W.: Superluminary universe: a possible solution to the initial value problem in cosmology. Int. J. Mod. Phys. D 2, 351 (1993). doi:10.1142/S0218271893000246. arXiv:gr-qc/9211020 · Zbl 0942.83523 · doi:10.1142/S0218271893000246
[105] Albrecht, A., Magueijo, J.: A time varying speed of light as a solution to cosmological puzzles. Phys. Rev. D 59, 043516 (1999). doi:10.1103/PhysRevD.59.043516. arXiv:astro-ph/9811018 · doi:10.1103/PhysRevD.59.043516
[106] Fertig, A., Lehners, J.L., Mallwitz, E.: Conflation: a new type of accelerated expansion. JCAP 1608(08), 073 (2016). doi:10.1088/1475-7516/2016/08/073. arXiv:1507.04742 · doi:10.1088/1475-7516/2016/08/073
[107] Hagedorn, R.: Statistical thermodynamics of strong interactions at high-energies. Nuovo Cim. Suppl. 3, 147 (1965)
[108] Polchinski, J.: String Theory, vol. 1, 2. Cambridge University Press, Cambridge (1998) · Zbl 1006.81521 · doi:10.1017/CBO9780511816079
[109] Sakellariadou, M.: Numerical experiments in string cosmology. Nucl. Phys. B 468, 319 (1996). arXiv:hep-th/9511075 · doi:10.1016/0550-3213(96)00123-X
[110] Easther, R., Greene, B.R., Jackson, M.G.: Cosmological string gas on orbifolds. Phys. Rev. D 66, 023502 (2002). arXiv:hep-th/0204099 · doi:10.1103/PhysRevD.66.023502
[111] Easther, R., Greene, B.R., Jackson, M.G., Kabat, D.N.: String windings in the early universe. JCAP 0502, 009 (2005). doi:10.1088/1475-7516/2005/02/009. arXiv:hep-th/0409121 · doi:10.1088/1475-7516/2005/02/009
[112] Greene, B.; Kabat, D.; Marnerides, S., No article title, Phys. Rev. D, 82, 043528 (2010) · doi:10.1103/PhysRevD.82.043528
[113] Greene, B., Kabat, D., Marnerides, S.: On three dimensions as the preferred dimensionality of space via the Brandenberger-Vafa mechanism. Phys. Rev. D 88, 043527 (2013). doi:10.1103/PhysRevD.88.043527. arXiv:1212.2115 · doi:10.1103/PhysRevD.88.043527
[114] Danos, R., Frey, A.R., Mazumdar, A.: Interaction rates in string gas cosmology. Phys. Rev. D 70, 106010 (2004). arXiv:hep-th/0409162 · doi:10.1103/PhysRevD.70.106010
[115] Watson, S., Brandenberger, R.: Stabilization of extra dimensions at tree level. JCAP 0311, 008 (2003). arXiv:hep-th/0307044 · doi:10.1088/1475-7516/2003/11/008
[116] Patil, S.P., Brandenberger, R.: Radion stabilization by stringy effects in general relativity and dilaton gravity. Phys. Rev. D 71, 103522 (2005). arXiv:hep-th/0401037 · doi:10.1103/PhysRevD.71.103522
[117] Patil, S.P., Brandenberger, R.H.: The cosmology of massless string modes. JCAP 0601, 005 (2006). doi:10.1088/1475-7516/2006/01/005
[118] Watson, S.: Moduli stabilization with the string Higgs effect. Phys. Rev. D 70, 066005 (2004). arXiv:hep-th/0404177 · doi:10.1103/PhysRevD.70.066005
[119] Watson, S.: Stabilizing moduli with string cosmology, arXiv:hep-th/0409281 · Zbl 1250.83031
[120] Kaya, A.: On winding branes and cosmological evolution of extra dimensions in string theory. Class. Quant. Grav. 20, 4533 (2003). arXiv:hep-th/0302118 · Zbl 1045.83068 · doi:10.1088/0264-9381/20/21/002
[121] Kaya, A., Rador, T.: Wrapped branes and compact extra dimensions in cosmology. Phys. Lett. B 565, 19 (2003). arXiv:hep-th/0301031 · Zbl 1028.83532 · doi:10.1016/S0370-2693(03)00760-3
[122] Brandenberger, R., Cheung, Y.K., Watson, S.: Moduli stabilization with string gases and fluxes. JHEP 0605, 025 (2006). arXiv:hep-th/0501032
[123] Kaya, A.: Brane gases and stabilization of shape moduli with momentum and winding stress. Phys. Rev. D 72, 066006 (2005). arXiv:hep-th/0504208 · doi:10.1103/PhysRevD.72.066006
[124] Danos, R.J., Frey, A.R., Brandenberger, R.H.: Stabilizing moduli with thermal matter and nonperturbative effects. Phys. Rev. D 77, 126009 (2008). arXiv:0802.1557 · doi:10.1103/PhysRevD.77.126009
[125] Mishra, S., Xue, W., Brandenberger, R., Yajnik, U.: Supersymmetry breaking and dilaton stabilization in string gas cosmology. JCAP 1209, 015 (2012). doi:10.1088/1475-7516/2012/09/015. arXiv:1103.1389 · doi:10.1088/1475-7516/2012/09/015
[126] Brandenberger, R.H.: String gas cosmology: progress and problems. Class. Quant. Grav. 28, 204005 (2011). doi:10.1088/0264-9381/28/20/204005. arXiv:1105.3247 · Zbl 1228.83120 · doi:10.1088/0264-9381/28/20/204005
[127] Brandenberger, RH; Erdmenger, J. (ed.), String gas cosmology, 193-230 (2009), New York · doi:10.1002/9783527628063.ch6
[128] Brandenberger, R.H., Nayeri, A., Patil, S.P., Vafa, C.: String gas cosmology and structure formation. Int. J. Mod. Phys. A 22, 3621 (2007). arXiv:hep-th/0608121 · Zbl 1141.83310 · doi:10.1142/S0217751X07037159
[129] Battefeld, T., Watson, S.: String gas cosmology. Rev. Mod. Phys. 78, 435 (2006). arXiv:hep-th/0510022 · Zbl 1205.83068 · doi:10.1103/RevModPhys.78.435
[130] Deo, N., Jain, S., Narayan, O., Tan, C.I.: The effect of topology on the thermodynamic limit for a string gas. Phys. Rev. D 45, 3641 (1992) · doi:10.1103/PhysRevD.45.3641
[131] Nayeri, A.: Inflation free, stringy generation of scale-invariant cosmological fluctuations in D = 3 + 1 dimensions, arXiv:hep-th/0607073
[132] Green, M.B., Schwarz, J.H., Witten, E.: Superstring Theory, vol. 1, 2. Cambridge University Press, Cambridge (1987) · Zbl 0619.53002
[133] Peter, P., Pinto-Neto, N.: Primordial perturbations in a non singular bouncing universe model. Phys. Rev. D 66, 063509 (2002). doi:10.1103/PhysRevD.66.063509. arXiv:hep-th/0203013 · doi:10.1103/PhysRevD.66.063509
[134] Cline, J.M., Jeon, S., Moore, G.D.: The Phantom menaced: constraints on low-energy effective ghosts. Phys. Rev. D 70, 043543 (2004). doi:10.1103/PhysRevD.70.043543. arXiv:hep-ph/0311312 · doi:10.1103/PhysRevD.70.043543
[135] Adams, A., Arkani-Hamed, N., Dubovsky, S., Nicolis, A., Rattazzi, R.: Causality, analyticity and an IR obstruction to UV completion. JHEP 0610, 014 (2006). doi:10.1088/1126-6708/2006/10/014. arXiv:hep-th/0602178 · doi:10.1088/1126-6708/2006/10/014
[136] Cai, Y.F., Qiu, T., Piao, Y.S., Li, M., Zhang, X.: Bouncing universe with quintom matter. JHEP 0710, 071 (2007). doi:10.1088/1126-6708/2007/10/071. arXiv:0704.1090 · doi:10.1088/1126-6708/2007/10/071
[137] Cai, Y.F., Qiu, T., Brandenberger, R., Piao, Y.S., Zhang, X.: On perturbations of quintom bounce. JCAP 0803, 013 (2008). doi:10.1088/1475-7516/2008/03/013. arXiv:0711.2187 · doi:10.1088/1475-7516/2008/03/013
[138] Cai, Y.F., Zhang, X.: Evolution of metric perturbations in quintom bounce model. JCAP 0906, 003 (2009). doi:10.1088/1475-7516/2009/06/003. arXiv:0808.2551 · doi:10.1088/1475-7516/2009/06/003
[139] Parker, L., Fulling, S.A.: Quantized matter fields and the avoidance of singularities in general relativity. Phys. Rev. D 7, 2357 (1973). doi:10.1103/PhysRevD.7.2357 · doi:10.1103/PhysRevD.7.2357
[140] Lee, T.D., Wick, G.C.: Negative metric and the unitarity of the S matrix. Nucl. Phys. B 9, 209 (1969) · Zbl 0165.58203 · doi:10.1016/0550-3213(69)90098-4
[141] Lee, T.D., Wick, G.C.: Finite theory of quantum electrodynamics. Phys. Rev. D 2, 1033 (1970) · Zbl 1227.81252 · doi:10.1103/PhysRevD.2.1033
[142] Cai, Y.F., Qiu, T.T., Brandenberger, R., Zhang, X.M.: A nonsingular cosmology with a scale-invariant spectrum of cosmological perturbations from Lee-Wick theory. Phys. Rev. D 80, 023511 (2009). doi:10.1103/PhysRevD.80.023511. arXiv:0810.4677 · doi:10.1103/PhysRevD.80.023511
[143] Bars, I., Chen, S.H., Steinhardt, P.J., Turok, N.: Antigravity and the big crunch/big bang transition. Phys. Lett. B 715, 278 (2012). doi:10.1016/j.physletb.2012.07.071. arXiv:1112.2470 · doi:10.1016/j.physletb.2012.07.071
[144] Bars, I., Steinhardt, P., Turok, N.: Local conformal symmetry in physics and cosmology. Phys. Rev. D 89(4), 043515 (2014). doi:10.1103/PhysRevD.89.043515. arXiv:1307.1848 · Zbl 1338.81312 · doi:10.1103/PhysRevD.89.043515
[145] Bars, I., Steinhardt, P., Turok, N.: Sailing through the big crunch-big bang transition. Phys. Rev. D 89(6), 061302 (2014). doi:10.1103/PhysRevD.89.061302. arXiv:1312.0739 · doi:10.1103/PhysRevD.89.061302
[146] Gielen, S., Turok, N.: A perfect bounce. Phys. Rev. Lett. 117, 021301 (2016). doi:10.1103/physrevlett.117.021301. arXiv:1510.00699
[147] Arkani-Hamed, N., Cheng, H.C., Luty, M.A., Mukohyama, S.: Ghost condensation and a consistent infrared modification of gravity. JHEP 0405, 074 (2004). doi:10.1088/1126-6708/2004/05/074. arXiv:hep-th/0312099 · doi:10.1088/1126-6708/2004/05/074
[148] Abramo, L.R., Peter, P.: K-bounce. JCAP 0709, 001 (2007). doi:10.1088/1475-7516/2007/09/001. arXiv:0705.2893 · doi:10.1088/1475-7516/2007/09/001
[149] Lin, C., Brandenberger, R.H., Perreault Levasseur, L.: A matter bounce by means of ghost condensation. JCAP 1104, 019 (2011). doi:10.1088/1475-7516/2011/04/019. arXiv:1007.2654 · doi:10.1088/1475-7516/2011/04/019
[150] Nicolis, A., Rattazzi, R., Trincherini, E.: The Galileon as a local modification of gravity. Phys. Rev. D 79, 064036 (2009). doi:10.1103/PhysRevD.79.064036. arXiv:0811.2197 · doi:10.1103/PhysRevD.79.064036
[151] Qiu, T., Evslin, J., Cai, Y.F., Li, M., Zhang, X.: Bouncing Galileon cosmologies. JCAP 1110, 036 (2011). doi:10.1088/1475-7516/2011/10/036. arXiv:1108.0593 · doi:10.1088/1475-7516/2011/10/036
[152] Easson, D.A., Sawicki, I., Vikman, A.: G-bounce. JCAP 1111, 021 (2011). doi:10.1088/1475-7516/2011/11/021. arXiv:1109.1047 · doi:10.1088/1475-7516/2011/11/021
[153] Cai, Y.F., Easson, D.A., Brandenberger, R.: Towards a nonsingular bouncing cosmology. JCAP 1208, 020 (2012). doi:10.1088/1475-7516/2012/08/020. arXiv:1206.2382 · doi:10.1088/1475-7516/2012/08/020
[154] Cai, Y.F., McDonough, E., Duplessis, F., Brandenberger, R.H.: Two field matter bounce cosmology. JCAP 1310, 024 (2013). doi:10.1088/1475-7516/2013/10/024. arXiv:1305.5259 · doi:10.1088/1475-7516/2013/10/024
[155] Ijjas, A., Steinhardt, P.J.: Classically stable non-singular cosmological bounces. Phys. Rev. Lett. 117(12), 121304 (2016). doi:10.1103/PhysRevLett.117.121304. arXiv:1606.08880 · doi:10.1103/PhysRevLett.117.121304
[156] Libanov, M., Mironov, S., Rubakov, V.: Generalized Galileons: instabilities of bouncing and genesis cosmologies and modified genesis. JCAP 1608(08), 037 (2016). doi:10.1088/1475-7516/2016/08/037. arXiv:1605.05992 · doi:10.1088/1475-7516/2016/08/037
[157] Kobayashi, T.: Generic instabilities of nonsingular cosmologies in Horndeski theory: a no-go theorem. Phys. Rev. D 94(4), 043511 (2016). doi:10.1103/PhysRevD.94.043511. arXiv:1606.05831 · doi:10.1103/PhysRevD.94.043511
[158] Ijjas, A., Steinhardt, P.J.: Fully stable cosmological solutions with a non-singular classical bounce, arXiv:1609.01253 · Zbl 1369.85008
[159] Alexander, S., Bambi, C., Marciano, A., Modesto, L.: Fermi-bounce Cosmology and scale invariant power-spectrum. Phys. Rev. D 90(12), 123510 (2014). doi:10.1103/PhysRevD.90.123510. arXiv:1402.5880 · doi:10.1103/PhysRevD.90.123510
[160] Li, C., Cheung, Y.K.E.: The scale invariant power spectrum of the primordial curvature perturbations from the coupled scalar tachyon bounce cosmos. JCAP 1407, 008 (2014). doi:10.1088/1475-7516/2014/07/008. arXiv:1401.0094 · doi:10.1088/1475-7516/2014/07/008
[161] Brandenberger, R.H., Cai, Y.F., Wan, Y., Zhang, X.: Nonsingular cosmology from an unstable higgs field, arXiv:1506.06770 · Zbl 1357.83016
[162] Biswas, T., Mazumdar, A., Siegel, W.: Bouncing universes in string-inspired gravity. JCAP 0603, 009 (2006). doi:10.1088/1475-7516/2006/03/009. arXiv:hep-th/0508194 · Zbl 1236.83020 · doi:10.1088/1475-7516/2006/03/009
[163] Biswas, T., Brandenberger, R., Mazumdar, A., Siegel, W.: Non-perturbative gravity, Hagedorn bounce & CMB. JCAP 0712, 011 (2007). doi:10.1088/1475-7516/2007/12/011. arXiv:hep-th/0610274 · doi:10.1088/1475-7516/2007/12/011
[164] Koshelev, A.S.: Stable analytic bounce in non-local Einstein-Gauss-Bonnet cosmology. Class. Quant. Grav. 30, 155001 (2013). doi:10.1088/0264-9381/30/15/155001. arXiv:1302.2140 · Zbl 1273.83187 · doi:10.1088/0264-9381/30/15/155001
[165] Horava, P.: Quantum gravity at a Lifshitz point. Phys. Rev. D 79, 084008 (2009). doi:10.1103/PhysRevD.79.084008. arXiv:0901.3775 · doi:10.1103/PhysRevD.79.084008
[166] Brandenberger, R.: Matter bounce in Horava-Lifshitz cosmology. Phys. Rev. D 80, 043516 (2009). doi:10.1103/PhysRevD.80.043516. arXiv:0904.2835 · doi:10.1103/PhysRevD.80.043516
[167] Mukohyama, S., Nakayama, K., Takahashi, F., Yokoyama, S.: Phenomenological aspects of Horava-Lifshitz cosmology. Phys. Lett. B 679, 6 (2009). doi:10.1016/j.physletb.2009.07.005. arXiv:0905.0055 · doi:10.1016/j.physletb.2009.07.005
[168] Ferreira, E.G.M., Brandenberger, R.: The trans-Planckian problem in the healthy extension of Horava-Lifshitz gravity. Phys. Rev. D 86, 043514 (2012). doi:10.1103/PhysRevD.86.043514. arXiv:1204.5239 · doi:10.1103/PhysRevD.86.043514
[169] Gao, X., Wang, Y., Brandenberger, R., Riotto, A.: Cosmological perturbations in Horava-Lifshitz gravity. Phys. Rev. D 81, 083508 (2010). doi:10.1103/PhysRevD.81.083508. arXiv:0905.3821 · doi:10.1103/PhysRevD.81.083508
[170] Piao, Y.S.: Primordial perturbation in Horava-Lifshitz cosmology. Phys. Lett. B 681, 1 (2009). doi:10.1016/j.physletb.2009.09.047. arXiv:0904.4117 · doi:10.1016/j.physletb.2009.09.047
[171] Gao, X., Wang, Y., Xue, W., Brandenberger, R.: Fluctuations in a Horava-Lifshitz bouncing cosmology. JCAP 1002, 020 (2010). doi:10.1088/1475-7516/2010/02/020. arXiv:0911.3196 · doi:10.1088/1475-7516/2010/02/020
[172] Blas, D., Pujolas, O., Sibiryakov, S.: Models of non-relativistic quantum gravity: the good, the bad and the healthy. JHEP 1104, 018 (2011). doi:10.1007/JHEP04(2011)018. arXiv:1007.3503 · Zbl 1250.83031 · doi:10.1007/JHEP04(2011)018
[173] Cerioni, A., Brandenberger, R.H.: Cosmological Perturbations in the ’Healthy Extension’ of Horava-Lifshitz gravity, arXiv:1008.3589
[174] Cerioni, A., Brandenberger, R.H.: Cosmological perturbations in the projectable version of Horava-Lifshitz gravity. JCAP 1108, 015 (2011). doi:10.1088/1475-7516/2011/08/015. arXiv:1007.1006 · doi:10.1088/1475-7516/2011/08/015
[175] Bamba, K., Makarenko, A.N., Myagky, A.N., Nojiri, S., Odintsov, S.D.: Bounce cosmology from \[F(R)F\](R) gravity and \[F(R)F\](R) bigravity. JCAP 1401, 008 (2014). doi:10.1088/1475-7516/2014/01/008. arXiv:1309.3748 · doi:10.1088/1475-7516/2014/01/008
[176] Bamba, K., Makarenko, A.N., Myagky, A.N., Odintsov, S.D.: Bouncing cosmology in modified Gauss-Bonnet gravity. Phys. Lett. B 732, 349 (2014). doi:10.1016/j.physletb.2014.04.004. arXiv:1403.3242 · Zbl 1360.83082 · doi:10.1016/j.physletb.2014.04.004
[177] Oikonomou, V.K.: Phys. Rev. D 92(12), 124027 (2015). doi:10.1103/PhysRevD.92.124027. arXiv:1509.05827
[178] Nojiri, S., Odintsov, S.D., Oikonomou, V.K.: The bounce universe history from unimodular \[F(R)F\](R) gravity, arXiv:1601.04112 · Zbl 1347.83031
[179] Bamba, K., Makarenko, A.N., Myagky, A.N., Odintsov, S.D.: Bounce universe from string-inspired Gauss-Bonnet gravity. JCAP 04, 001 (2015). doi:10.1088/1475-7516/2015/04/001. arXiv:1411.3852 · doi:10.1088/1475-7516/2015/04/001
[180] Haro, J., Makarenko, A.N., Odintsov, S.D., Oikonomou, V.K.: Bouncing loop quantum cosmology in Gauss-Bonnet gravity. Phys. Rev. D 92(12), 124026 (2015). arXiv:1506.08273 · doi:10.1103/PhysRevD.92.124026
[181] Cai, Y.F., Chen, S.H., Dent, J.B., Dutta, S., Saridakis, E.N.: Matter bounce cosmology with the f(T) gravity. Class. Quant. Grav. 28, 215011 (2011). doi:10.1088/0264-9381/28/21/215011. arXiv:1104.4349 · Zbl 1230.83074 · doi:10.1088/0264-9381/28/21/215011
[182] Desai, S., Poplawski, N.J.: Non-parametric reconstruction of an inflaton potential from Einstein-Cartan-Sciama-Kibble gravity with particle production. Phys. Lett. B 755, 183 (2016). doi:10.1016/j.physletb.2016.02.014. arXiv:1510.08834 · doi:10.1016/j.physletb.2016.02.014
[183] Kehagias, A., Kiritsis, E.: Mirage cosmology. JHEP 9911, 022 (1999). doi:10.1088/1126-6708/1999/11/022. arXiv:hep-th/9910174 · Zbl 0955.83034 · doi:10.1088/1126-6708/1999/11/022
[184] Brandenberger, R., Firouzjahi, H., Saremi, O.: Cosmological perturbations on a bouncing brane. JCAP 0711, 028 (2007). doi:10.1088/1475-7516/2007/11/028. arXiv:0707.4181 · doi:10.1088/1475-7516/2007/11/028
[185] Shtanov, Y., Sahni, V.: Bouncing brane worlds. Phys. Lett. B 557, 1 (2003). doi:10.1016/S0370-2693(03)00179-5. arXiv:gr-qc/0208047 · Zbl 1009.83068 · doi:10.1016/S0370-2693(03)00179-5
[186] Brandenberger, R.H., Mukhanov, V.F., Sornborger, A.: A cosmological theory without singularities. Phys. Rev. D 48, 1629 (1993). doi:10.1103/PhysRevD.48.1629. arXiv:gr-qc/9303001 · doi:10.1103/PhysRevD.48.1629
[187] Boisseau, B., Giacomini, H., Polarski, D., Starobinsky, A.A.: Bouncing universes in scalar-tensor gravity models admitting negative potentials. JCAP 1507, 002 (2015). doi:10.1088/1475-7516/2015/07/002. arXiv:1504.07927 · doi:10.1088/1475-7516/2015/07/002
[188] Boisseau, B., Giacomini, H., Polarski, D.: Scalar field cosmologies with inverted potentials. JCAP 1510, 033 (2015). doi:10.1088/1475-7516/2015/10/033. arXiv:1507.00792 · doi:10.1088/1475-7516/2015/10/033
[189] Kounnas, C., Partouche, H., Toumbas, N.: S-brane to thermal non-singular string cosmology. Class. Quant. Grav. 29, 095014 (2012). arXiv:1111.5816 · Zbl 1247.83279 · doi:10.1088/0264-9381/29/9/095014
[190] Angelantonj, C., Kounnas, C., Partouche, H., Toumbas, N.: Resolution of Hagedorn singularity in superstrings with gravito-magnetic fluxes. Nucl. Phys. B 809, 291 (2009). doi:10.1016/j.nuclphysb.2008.10.010. arXiv:0808.1357 · Zbl 1192.81250 · doi:10.1016/j.nuclphysb.2008.10.010
[191] Kounnas, C., Partouche, H., Toumbas, N.: Thermal duality and non-singular cosmology in d-dimensional superstrings. Nucl. Phys. B 855, 280 (2012). arXiv:1106.0946 · Zbl 1229.83062 · doi:10.1016/j.nuclphysb.2011.10.010
[192] Gutperle, M., Strominger, A.: Space-like branes. JHEP 0204, 018 (2002). doi:10.1088/1126-6708/2002/04/018. arXiv:hep-th/0202210 · doi:10.1088/1126-6708/2002/04/018
[193] Brandenberger, R.H., Kounnas, C., Partouche, H., Patil, S.P., Toumbas, N.: Cosmological perturbations across an S-brane. JCAP 1403, 015 (2014). arXiv:1312.2524 · doi:10.1088/1475-7516/2014/03/015
[194] Maldacena, J.M.: The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38, 1113 (1999) [Adv. Theor. Math. Phys. 2, 231 (1998)]. arXiv:hep-th/9711200 · Zbl 0914.53047
[195] Turok, N., Craps, B., Hertog, T.: From big crunch to big bang with AdS/CFT, arXiv:0711.1824
[196] Craps, B., Hertog, T., Turok, N.: On the quantum resolution of cosmological singularities using AdS/CFT. Phys. Rev. D 86, 043513 (2012). arXiv:0712.4180 · doi:10.1103/PhysRevD.86.043513
[197] Hertog, T., Horowitz, G.T.: Holographic description of AdS cosmologies. JHEP 0504, 005 (2005). arXiv:hep-th/0503071 · doi:10.1088/1126-6708/2005/04/005
[198] Brandenberger, R.H., Cai, Y.F., Das, S.R., Ferreira, E.G.M., Morrison, I.A., Wang, Y.: Fluctuations in a cosmology with a space-like singularity and their gauge theory dual description. Phys. Rev. D 94(8), 083508 (2016). doi:10.1103/PhysRevD.94.083508. arXiv:1601.00231
[199] Ferreira, E.G.M., Brandenberger, R.: Holographic curvature perturbations in a cosmology with a space-like singularity. JCAP 1607(7), 030 (2016). doi:10.1088/1475-7516/2016/07/030. arXiv:1602.08152
[200] Das, S.R., Michelson, J., Narayan, K., Trivedi, S.P.: Time dependent cosmologies and their duals. Phys. Rev. D 74, 026002 (2006). arXiv:hep-th/0602107 · doi:10.1103/PhysRevD.74.026002
[201] Awad, A., Das, S.R., Narayan, K., Trivedi, S.P.: Gauge theory duals of cosmological backgrounds and their energy momentum tensors. Phys. Rev. D 77, 046008 (2008). arXiv:0711.2994 · doi:10.1103/PhysRevD.77.046008
[202] Chu, C.S., Ho, P.M.: Time-dependent AdS/CFT duality and null singularity. JHEP 0604, 013 (2006). arXiv:hep-th/0602054
[203] Chu, C.S., Ho, P.M.: Time-dependent AdS/CFT duality. II. Holographic reconstruction of bulk metric and possible resolution of singularity. JHEP 0802, 058 (2008). arXiv:0710.2640 · doi:10.1088/1126-6708/2008/02/058
[204] Cornalba, L., Costa, M.S.: A new cosmological scenario in string theory. Phys. Rev. D 66, 066001 (2002). doi:10.1103/PhysRevD.66.066001. arXiv:hep-th/0203031 · doi:10.1103/PhysRevD.66.066001
[205] Cornalba, L., Costa, M.S.: Time dependent orbifolds and string cosmology. Fortsch. Phys. 52, 145 (2004). doi:10.1002/prop.200310123. arXiv:hep-th/0310099 · Zbl 1040.81075 · doi:10.1002/prop.200310123
[206] Cheung, Y.K.E., Song, X., Li, S., Li, Y., Zhu, Y.: The CST Bounce Universe model—a parametric study. arXiv:1601.03807
[207] Hartle, J.B., Hawking, S.W.: Wave function of the universe. Phys. Rev. D 28, 2960 (1983). doi:10.1103/PhysRevD.28.2960 · Zbl 1370.83118 · doi:10.1103/PhysRevD.28.2960
[208] Vilenkin, A.: The birth of inflationary universes. Phys. Rev. D 27, 2848 (1983). doi:10.1103/PhysRevD.27.2848 · doi:10.1103/PhysRevD.27.2848
[209] Linde, A.D.: Quantum creation of the inflationary universe. Lett. Nuovo Cim. 39, 401 (1984). doi:10.1007/BF02790571 · doi:10.1007/BF02790571
[210] Gielen, S., Sindoni, L.: Quantum cosmology from group field theory condensates: a review. SIGMA 12, 082 (2016). doi:10.3842/SIGMA.2016.082. arXiv:1602.08104 · Zbl 1347.83015 · doi:10.3842/SIGMA.2016.082
[211] Gielen, S., Oriti, D., Sindoni, L.: Cosmology from group field theory formalism for quantum gravity. Phys. Rev. Lett. 111(3), 031301 (2013). doi:10.1103/PhysRevLett.111.031301. arXiv:1303.3576 · doi:10.1103/PhysRevLett.111.031301
[212] Bojowald, M.: Loop quantum cosmology. Living Rev. Rel. 11, 4 (2008) · Zbl 1316.83035 · doi:10.12942/lrr-2008-4
[213] Ashtekar, A.: Singularity resolution in loop quantum cosmology: a brief overview. J. Phys. Conf. Ser. 189, 012003 (2009). doi:10.1088/1742-6596/189/1/012003. arXiv:0812.4703 · doi:10.1088/1742-6596/189/1/012003
[214] Ashtekar, A., Barrau, A.: Loop quantum cosmology: from pre-inflationary dynamics to observations. Class. Quant. Grav. 32(23), 234001 (2015). doi:10.1088/0264-9381/32/23/234001. arXiv:1504.07559 · Zbl 1329.83203 · doi:10.1088/0264-9381/32/23/234001
[215] Wilson-Ewing, E.: The matter bounce scenario in loop quantum cosmology. JCAP 1303, 026 (2013). doi:10.1088/1475-7516/2013/03/026. arXiv:1211.6269 · doi:10.1088/1475-7516/2013/03/026
[216] Cai, Y.F., Wilson-Ewing, E.: Non-singular bounce scenarios in loop quantum cosmology and the effective field description. JCAP 1403, 026 (2014). doi:10.1088/1475-7516/2014/03/026. arXiv:1402.3009 · doi:10.1088/1475-7516/2014/03/026
[217] de Cesare, M., Sakellariadou, M.: Accelerated expansion of the Universe without an inflaton and resolution of the initial singularity from GFT condensates. Phys. Lett. B 764, 49 (2017). doi:10.1016/j.physletb.2016.10.051.arXiv:1603.01764 · Zbl 1369.83119
[218] Peter, P., Vitenti, S.D.P.: The simplest possible bouncing quantum cosmological model. Mod. Phys. Lett. A 31(21), 1640006 (2016). doi:10.1142/S021773231640006X. arXiv:1603.02342 · Zbl 1344.83065 · doi:10.1142/S021773231640006X
[219] Chowdhury, D., Sreenath, V., Sriramkumar, L.: The tensor bi-spectrum in a matter bounce. JCAP 1511, 002 (2015). doi:10.1088/1475-7516/2015/11/002. arXiv:1506.06475 · doi:10.1088/1475-7516/2015/11/002
[220] Maldacena, J.M.: Non-Gaussian features of primordial fluctuations in single field inflationary models. JHEP 0305, 013 (2003). doi:10.1088/1126-6708/2003/05/013. arXiv:astro-ph/0210603 · doi:10.1088/1126-6708/2003/05/013
[221] Babich, D., Creminelli, P., Zaldarriaga, M.: The shape of non-Gaussianities. JCAP 0408, 009 (2004). doi:10.1088/1475-7516/2004/08/009. arXiv:astro-ph/0405356 · doi:10.1088/1475-7516/2004/08/009
[222] Baumann, D.: Inflation, arXiv:0907.5424 · Zbl 1241.83003
[223] Battefeld, T., Grieb, J.: Anatomy of bispectra in general single-field inflation—modal expansions. JCAP 1112, 003 (2011). doi:10.1088/1475-7516/2011/12/003. arXiv:1110.1369 · doi:10.1088/1475-7516/2011/12/003
[224] Ade, P.A.R. et al.: Planck Collaboration, Planck 2015 results. vol. XVII. Constraints on primordial non-Gaussianity. Astron. Astrophys. 594, A17 (2016). doi:10.1051/0004-6361/201525836. arXiv:1502.01592
[225] Creminelli, P.: On non-Gaussianities in single-field inflation. JCAP 0310, 003 (2003). doi:10.1088/1475-7516/2003/10/003. arXiv:astro-ph/0306122 · doi:10.1088/1475-7516/2003/10/003
[226] Cai, Y.F., Xue, W., Brandenberger, R., Zhang, X.: Non-Gaussianity in a matter bounce. JCAP 0905, 011 (2009). doi:10.1088/1475-7516/2009/05/011. arXiv:0903.0631 · doi:10.1088/1475-7516/2009/05/011
[227] Lehners, J.L., Steinhardt, P.J.: Non-Gaussian density fluctuations from entropically generated curvature perturbations in Ekpyrotic models, Phys. Rev. D 77, 063533 (2008) Erratum: Phys. Rev. D 79, 129903 (2009) doi:10.1103/PhysRevD.79.129903, 10.1103/PhysRevD.77.063533. arXiv:0712.3779
[228] Lehners, J.L., Steinhardt, P.J.: Intuitive understanding of non-gaussianity in ekpyrotic and cyclic models, Phys. Rev. D 78, 023506 (2008) Erratum: Phys. Rev. D 79, 129902 (2009) doi:10.1103/PhysRevD.78.023506, 10.1103/PhysRevD.79.129902. arXiv:0804.1293
[229] Lehners, J.L., Steinhardt, P.J.: Non-Gaussianity generated by the entropic mechanism in bouncing cosmologies made simple. Phys. Rev. D 80, 103520 (2009). doi:10.1103/PhysRevD.80.103520. arXiv:0909.2558 · doi:10.1103/PhysRevD.80.103520
[230] Qiu, T., Gao, X., Saridakis, E.N.: Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations. Phys. Rev. D 88(4), 043525 (2013). doi:10.1103/PhysRevD.88.043525. arXiv:1303.2372 · doi:10.1103/PhysRevD.88.043525
[231] Li, M.: Note on the production of scale-invariant entropy perturbation in the Ekpyrotic universe. Phys. Lett. B 724, 192 (2013). doi:10.1016/j.physletb.2013.06.035. arXiv:1306.0191 · Zbl 1331.83084 · doi:10.1016/j.physletb.2013.06.035
[232] Fertig, A., Lehners, J.L., Mallwitz, E.: Ekpyrotic perturbations with small non-Gaussian corrections. Phys. Rev. D 89(10), 103537 (2014). doi:10.1103/PhysRevD.89.103537. arXiv:1310.8133 · doi:10.1103/PhysRevD.89.103537
[233] Fertig, A., Lehners, J.L.: The non-minimal ekpyrotic trispectrum. JCAP 1601(01), 026 (2016). doi:10.1088/1475-7516/2016/01/026. arXiv:1510.03439 · doi:10.1088/1475-7516/2016/01/026
[234] Gao, X., Lilley, M., Peter, P.: Production of non-gaussianities through a positive spatial curvature bouncing phase. JCAP 1407, 010 (2014). doi:10.1088/1475-7516/2014/07/010. arXiv:1403.7958 · doi:10.1088/1475-7516/2014/07/010
[235] Gao, X., Lilley, M., Peter, P.: Non-Gaussianity excess problem in classical bouncing cosmologies. Phys. Rev. D 91(2), 023516 (2015). doi:10.1103/PhysRevD.91.023516. arXiv:1406.4119 · doi:10.1103/PhysRevD.91.023516
[236] Quintin, J., Sherkatghanad, Z., Cai, Y.F., Brandenberger, R.H.: Evolution of cosmological perturbations and the production of non-Gaussianities through a nonsingular bounce: Indications for a no-go theorem in single field matter bounce cosmologies. Phys. Rev. D 92(6), 063532 (2015). doi:10.1103/PhysRevD.92.063532. arXiv:1508.04141 · doi:10.1103/PhysRevD.92.063532
[237] Chen, B., Wang, Y., Xue, W., Brandenberger, R.: String gas cosmology and non-Gaussianities. Universe 3(3), 2 (2015). arXiv:0712.2477
[238] Copeland, E.J., Myers, R.C., Polchinski, J.: Cosmic F and D strings. JHEP 0406, 013 (2004). doi:10.1088/1126-6708/2004/06/013. arXiv:hep-th/0312067 · doi:10.1088/1126-6708/2004/06/013
[239] Witten, E.: Cosmic superstrings. Phys. Lett. B 153, 243 (1985). doi:10.1016/0370-2693(85)90540-4 · doi:10.1016/0370-2693(85)90540-4
[240] Brandenberger, R.H.: Searching for cosmic strings in new observational windows. Nucl. Phys. Proc. Suppl. 246-247, 45 (2014). doi:10.1016/j.nuclphysbps.2013.10.064. arXiv:1301.2856 · doi:10.1016/j.nuclphysbps.2013.10.064
[241] Lehners, J.L., Wilson-Ewing, E.: Running of the scalar spectral index in bouncing cosmologies. JCAP 1510(10), 038 (2015). doi:10.1088/1475-7516/2015/10/038. arXiv:1507.08112 · doi:10.1088/1475-7516/2015/10/038
[242] Brandenberger, R.H., Nayeri, A., Patil, S.P.: Closed string thermodynamics and a blue tensor spectrum. Phys. Rev. D 90(6), 067301 (2014). doi:10.1103/PhysRevD.90.067301. arXiv:1403.4927 · doi:10.1103/PhysRevD.90.067301
[243] Boyle, L.A., Steinhardt, P.J., Turok, N.: The cosmic gravitational wave background in a cyclic universe. Phys. Rev. D 69, 127302 (2004). doi:10.1103/PhysRevD.69.127302. arXiv:hep-th/0307170 · doi:10.1103/PhysRevD.69.127302
[244] Martin, J., Ringeval, C., Vennin, V.: How well can future CMB missions constrain cosmic inflation? JCAP 1410(10), 038 (2014). doi:10.1088/1475-7516/2014/10/038. arXiv:1407.4034 · doi:10.1088/1475-7516/2014/10/038
[245] Allen, L.E., Wands, D.: Cosmological perturbations through a simple bounce. Phys. Rev. D 70, 063515 (2004). doi:10.1103/PhysRevD.70.063515. arXiv:astro-ph/0404441 · doi:10.1103/PhysRevD.70.063515
[246] Cai, Y.F., Brandenberger, R., Zhang, X.: The matter bounce curvaton scenario. JCAP 1103, 003 (2011). doi:10.1088/1475-7516/2011/03/003. arXiv:1101.0822 · doi:10.1088/1475-7516/2011/03/003
[247] Kobayashi, T., Yamaguchi, M., Yokoyama, J.: G-inflation: Inflation driven by the Galileon field. Phys. Rev. Lett. 105, 231302 (2010). doi:10.1103/PhysRevLett.105.231302. arXiv:1008.0603 · doi:10.1103/PhysRevLett.105.231302
[248] Liddle, A.R., Lyth, D.H.: The cold dark matter density perturbation. Phys. Rep. 231, 1 (1993). doi:10.1016/0370-1573(93)90114-S. arXiv:astro-ph/9303019 · doi:10.1016/0370-1573(93)90114-S
[249] Bonvin, C., Durrer, R., Maartens, R.: Can primordial magnetic fields be the origin of the BICEP2 data? Phys. Rev. Lett. 112(19), 191303 (2014). doi:10.1103/PhysRevLett.112.191303. arXiv:1403.6768 · doi:10.1103/PhysRevLett.112.191303
[250] Durrer, R., Figueroa, D.G., Kunz, M.: Can self-ordering scalar fields explain the BICEP \[2 BB\]-mode signal? JCAP 1408, 029 (2014). doi:10.1088/1475-7516/2014/08/029. arXiv:1404.3855 · doi:10.1088/1475-7516/2014/08/029
[251] Danos, R.J., Brandenberger, R.H., Holder, G.: A signature of cosmic strings wakes in the CMB polarization. Phys. Rev. D 82, 023513 (2010). doi:10.1103/PhysRevD.82.023513. arXiv:1003.0905 · doi:10.1103/PhysRevD.82.023513
[252] Goldwirth, D.S., Piran, T.: Initial conditions for inflation. Phys. Rep. 214, 223 (1992). doi:10.1016/0370-1573(92)90073-9 · doi:10.1016/0370-1573(92)90073-9
[253] Brandenberger, R.H., Kung, J.H.: Chaotic inflation as an attractor in initial condition space. Phys. Rev. D 42, 1008 (1990). doi:10.1103/PhysRevD.42.1008 · doi:10.1103/PhysRevD.42.1008
[254] Feldman, H.A., Brandenberger, R.H.: Chaotic inflation with metric and matter perturbations. Phys. Lett. B 227, 359 (1989). doi:10.1016/0370-2693(89)90944-1 · doi:10.1016/0370-2693(89)90944-1
[255] Brandenberger, R.: Initial conditions for inflation—a short review. Int. J. Mod. Phys. D 26(1), 1740002 (2017). doi:10.1142/S0218271817400028. arXiv:1601.01918
[256] East, W.E., Kleban, M., Linde, A., Senatore, L.: Beginning inflation in an inhomogeneous universe. JCAP 1609(9), 010 (2016). doi:10.1088/1475-7516/2016/09/010. arXiv:1511.05143
[257] Clough, K., Lim, E.A., DiNunno, B.S., Fischler, W., Flauger, R., Paban, S.: Robustness of inflation to inhomogeneous initial conditions, arXiv:1608.04408 · Zbl 1515.83325
[258] Buonanno, A., Damour, T., Veneziano, G.: Pre-big bang bubbles from the gravitational instability of generic string vacua. Nucl. Phys. B 543, 275 (1999). doi:10.1016/S0550-3213(98)00805-0. arXiv:hep-th/9806230 · Zbl 0953.83075 · doi:10.1016/S0550-3213(98)00805-0
[259] Carroll. S.M., Chen, J.: Does inflation provide natural initial conditions for the universe?, Gen. Rel. Grav. 37, 1671 (2005) [Int. J. Mod. Phys. D 14, 2335 (2005)] doi:10.1142/S0218271805008054. arXiv:gr-qc/0505037 · Zbl 1082.83038
[260] Peter, P., Pinto-Neto, N.: Cosmology without inflation. Phys. Rev. D 78, 063506 (2008). doi:10.1103/PhysRevD.78.063506. arXiv:0809.2022 · doi:10.1103/PhysRevD.78.063506
[261] Maier, R., Pereira, S., Pinto-Neto, N., Siffert, B.B.: Bouncing models with a cosmological constant. Phys. Rev. D 85, 023508 (2012). doi:10.1103/PhysRevD.85.023508. arXiv:1111.0946 · doi:10.1103/PhysRevD.85.023508
[262] Cai, Y.F., Brandenberger, R., Peter, P.: Anisotropy in a nonsingular bounce. Class. Quant. Grav. 30, 075019 (2013). doi:10.1088/0264-9381/30/7/075019. arXiv:1301.4703 · Zbl 1266.83174 · doi:10.1088/0264-9381/30/7/075019
[263] Belinsky, V., Khalatnikov, I., Lifshitz, E.: Oscillatory approach to a singular point in the relativistic cosmology. Adv. Phys. 19, 525 (1970) · doi:10.1080/00018737000101171
[264] Lifshitz, E., Khalatnikov, I.: Investigations in relativistic cosmology. Adv. Phys. 12, 185 (1963) · Zbl 0112.44306 · doi:10.1080/00018736300101283
[265] Erickson, J.K., Wesley, D.H., Steinhardt, P.J., Turok, N.: Kasner and mixmaster behavior in universes with equation of state \[w \gg 1\] w≫1. Phys. Rev. D69, 063514 (2004). doi:10.1103/PhysRevD.69.063514. arXiv:hep-th/0312009 · doi:10.1103/PhysRevD.69.063514
[266] Garfinkle, D., Lim, W.C., Pretorius, F., Steinhardt, P.J.: Evolution to a smooth universe in an ekpyrotic contracting phase with \[w \gg 1\] w≫1. Phys. Rev. D 78, 083537 (2008). doi:10.1103/PhysRevD.78.083537. arXiv:0808.0542 · doi:10.1103/PhysRevD.78.083537
[267] Karouby, J., Brandenberger, R.: A radiation bounce from the Lee-Wick construction? Phys. Rev. D 82, 063532 (2010). doi:10.1103/PhysRevD.82.063532. arXiv:1004.4947 · doi:10.1103/PhysRevD.82.063532
[268] Bozza, V., Bruni, M.: A solution to the anisotropy problem in bouncing cosmologies. JCAP 0910, 014 (2009). doi:10.1088/1475-7516/2009/10/014. arXiv:0909.5611 · doi:10.1088/1475-7516/2009/10/014
[269] Qiu, T., Gao, X., Saridakis, E.N.: Towards anisotropy-free and nonsingular bounce cosmology with scale-invariant perturbations. Phys. Rev. D 88(4), 043525 (2013). doi:10.1103/PhysRevD.88.043525. arXiv:1303.2372 · doi:10.1103/PhysRevD.88.043525
[270] Barrow, J.D., Ganguly, C.: Evolution of initially contracting Bianchi Class A models in the presence of an ultra-stiff anisotropic pressure fluid. Class. Quant. Grav. 33(12), 125004 (2016). doi:10.1088/0264-9381/33/12/125004. arXiv:1510.01095 · Zbl 1342.83518 · doi:10.1088/0264-9381/33/12/125004
[271] Barrow, J.D., Yamamoto, K.: Anisotropic pressures at ultra-stiff singularities and the stability of cyclic universes. Phys. Rev. D 82, 063516 (2010). doi:10.1103/PhysRevD.82.063516. arXiv:1004.4767 · doi:10.1103/PhysRevD.82.063516
[272] Battefeld, D., Battefeld, T.: The relic problem of string gas cosmology. Phys. Rev. D 80, 063518 (2009). doi:10.1103/PhysRevD.80.063518. arXiv:0907.2443 · Zbl 1290.81100 · doi:10.1103/PhysRevD.80.063518
[273] Braun, V., He, Y.H., Ovrut, B.A., Pantev, T.: The exact MSSM spectrum from string theory. JHEP 0605, 043 (2006). doi:10.1088/1126-6708/2006/05/043. arXiv:hep-th/0512177 · doi:10.1088/1126-6708/2006/05/043
[274] Braun, V., He, Y.H., Ovrut, B.A.: Supersymmetric hidden sectors for heterotic standard models. JHEP 1309, 008 (2013). doi:10.1007/JHEP09(2013)008. arXiv:1301.6767 · doi:10.1007/JHEP09(2013)008
[275] Li, C., Brandenberger, R.H., Cheung, Y.K.E.: Big bounce genesis. Phys. Rev. D 90(12), 123535 (2014). doi:10.1103/PhysRevD.90.123535. arXiv:1403.5625 · doi:10.1103/PhysRevD.90.123535
[276] Cheung, Y.K.E., Kang, J.U., Li, C.: Dark matter in a bouncing universe. JCAP 1411(11), 001 (2014). doi:10.1088/1475-7516/2014/11/001. arXiv:1408.4387 · doi:10.1088/1475-7516/2014/11/001
[277] Vitenti, S.D.P., Pinto-Neto, N.: Large adiabatic scalar perturbations in a regular bouncing universe. Phys. Rev. D 85, 023524 (2012). doi:10.1103/PhysRevD.85.023524. arXiv:1111.0888 · doi:10.1103/PhysRevD.85.023524
[278] Xue, B., Steinhardt, P.J.: Evolution of curvature and anisotropy near a nonsingular bounce. Phys. Rev. D 84, 083520 (2011). doi:10.1103/PhysRevD.84.083520. arXiv:1106.1416 · doi:10.1103/PhysRevD.84.083520
[279] Pinto-Neto, N., Vitenti, S.D.P.: Comment on Growth of covariant perturbations in the contracting phase of a bouncing universe? Phys. Rev. D 89(2), 028301 (2014). doi:10.1103/PhysRevD.89.028301. arXiv:1312.7790 · doi:10.1103/PhysRevD.89.028301
[280] Kunze, K.E.: Cosmological magnetic fields. Plasma Phys. Control. Fusion 55, 124026 (2013). doi:10.1088/0741-3335/55/12/124026. arXiv:1307.2153 · doi:10.1088/0741-3335/55/12/124026
[281] Arkani-Hamed, N., Cheng, H.C., Luty, M.A., Mukohyama, S.: Ghost condensation and a consistent infrared modification of gravity. JHEP 0405, 074 (2004). doi:10.1088/1126-6708/2004/05/074. arXiv:hep-th/0312099 · doi:10.1088/1126-6708/2004/05/074
[282] Creminelli, P., Luty, M.A., Nicolis, A., Senatore, L.: Starting the universe: stable violation of the null energy condition and non-standard cosmologies. JHEP 0612, 080 (2006). doi:10.1088/1126-6708/2006/12/080. arXiv:hep-th/0606090 · Zbl 1226.83089 · doi:10.1088/1126-6708/2006/12/080
[283] Elder, B., Joyce, A., Khoury, J.: From satisfying to violating the null energy condition. Phys. Rev. D 89(4), 044027 (2014). doi:10.1103/PhysRevD.89.044027. arXiv:1311.5889 · doi:10.1103/PhysRevD.89.044027
[284] Nicolis, A., Rattazzi, R., Trincherini, E.: The Galileon as a local modification of gravity. Phys. Rev. D 79, 064036 (2009). doi:10.1103/PhysRevD.79.064036. arXiv:0811.2197 · doi:10.1103/PhysRevD.79.064036
[285] Creminelli, P., Hinterbichler, K., Khoury, J., Nicolis, A., Trincherini, E.: Subluminal Galilean genesis. JHEP 1302, 006 (2013). doi:10.1007/JHEP02(2013)006. arXiv:1209.3768 · Zbl 1342.83236 · doi:10.1007/JHEP02(2013)006
[286] Biswas, T., Koivisto, T., Mazumdar, A.: Towards a resolution of the cosmological singularity in non-local higher derivative theories of gravity. JCAP 1011, 008 (2010). doi:10.1088/1475-7516/2010/11/008. arXiv:1005.0590 · doi:10.1088/1475-7516/2010/11/008
[287] Dubovsky, S., Gregoire, T., Nicolis, A., Rattazzi, R.: Null energy condition and superluminal propagation. JHEP 0603, 025 (2006). doi:10.1088/1126-6708/2006/03/025. arXiv:hep-th/0512260 · Zbl 1226.83090 · doi:10.1088/1126-6708/2006/03/025
[288] Rubakov, V.A.: The null energy condition and its violation. Phys. Usp. 57, 128 (2014). doi:10.3367/UFNe.0184.201402b.0137. arXiv:1401.4024 · doi:10.3367/UFNe.0184.201402b.0137
[289] Misner, C.W.: Mixmaster universe. Phys. Rev. Lett. 22, 1071 (1969). doi:10.1103/PhysRevLett.22.1071 · Zbl 0177.28701 · doi:10.1103/PhysRevLett.22.1071
[290] Vafa, C.: The string landscape and the swampland, arXiv:hep-th/0509212 · Zbl 1117.81117
[291] Arkani-Hamed, N., Motl, L., Nicolis, A., Vafa, C.: The string landscape, black holes and gravity as the weakest force. JHEP 0706, 060 (2007). doi:10.1088/1126-6708/2007/06/060. arXiv:hep-th/0601001 · doi:10.1088/1126-6708/2007/06/060
[292] Martin, J., Ringeval, C., Trotta, R., Vennin, V.: The best inflationary models after Planck. JCAP 1403, 039 (2014). doi:10.1088/1475-7516/2014/03/039. arXiv:1312.3529 · doi:10.1088/1475-7516/2014/03/039
[293] Brandenberger, R.H.: Processing of cosmological perturbations in a cyclic cosmology. Phys. Rev. D 80, 023535 (2009). doi:10.1103/PhysRevD.80.023535. arXiv:0905.1514 · doi:10.1103/PhysRevD.80.023535
[294] Steinhardt, P.J., Turok, N.: Cosmic evolution in a cyclic universe. Phys. Rev. D 65, 126003 (2002). doi:10.1103/PhysRevD.65.126003. arXiv:hep-th/0111098 · doi:10.1103/PhysRevD.65.126003
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