Abstract
In a recent paper we developed a string cosmology background from classical string geometry. Here, we show that this background yields a solution to the size and horizon problems of Standard Big Bang cosmology while remaining compatible with the Transplanckian Censorship Conjecture. We also take a first look at the evolution of cosmological perturbations in this model.
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M.B. Green, J.H. Schwarz and L. Brink, N = 4 Yang-Mills and N = 8 supergravity as limits of string theories, Nucl. Phys. B 198 (1982) 474 [INSPIRE].
K. Kikkawa and M. Yamasaki, Casimir effects in superstring theories, Phys. Lett. B 149 (1984) 357 [INSPIRE].
N. Sakai and I. Senda, Vacuum energies of string compactified on torus, Prog. Theor. Phys. 75 (1986) 692 [Erratum ibid. 77 (1987) 773] [INSPIRE].
E. Alvarez, L. Álvarez-Gaumé and Y. Lozano, An introduction to T duality in string theory, Nucl. Phys. B Proc. Suppl. 41 (1995) 1 [hep-th/9410237] [INSPIRE].
T. Boehm and R. Brandenberger, On T duality in brane gas cosmology, JCAP 06 (2003) 008 [hep-th/0208188] [INSPIRE].
N. Deo, S. Jain and C.-I. Tan, String statistical mechanics above Hagedorn energy density, Phys. Rev. D 40 (1989) 2626 [INSPIRE].
R.H. Brandenberger and C. Vafa, Superstrings in the Early universe, Nucl. Phys. B 316 (1989) 391 [INSPIRE].
R. Hagedorn, Statistical thermodynamics of strong interactions at high-energies, Nuovo Cim. Suppl. 3 (1965) 147 [INSPIRE].
J. Kripfganz and H. Perlt, Cosmological impact of winding strings, Class. Quant. Grav. 5 (1988) 453 [INSPIRE].
A. Nayeri, R.H. Brandenberger and C. Vafa, Producing a scale-invariant spectrum of perturbations in a Hagedorn phase of string cosmology, Phys. Rev. Lett. 97 (2006) 021302 [hep-th/0511140] [INSPIRE].
R.H. Brandenberger, A. Nayeri and S.P. Patil, Closed string thermodynamics and a blue tensor spectrum, Phys. Rev. D 90 (2014) 067301 [arXiv:1403.4927] [INSPIRE].
R.H. Brandenberger, A. Nayeri, S.P. Patil and C. Vafa, Tensor modes from a primordial Hagedorn phase of string cosmology, Phys. Rev. Lett. 98 (2007) 231302 [hep-th/0604126] [INSPIRE].
B. Chen, Y. Wang, W. Xue and R. Brandenberger, String gas cosmology and non-Gaussianities, The Universe 3 (2015) 2 [arXiv:0712.2477] [INSPIRE].
R.H. Brandenberger, String gas cosmology: progress and problems, Class. Quant. Grav. 28 (2011) 204005 [arXiv:1105.3247] [INSPIRE].
R.H. Brandenberger, String gas cosmology, arXiv:0808.0746 [INSPIRE].
T. Battefeld and S. Watson, String gas cosmology, Rev. Mod. Phys. 78 (2006) 435 [hep-th/0510022] [INSPIRE].
S.P. Patil and R. Brandenberger, Radion stabilization by stringy effects in general relativity, Phys. Rev. D 71 (2005) 103522 [hep-th/0401037] [INSPIRE].
S.P. Patil and R.H. Brandenberger, The cosmology of massless string modes, JCAP 01 (2006) 005 [hep-th/0502069] [INSPIRE].
S. Watson and R. Brandenberger, Stabilization of extra dimensions at tree level, JCAP 11 (2003) 008 [hep-th/0307044] [INSPIRE].
S. Watson, Moduli stabilization with the string Higgs effect, Phys. Rev. D 70 (2004) 066005 [hep-th/0404177] [INSPIRE].
R. Brandenberger, Y.-K.E. Cheung and S. Watson, Moduli stabilization with string gases and fluxes, JHEP 05 (2006) 025 [hep-th/0501032] [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].
S. Mishra, W. Xue, R. Brandenberger and U. Yajnik, Supersymmetry breaking and dilaton stabilization in string gas cosmology, JCAP 09 (2012) 015 [arXiv:1103.1389] [INSPIRE].
M. Gasperini and G. Veneziano, Pre-Big Bang in string cosmology, Astropart. Phys. 1 (1993) 317 [hep-th/9211021] [INSPIRE].
A.A. Tseytlin and C. Vafa, Elements of string cosmology, Nucl. Phys. B 372 (1992) 443 [hep-th/9109048] [INSPIRE].
M. Gasperini and G. Veneziano, The Pre-Big Bang scenario in string cosmology, Phys. Rept. 373 (2003) 1 [hep-th/0207130] [INSPIRE].
M.J. Duff, Duality rotations in string theory, Nucl. Phys. B 335 (1990) 610 [INSPIRE].
A.A. Tseytlin, Duality symmetric string theory and the cosmological constant problem, Phys. Rev. Lett. 66 (1991) 545 [INSPIRE].
T. Kugo and B. Zwiebach, Target space duality as a symmetry of string field theory, Prog. Theor. Phys. 87 (1992) 801 [hep-th/9201040] [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].
G. Aldazabal, D. Marques and C. Núñez, Double field theory: a pedagogical review, Class. Quant. Grav. 30 (2013) 163001 [arXiv:1305.1907] [INSPIRE].
R. Brandenberger, R. Costa, G. Franzmann and A. Weltman, Point particle motion in double field theory and a singularity-free cosmological solution, Phys. Rev. D 97 (2018) 063530 [arXiv:1710.02412] [INSPIRE].
R. Brandenberger, R. Costa, G. Franzmann and A. Weltman, Dual spacetime and nonsingular string cosmology, Phys. Rev. D 98 (2018) 063521 [arXiv:1805.06321] [INSPIRE].
R. 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. Brandenberger and G. Franzmann, T -dual cosmological solutions in double field theory. II., Phys. Rev. D 99 (2019) 063521 [arXiv:1901.01209] [INSPIRE].
O. Hohm and B. Zwiebach, Duality invariant cosmology to all orders in α′, Phys. Rev. D 100 (2019) 126011 [arXiv:1905.06963] [INSPIRE].
H. Bernardo, R. Brandenberger and G. Franzmann, O(d, d) covariant string cosmology to all orders in α′, JHEP 02 (2020) 178 [arXiv:1911.00088] [INSPIRE].
H. Bernardo and G. Franzmann, α′-cosmology: solutions and stability analysis, JHEP 05 (2020) 073 [arXiv:2002.09856] [INSPIRE].
H. Bernardo, R. Brandenberger and G. Franzmann, String Cosmology backgrounds from Classical String Geometry, arXiv:2005.08324 [INSPIRE].
R. Brandenberger, Fundamental physics, the swampland of effective field theory and early universe cosmology, in the proceedings of the 11th International Symposium on Quantum Theory and Symmetries, July 1–5, Montreal, Canada (2019), arXiv:1911.06058 [INSPIRE].
A. Bedroya and C. Vafa, Trans-Planckian censorship and the swampland, JHEP 09 (2020) 123 [arXiv:1909.11063] [INSPIRE].
C. Kiefer, D. Polarski and A.A. Starobinsky, Quantum to classical transition for fluctuations in the early universe, Int. J. Mod. Phys. D 7 (1998) 455 [gr-qc/9802003] [INSPIRE].
A. Bedroya, R. Brandenberger, M. Loverde and C. Vafa, Trans-Planckian censorship and inflationary cosmology, Phys. Rev. D 101 (2020) 103502 [arXiv:1909.11106] [INSPIRE].
V.F. Mukhanov, H.A. Feldman and R.H. Brandenberger, Theory of cosmological perturbations. Part 1. Classical perturbations. Part 2. Quantum theory of perturbations. Part 3. Extensions, Phys. Rept. 215 (1992) 203 [INSPIRE].
M. Sasaki, Large scale quantum fluctuations in the inflationary universe, Prog. Theor. Phys. 76 (1986) 1036 [INSPIRE].
V.F. Mukhanov, Quantum Theory of Gauge Invariant Cosmological Perturbations, Sov. Phys. JETP 67 (1988) 1297 [Zh. Eksp. Teor. Fiz. 94N7 (1988) 1] [INSPIRE].
M. Gasperini, Inflation and initial conditions in the Pre-Big Bang scenario, Phys. Rev. D 61 (2000) 087301 [gr-qc/9902060] [INSPIRE].
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Bernardo, H., Brandenberger, R. & Franzmann, G. Solution of the size and horizon problems from classical string geometry. J. High Energ. Phys. 2020, 155 (2020). https://doi.org/10.1007/JHEP10(2020)155
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DOI: https://doi.org/10.1007/JHEP10(2020)155