Revisiting non-Gaussianity in multifield inflation with curved field space. (English) Zbl 1434.85014
Summary: Recent studies of inflation with multiple scalar fields have highlighted the importance of non-canonical kinetic terms in novel types of inflationary solutions. This motivates a thorough analysis of non-Gaussianities in this context, which we revisit here by studying the primordial bispectrum in a general two-field model. Our main result is the complete cubic action for inflationary fluctuations written in comoving gauge, i.e. in terms of the curvature perturbation and the entropic mode. Although full expressions for the cubic action have already been derived in terms of fields fluctuations in the flat gauge, their applicability is mostly restricted to numerical evaluations. Our form of the action is instead amenable to several analytical approximations, as our calculation in terms of the directly observable quantity makes manifest the scaling of every operator in terms of the slow-roll parameters, what is essentially a generalization of Maldacena’s single-field result to non-canonical two-field models. As an important application we derive the single-field effective field theory that is valid when the entropic mode is heavy and may be integrated out, underlining the observable effects that derive from a curved field space.
MSC:
| 85A40 | Astrophysical cosmology |
| 83F05 | Relativistic cosmology |
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
| 62P35 | Applications of statistics to physics |
| 81T12 | Effective quantum field theories |
| 83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |
References:
| [1] | Planck collaboration, Planck 2018 results. IX. Constraints on primordial non-Gaussianity, arXiv:1905.05697 [INSPIRE]. |
| [2] | Wands, D., Local non-Gaussianity from inflation, Class. Quant. Grav., 27, 124002 (2010) · Zbl 1190.83132 · doi:10.1088/0264-9381/27/12/124002 |
| [3] | Chen, X., Primordial non-Gaussianities from inflation models, Adv. Astron., 2010, 638979 (2010) · doi:10.1155/2010/638979 |
| [4] | Wang, Y., Inflation, cosmic perturbations and non-gaussianities, Commun. Theor. Phys., 62, 109 (2014) · Zbl 1294.83001 · doi:10.1088/0253-6102/62/1/19 |
| [5] | Renaux-Petel, S., Primordial non-Gaussianities after Planck 2015: an introductory review, Comptes Rendus Physique, 16, 969 (2015) · doi:10.1016/j.crhy.2015.08.003 |
| [6] | P.D. Meerburg et al., Primordial non-Gaussianity, arXiv:1903.04409 [INSPIRE]. |
| [7] | X. Chen and Y. Wang, Large non-Gaussianities with intermediate shapes from quasi-single field inflation, Phys. Rev.D 81 (2010) 063511 [arXiv:0909.0496] [INSPIRE]. |
| [8] | A.J. Tolley and M. Wyman, The Gelaton scenario: equilateral non-Gaussianity from multi-field dynamics, Phys. Rev.D 81 (2010) 043502 [arXiv:0910.1853] [INSPIRE]. |
| [9] | Cremonini, S.; Lalak, Z.; Turzynski, K., Strongly coupled perturbations in two-field inflationary models, JCAP, 03, 016 (2011) · doi:10.1088/1475-7516/2011/03/016 |
| [10] | Achucarro, A., Features of heavy physics in the CMB power spectrum, JCAP, 01, 030 (2011) · doi:10.1088/1475-7516/2011/01/030 |
| [11] | Achucarro, A., Effective theories of single field inflation when heavy fields matter, JHEP, 05, 066 (2012) · doi:10.1007/JHEP05(2012)066 |
| [12] | Mcallister, L.; Renaux-Petel, S.; Xu, G., A statistical approach to multifield inflation: many-field perturbations beyond slow roll, JCAP, 10, 046 (2012) · doi:10.1088/1475-7516/2012/10/046 |
| [13] | Burgess, Cp; Horbatsch, Mw; Patil, S., Inflating in a trough: single-field effective theory from multiple-field curved valleys, JHEP, 01, 133 (2013) · Zbl 1342.83232 · doi:10.1007/JHEP01(2013)133 |
| [14] | N. Arkani-Hamed and J. Maldacena, Cosmological collider physics, arXiv:1503.08043 [INSPIRE]. |
| [15] | Flauger, R.; Mirbabayi, M.; Senatore, L.; Silverstein, E., Productive Interactions: heavy particles and non-Gaussianity, JCAP, 10, 058 (2017) · Zbl 1515.83348 · doi:10.1088/1475-7516/2017/10/058 |
| [16] | Lee, H.; Baumann, D.; Pimentel, Gl, Non-Gaussianity as a particle detector, JHEP, 12, 040 (2016) · Zbl 1390.83465 · doi:10.1007/JHEP12(2016)040 |
| [17] | Chen, X.; Wang, Y.; Xianyu, Z-Z, Standard model background of the cosmological collider, Phys. Rev. Lett., 118, 261302 (2017) · doi:10.1103/PhysRevLett.118.261302 |
| [18] | Chen, X.; Loeb, A.; Xianyu, Z-Z, Unique fingerprints of alternatives to inflation in the primordial power spectrum, Phys. Rev. Lett., 122, 121301 (2019) · doi:10.1103/PhysRevLett.122.121301 |
| [19] | N. Arkani-Hamed, D. Baumann, H. Lee and G.L. Pimentel, The cosmological bootstrap: inflationary correlators from symmetries and singularities, arXiv:1811.00024 [INSPIRE]. · Zbl 1436.85001 |
| [20] | Creminelli, P.; Luty, Ma; Nicolis, A.; Senatore, L., Starting the universe: stable violation of the null energy condition and non-standard cosmologies, JHEP, 12, 080 (2006) · Zbl 1226.83089 · doi:10.1088/1126-6708/2006/12/080 |
| [21] | Cheung, C., The effective field theory of inflation, JHEP, 03, 014 (2008) · doi:10.1088/1126-6708/2008/03/014 |
| [22] | S. Renaux-Petel and K. Turzyński, Geometrical destabilization of inflation, Phys. Rev. Lett.117 (2016) 141301 [arXiv:1510.01281] [INSPIRE]. · Zbl 1515.83437 |
| [23] | Brown, Ar, Hyperbolic inflation, Phys. Rev. Lett., 121, 251601 (2018) · doi:10.1103/PhysRevLett.121.251601 |
| [24] | Mizuno, S.; Mukohyama, S., Primordial perturbations from inflation with a hyperbolic field-space, Phys. Rev., D 96, 103533 (2017) |
| [25] | Christodoulidis, P.; Roest, D.; Sfakianakis, Ei, Angular inflation in multi-field α-attractors, JCAP, 11, 002 (2019) · Zbl 1543.83190 · doi:10.1088/1475-7516/2019/11/002 |
| [26] | Garcia-Saenz, S.; Renaux-Petel, S.; Ronayne, J., Primordial fluctuations and non-Gaussianities in sidetracked inflation, JCAP, 07, 057 (2018) · Zbl 1527.83134 · doi:10.1088/1475-7516/2018/07/057 |
| [27] | Bjorkmo, T.; Marsh, Mcd, Hyperinflation generalised: from its attractor mechanism to its tension with the ‘swampland conditions’, JHEP, 04, 172 (2019) · doi:10.1007/JHEP04(2019)172 |
| [28] | Fumagalli, J., Hyper non-Gaussianities in inflation with strongly non-geodesic motion, Phys. Rev. Lett., 123, 201302 (2019) · doi:10.1103/PhysRevLett.123.201302 |
| [29] | Bjorkmo, T., Rapid-turn inflationary attractors, Phys. Rev. Lett., 122, 251301 (2019) · doi:10.1103/PhysRevLett.122.251301 |
| [30] | P. Christodoulidis, D. Roest and E.I. Sfakianakis, Attractors, bifurcations and curvature in multi-field inflation, arXiv:1903.03513 [INSPIRE]. · Zbl 1492.83087 |
| [31] | Christodoulidis, P.; Roest, D.; Sfakianakis, Ei, Scaling attractors in multi-field inflation, JCAP, 12, 059 (2019) · Zbl 1543.83189 · doi:10.1088/1475-7516/2019/12/059 |
| [32] | V. Aragam, S. Paban and R. Rosati, Multi-field inflation in high-slope potentials, arXiv:1905.07495 [INSPIRE]. · Zbl 1491.83042 |
| [33] | Hetz, A.; Palma, Ga, Sound speed of primordial fluctuations in supergravity inflation, Phys. Rev. Lett., 117, 101301 (2016) · doi:10.1103/PhysRevLett.117.101301 |
| [34] | Achúcarro, Ana; Atal, Vicente; Germani, Cristiano; Palma, Gonzalo A., Cumulative effects in inflation with ultra-light entropy modes, Journal of Cosmology and Astroparticle Physics, 2017, 2, 013-013 (2017) · Zbl 1515.83270 · doi:10.1088/1475-7516/2017/02/013 |
| [35] | S. Renaux-Petel, K. Turzyński and V. Vennin, Geometrical destabilization, premature end of inflation and Bayesian model selection, JCAP11 (2017) 006 [arXiv:1706.01835] [INSPIRE]. · Zbl 1515.83437 |
| [36] | A. Achúcarro et al., Universality of multi-field α-attractors, JCAP04 (2018) 028 [arXiv:1711.09478] [INSPIRE]. · Zbl 1536.83135 |
| [37] | Linde, A., Hypernatural inflation, JCAP, 07, 035 (2018) · Zbl 1527.83097 · doi:10.1088/1475-7516/2018/07/035 |
| [38] | X. Chen et al., Landscape tomography through primordial non-Gaussianity, Phys. Rev.D 98 (2018) 083528 [arXiv:1804.07315] [INSPIRE]. |
| [39] | A. Achúcarro and G.A. Palma, The string swampland constraints require multi-field inflation, JCAP02 (2019) 041 [arXiv:1807.04390] [INSPIRE]. · Zbl 1541.83084 |
| [40] | A. Achúcarro, S. Céspedes, A.-C. Davis and G.A. Palma, Constraints on holographic multifield inflation and models based on the Hamilton-Jacobi formalism, Phys. Rev. Lett.122 (2019) 191301 [arXiv:1809.05341] [INSPIRE]. |
| [41] | A. Achúcarro et al., Shift-symmetric orbital inflation: single field or multi-field?, arXiv:1901.03657 [INSPIRE]. |
| [42] | Grocholski, O., On backreaction effects in geometrical destabilisation of inflation, JCAP, 05, 008 (2019) · Zbl 1481.83108 · doi:10.1088/1475-7516/2019/05/008 |
| [43] | Cicoli, M.; Guidetti, V.; Pedro, Fg, Geometrical destabilisation of ultra-light axions in string inflation, JCAP, 05, 046 (2019) · Zbl 1481.83098 · doi:10.1088/1475-7516/2019/05/046 |
| [44] | Mizuno, S.; Mukohyama, S.; Pi, S.; Zhang, Y-L, Hyperbolic field space and swampland conjecture for DBI scalar, JCAP, 09, 072 (2019) · Zbl 1541.83091 · doi:10.1088/1475-7516/2019/09/072 |
| [45] | G. Panagopoulos and E. Silverstein, Primordial black holes from non-Gaussian tails, arXiv:1906.02827 [INSPIRE]. |
| [46] | R. Bravo, G.A. Palma and S. Riquelme, A tip for landscape riders: multi-field inflation can fulfill the swampland distance conjecture, arXiv:1906.05772 [INSPIRE]. · Zbl 1489.83074 |
| [47] | A. Achúcarro and Y. Welling, Orbital inflation: inflating along an angular isometry of field space, arXiv:1907.02020 [INSPIRE]. |
| [48] | Elliston, J.; Seery, D.; Tavakol, R., The inflationary bispectrum with curved field-space, JCAP, 11, 060 (2012) · doi:10.1088/1475-7516/2012/11/060 |
| [49] | D.J. Mulryne and J.W. Ronayne, PyTransport: a Python package for the calculation of inflationary correlation functions, arXiv:1609.00381 [INSPIRE]. |
| [50] | Dias, M.; Frazer, J.; Mulryne, Dj; Seery, D., Numerical evaluation of the bispectrum in multiple field inflation — The transport approach with code, JCAP, 12, 033 (2016) · doi:10.1088/1475-7516/2016/12/033 |
| [51] | D. Seery, CppTransport: a platform to automate calculation of inflationary correlation functions, arXiv:1609.00380 [INSPIRE]. |
| [52] | J.W. Ronayne and D.J. Mulryne, Numerically evaluating the bispectrum in curved field-space — with PyTransport 2.0, JCAP01 (2018) 023 [arXiv:1708.07130] [INSPIRE]. · Zbl 1527.83166 |
| [53] | Butchers, S.; Seery, D., Numerical evaluation of inflationary 3-point functions on curved field space — with the transport method & CppTransport, JCAP, 07, 031 (2018) · doi:10.1088/1475-7516/2018/07/031 |
| [54] | J.M. Maldacena, Non-Gaussian features of primordial fluctuations in single field inflationary models, JHEP05 (2003) 013 [astro-ph/0210603] [INSPIRE]. |
| [55] | C. Armendariz-Picon, T. Damour and V.F. Mukhanov, k-inflation, Phys. Lett.B 458 (1999) 209 [hep-th/9904075] [INSPIRE]. · Zbl 0992.83096 |
| [56] | Garriga, J.; Mukhanov, Vf, Perturbations in k-inflation, Phys. Lett., B 458, 219 (1999) · Zbl 0992.83097 · doi:10.1016/S0370-2693(99)00602-4 |
| [57] | D. Seery and J.E. Lidsey, Primordial non-Gaussianities in single field inflation, JCAP06 (2005) 003 [astro-ph/0503692] [INSPIRE]. |
| [58] | Chen, X.; Huang, M-X; Kachru, S.; Shiu, G., Observational signatures and non-Gaussianities of general single field inflation, JCAP, 01, 002 (2007) · doi:10.1088/1475-7516/2007/01/002 |
| [59] | S. Groot Nibbelink and B.J.W. van Tent, Density perturbations arising from multiple field slow roll inflation, hep-ph/0011325 [INSPIRE]. · Zbl 1005.83053 |
| [60] | S. Groot Nibbelink and B.J.W. van Tent, Scalar perturbations during multiple field slow-roll inflation, Class. Quant. Grav.19 (2002) 613 [hep-ph/0107272] [INSPIRE]. · Zbl 1005.83053 |
| [61] | J.-O. Gong and T. Tanaka, A covariant approach to general field space metric in multi-field inflation, JCAP03 (2011) 015 [Erratum ibid.02 (2012) E01] [arXiv:1101.4809] [INSPIRE]. |
| [62] | R.L. Arnowitt, S. Deser and C.W. Misner, The dynamics of general relativity, Gen. Rel. Grav.40 (2008) 1997 [gr-qc/0405109] [INSPIRE]. · Zbl 1152.83320 |
| [63] | Salopek, Ds, Nonlinear evolution of long-wavelength metric fluctuations in inflationary models, Phys. Rev., D 42, 3936 (1990) |
| [64] | Seery, David; Lidsey, James E., Primordial non-Gaussianities from multiple-field inflation, Journal of Cosmology and Astroparticle Physics, 2005, 9, 011-011 (2005) · doi:10.1088/1475-7516/2005/09/011 |
| [65] | Langlois, D.; Renaux-Petel, S., Perturbations in generalized multi-field inflation, JCAP, 04, 017 (2008) · doi:10.1088/1475-7516/2008/04/017 |
| [66] | D. Langlois, S. Renaux-Petel, D.A. Steer and T. Tanaka, Primordial perturbations and non-Gaussianities in DBI and general multi-field inflation, Phys. Rev.D 78 (2008) 063523 [arXiv:0806.0336] [INSPIRE]. |
| [67] | Tzavara, E.; Van Tent, B., Gauge-invariant perturbations at second order in two-field inflation, JCAP, 08, 023 (2012) · doi:10.1088/1475-7516/2012/08/023 |
| [68] | Tzavara, E.; Mizuno, S.; Van Tent, B., Covariant second-order perturbations in generalized two-field inflation, JCAP, 07, 027 (2014) · doi:10.1088/1475-7516/2014/07/027 |
| [69] | G.I. Rigopoulos, E.P.S. Shellard and B.J.W. van Tent, Non-linear perturbations in multiple-field inflation, Phys. Rev.D 73 (2006) 083521 [astro-ph/0504508] [INSPIRE]. |
| [70] | Langlois, David; Vernizzi, Filippo, Non-linear perturbations of cosmological scalar fields, Journal of Cosmology and Astroparticle Physics, 2007, 2, 017-017 (2007) · doi:10.1088/1475-7516/2007/02/017 |
| [71] | Renaux-Petel, S.; Tasinato, G., Nonlinear perturbations of cosmological scalar fields with non-standard kinetic terms, JCAP, 01, 012 (2009) |
| [72] | J.-L. Lehners and S. Renaux-Petel, Multifield cosmological perturbations at third order and the Ekpyrotic trispectrum, Phys. Rev.D 80 (2009) 063503 [arXiv:0906.0530] [INSPIRE]. |
| [73] | H. Collins, Primordial non-Gaussianities from inflation, arXiv:1101.1308 [INSPIRE]. |
| [74] | Jordan, Rd, Effective field equations for expectation values, Phys. Rev., D 33, 444 (1986) |
| [75] | Calzetta, E.; Hu, Bl, Closed-time-path functional formalism in curved spacetime: Application to cosmological back-reaction problems, Phys. Rev., D 35, 495 (1987) |
| [76] | S. Weinberg, Quantum contributions to cosmological correlations, Phys. Rev.D 72 (2005) 043514 [hep-th/0506236] [INSPIRE]. |
| [77] | Arroja, F.; Tanaka, T., A note on the role of the boundary terms for the non-Gaussianity in general k-inflation, JCAP, 05, 005 (2011) · doi:10.1088/1475-7516/2011/05/005 |
| [78] | Burrage, C.; Ribeiro, Rh; Seery, D., Large slow-roll corrections to the bispectrum of noncanonical inflation, JCAP, 07, 032 (2011) · doi:10.1088/1475-7516/2011/07/032 |
| [79] | G. Rigopoulos, Gauge invariance and non-Gaussianity in inflation, Phys. Rev.D 84 (2011) 021301 [arXiv:1104.0292] [INSPIRE]. |
| [80] | Baumann, D.; Green, D., Equilateral non-gaussianity and new physics on the horizon, JCAP, 09, 014 (2011) · doi:10.1088/1475-7516/2011/09/014 |
| [81] | Shiu, G.; Xu, J., Effective field theory and decoupling in multi-field inflation: an illustrative case study, Phys. Rev., D 84, 103509 (2011) |
| [82] | Cespedes, S.; Atal, V.; Palma, Ga, On the importance of heavy fields during inflation, JCAP, 05, 008 (2012) · doi:10.1088/1475-7516/2012/05/008 |
| [83] | Avgoustidis, A., Decoupling survives inflation: a critical look at effective field theory violations during inflation, JCAP, 06, 025 (2012) · doi:10.1088/1475-7516/2012/06/025 |
| [84] | Achucarro, A., Heavy fields, reduced speeds of sound and decoupling during inflation, Phys. Rev., D 86, 121301 (2012) |
| [85] | Gwyn, R.; Palma, Ga; Sakellariadou, M.; Sypsas, S., Effective field theory of weakly coupled inflationary models, JCAP, 04, 004 (2013) · doi:10.1088/1475-7516/2013/04/004 |
| [86] | S. Céspedes and G.A. Palma, Cosmic inflation in a landscape of heavy-fields, JCAP10 (2013) 051 [arXiv:1303.4703] [INSPIRE]. |
| [87] | Gong, J-O; Pi, S.; Sasaki, M., Equilateral non-Gaussianity from heavy fields, JCAP, 11, 043 (2013) · doi:10.1088/1475-7516/2013/11/043 |
| [88] | Gwyn, R.; Palma, Ga; Sakellariadou, M.; Sypsas, S., On degenerate models of cosmic inflation, JCAP, 10, 005 (2014) · doi:10.1088/1475-7516/2014/10/005 |
| [89] | Gong, J-O; Seo, M-S; Sypsas, S., Higher derivatives and power spectrum in effective single field inflation, JCAP, 03, 009 (2015) · doi:10.1088/1475-7516/2015/03/009 |
| [90] | Garcia-Saenz, S.; Renaux-Petel, S., Flattened non-Gaussianities from the effective field theory of inflation with imaginary speed of sound, JCAP, 11, 005 (2018) · Zbl 1527.85009 · doi:10.1088/1475-7516/2018/11/005 |
| [91] | P. Creminelli et al., Limits on non-Gaussianities from wmap data, JCAP05 (2006) 004 [astro-ph/0509029] [INSPIRE]. |
| [92] | Senatore, L.; Smith, Km; Zaldarriaga, M., Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data, JCAP, 01, 028 (2010) · doi:10.1088/1475-7516/2010/01/028 |
| [93] | Renaux-Petel, S., On the redundancy of operators and the bispectrum in the most general second-order scalar-tensor theory, JCAP, 02, 020 (2012) · doi:10.1088/1475-7516/2012/02/020 |
| [94] | A.A. Starobinsky, S. Tsujikawa and J. Yokoyama, Cosmological perturbations from multifield inflation in generalized Einstein theories, Nucl. Phys.B 610 (2001) 383 [astro-ph/0107555] [INSPIRE]. · Zbl 0971.83088 |
| [95] | F. Di Marco, F. Finelli and R. Brandenberger, Adiabatic and isocurvature perturbations for multifield generalized Einstein models, Phys. Rev.D 67 (2003) 063512 [astro-ph/0211276] [INSPIRE]. |
| [96] | F. Di Marco and F. Finelli, Slow-roll inflation for generalized two-field Lagrangians, Phys. Rev.D 71 (2005) 123502 [astro-ph/0505198] [INSPIRE]. |
| [97] | Lalak, Z.; Langlois, D.; Pokorski, S.; Turzynski, K., Curvature and isocurvature perturbations in two-field inflation, JCAP, 07, 014 (2007) · doi:10.1088/1475-7516/2007/07/014 |
| [98] | L. Pinol, S. Renaux-Petel and Y. Tada, Inflationary stochastic anomalies, Class. Quant. Grav.36 (2019) 07LT01 [arXiv:1806.10126] [INSPIRE]. · Zbl 1476.83195 |
| [99] | Burrage, C.; De Rham, C.; Seery, D.; Tolley, Aj, Galileon inflation, JCAP, 01, 014 (2011) · doi:10.1088/1475-7516/2011/01/014 |
| [100] | Goon, G.; Hinterbichler, K.; Joyce, A.; Trodden, M., Shapes of gravity: tensor non-gaussianity and massive spin-2 fields, JHEP, 10, 182 (2019) · Zbl 1427.83066 · doi:10.1007/JHEP10(2019)182 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
