Abstract
Recently, all duality invariant α′-corrections to the massless NS-NS sector of string theory on time-dependent backgrounds were classified and the form of their contribution to the action were calculated. In this paper we introduce matter sources in the resulting equations of motion in an O(d, d) covariant way. We show that either starting with the corrected equations and sourcing them with matter or considering corrections to the matter sourced lowest order equations give the same set of equations that defines string cosmology to all orders in α′. We also discuss perturbative and non-perturbative de Sitter solutions including matter.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Polchinski, String theory. Volume 1: An introduction to the bosonic string, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007).
J. Polchinski, String theory. Volume 2: Superstring theory and beyond, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2007).
R.H. Brandenberger and C. Vafa, Superstrings in the Early Universe, Nucl. Phys. B 316 (1989) 391 [INSPIRE].
A.A. Tseytlin and C. Vafa, Elements of string cosmology, Nucl. Phys. B 372 (1992) 443 [hep-th/9109048] [INSPIRE].
J. Erdmenger, String cosmology: Modern string theory concepts from the Big Bang to cosmic structure, John Wiley & Sons, Inc. (2009).
D. Baumann and L. McAllister, Inflation and String Theory, Cambridge Monographs on Mathematical Physics, Cambridge University Press (2015) [arXiv:1404.2601] [INSPIRE].
M. Gasperini, Elements of string cosmology, Cambridge University Press (2007).
K.A. Meissner and G. Veneziano, Symmetries of cosmological superstring vacua, Phys. Lett. B 267 (1991) 33 [INSPIRE].
K.A. Meissner and G. Veneziano, Manifestly O(d, d) invariant approach to space-time dependent string vacua, Mod. Phys. Lett. A 6 (1991) 3397 [hep-th/9110004] [INSPIRE].
G. Veneziano, Scale factor duality for classical and quantum strings, Phys. Lett. B 265 (1991) 287 [INSPIRE].
M. Gasperini and G. Veneziano, O(d, d) covariant string cosmology, Phys. Lett. B 277 (1992) 256 [hep-th/9112044] [INSPIRE].
A. Sen, O(d) ⊗ O(d) symmetry of the space of cosmological solutions in string theory, scale factor duality and two-dimensional black holes, Phys. Lett. B 271 (1991) 295 [INSPIRE].
R.R. Metsaev and A.A. Tseytlin, Order α′ (Two Loop) Equivalence of the String Equations of Motion and the σ-model Weyl Invariance Conditions: Dependence on the Dilaton and the Antisymmetric Tensor, Nucl. Phys. B 293 (1987) 385 [INSPIRE].
C.M. Hull and P.K. Townsend, The Two Loop β-function for σ Models With Torsion, Phys. Lett. B 191 (1987) 115 [INSPIRE].
D.J. Gross and J.H. Sloan, The Quartic Effective Action for the Heterotic String, Nucl. Phys. B 291 (1987) 41 [INSPIRE].
W. Siegel, Superspace duality in low-energy superstrings, Phys. Rev. D 48 (1993) 2826 [hep-th/9305073] [INSPIRE].
C. Hull and B. Zwiebach, Double Field Theory, JHEP 09 (2009) 099 [arXiv:0904.4664] [INSPIRE].
O. Hohm, D. Lüst and B. Zwiebach, The Spacetime of Double Field Theory: Review, Remarks and Outlook, Fortsch. Phys. 61 (2013) 926 [arXiv:1309.2977] [INSPIRE].
G. Aldazabal, D. Marques and C. Núñez, Double Field Theory: A Pedagogical Review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
O. Hohm, W. Siegel and B. Zwiebach, Doubled α′-geometry, JHEP 02 (2014) 065 [arXiv:1306.2970] [INSPIRE].
O. Hohm and B. Zwiebach, Double field theory at order α′, JHEP 11 (2014) 075 [arXiv:1407.3803] [INSPIRE].
D. Marques and C.A. Núñez, T-duality and α′-corrections, JHEP 10 (2015) 084 [arXiv:1507.00652] [INSPIRE].
W.H. Baron, J.J. Fernandez-Melgarejo, D. Marques and C. Núñez, The Odd story of α′-corrections, JHEP 04 (2017) 078 [arXiv:1702.05489] [INSPIRE].
H. Wu and H. Yang, Double Field Theory Inspired Cosmology, JCAP 07 (2014) 024 [arXiv:1307.0159] [INSPIRE].
R.H. Brandenberger, R. Costa, G. Franzmann and A. Weltman, T-dual cosmological solutions in double field theory, Phys. Rev. D 99 (2019) 023531 [arXiv:1809.03482] [INSPIRE].
H. Bernardo, R.H. Brandenberger and G. Franzmann, T-dual cosmological solutions in double field theory. II, Phys. Rev. D 99 (2019) 063521 [arXiv:1901.01209] [INSPIRE].
S. Angus, K. Cho and J.-H. Park, Einstein Double Field Equations, Eur. Phys. J. C 78 (2018) 500 [arXiv:1804.00964] [INSPIRE].
S. Angus, K. Cho, G. Franzmann, S. Mukohyama and J.-H. Park, O(D, D) completion of the Friedmann equations, arXiv:1905.03620 [INSPIRE].
K.A. Meissner, Symmetries of higher order string gravity actions, Phys. Lett. B 392 (1997) 298 [hep-th/9610131] [INSPIRE].
O. Hohm and B. Zwiebach, Duality invariant cosmology to all orders in α′ , Phys. Rev. D 100 (2019) 126011 [arXiv:1905.06963] [INSPIRE].
R.H. Brandenberger, String Gas Cosmology, in String Cosmology, J. Erdmenger ed., Wiley (2009), pp. 193–230 [arXiv:0808.0746] [INSPIRE].
T. Battefeld and S. Watson, String gas cosmology, Rev. Mod. Phys. 78 (2006) 435 [hep-th/0510022] [INSPIRE].
M. Gasperini and G. Veneziano, The Pre-big bang scenario in string cosmology, Phys. Rept. 373 (2003) 1 [hep-th/0207130] [INSPIRE].
J. Quintin, R.H. Brandenberger, M. Gasperini and G. Veneziano, Stringy black-hole gas in α′-corrected dilaton gravity, Phys. Rev. D 98 (2018) 103519 [arXiv:1809.01658] [INSPIRE].
O. Hohm and B. Zwiebach, Non-perturbative de Sitter vacua via α′ corrections, Int. J. Mod. Phys. D 28 (2019) 1943002 [arXiv:1905.06583] [INSPIRE].
T.D. Brennan, F. Carta and C. Vafa, The String Landscape, the Swampland and the Missing Corner, PoS(TASI2017)015 (2017) [arXiv:1711.00864] [INSPIRE].
E. Palti, The Swampland: Introduction and Review, Fortsch. Phys. 67 (2019) 1900037 [arXiv:1903.06239] [INSPIRE].
C. Krishnan, de Sitter, α′-Corrections & Duality Invariant Cosmology, JCAP 10 (2019) 009 [arXiv:1906.09257] [INSPIRE].
P. Wang, H. Wu and H. Yang, Are nonperturbative AdS vacua possible in bosonic string theory?, Phys. Rev. D 100 (2019) 046016 [arXiv:1906.09650] [INSPIRE].
P. Wang, H. Wu, H. Yang and S. Ying, Non-singular string cosmology via α′ corrections, JHEP 10 (2019) 263 [arXiv:1909.00830] [INSPIRE].
P. Wang, H. Wu, H. Yang and S. Ying, Construct α′ corrected or loop corrected solutions without curvature singularities, JHEP 01 (2020) 164 [arXiv:1910.05808] [INSPIRE].
T.R. Taylor and G. Veneziano, Dilaton Couplings at Large Distances, Phys. Lett. B 213 (1988) 450 [INSPIRE].
T. Damour, F. Piazza and G. Veneziano, Violations of the equivalence principle in a dilaton runaway scenario, Phys. Rev. D 66 (2002) 046007 [hep-th/0205111] [INSPIRE].
P. Touboul et al., MICROSCOPE Mission: First Results of a Space Test of the Equivalence Principle, Phys. Rev. Lett. 119 (2017) 231101 [arXiv:1712.01176] [INSPIRE].
R.J. Danos, A.R. Frey and R.H. Brandenberger, Stabilizing moduli with thermal matter and nonperturbative effects, Phys. Rev. D 77 (2008) 126009 [arXiv:0802.1557] [INSPIRE].
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
R. Brout, F. Englert and E. Gunzig, The Creation of the Universe as a Quantum Phenomenon, Annals Phys. 115 (1978) 78 [INSPIRE].
K. Sato, First Order Phase Transition of a Vacuum and Expansion of the Universe, Mon. Not. Roy. Astron. Soc. 195 (1981) 467 [INSPIRE].
G. Obied, H. Ooguri, L. Spodyneiko and C. Vafa, de Sitter Space and the Swampland, arXiv:1806.08362 [INSPIRE].
P. Agrawal, G. Obied, P.J. Steinhardt and C. Vafa, On the Cosmological Implications of the String Swampland, Phys. Lett. B 784 (2018) 271 [arXiv:1806.09718] [INSPIRE].
H. Bernardo, R.H. Brandenberger and G. Franzmann, in preparation.
A. Bedroya, R.H. Brandenberger, M. Loverde and C. Vafa, Trans-Planckian Censorship and Inflationary Cosmology, arXiv:1909.11106 [INSPIRE].
A. Bedroya and C. Vafa, Trans-Planckian Censorship and the Swampland, arXiv:1909.11063 [INSPIRE].
R.H. Brandenberger, Introduction to Early Universe Cosmology, PoS(ICFI2010)001 (2010) [arXiv:1103.2271] [INSPIRE].
R.H. Brandenberger, Beyond Standard Inflationary Cosmology, arXiv:1809.04926 [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1911.00088
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Bernardo, H., Brandenberger, R. & Franzmann, G. O(d, d) covariant string cosmology to all orders in α′. J. High Energ. Phys. 2020, 178 (2020). https://doi.org/10.1007/JHEP02(2020)178
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2020)178