Universality of the volume bound in slow-roll eternal inflation
Tóm tắt
It has recently been shown that in single field slow-roll inflation the total volume cannot grow by a factor larger than
$ {e^{{S_{dS}}/2}} $
without becoming infinite. The bound is saturated exactly at the phase transition to eternal inflation where the probability to produce infinite volume becomes non zero. We show that the bound holds sharply also in any space-time dimensions, when arbitrary higher-dimensional operators are included and in the multi-field inflationary case. The relation with the entropy of de Sitter and the universality of the bound strengthen the case for a deeper holographic interpretation. As a spin-off we provide the formalism to compute the probability distribution of the volume after inflation for generic multi-field models, which might help to address questions about the population of vacua of the landscape during slow-roll inflation.
Tài liệu tham khảo
Supernova Search Team collaboration, A.G. Riess et al., Observational evidence from supernovae for an accelerating universe and a cosmological constant, Astron. J. 116 (1998) 1009 [astro-ph/9805201] [INSPIRE].
Supernova Cosmology Project collaboration, S. Perlmutter et al., Measurements of Omega and Lambda from 42 high redshift supernovae, Astrophys. J. 517 (1999) 565 [astro-ph/9812133] [INSPIRE].
WMAP collaboration, E. Komatsu et al., Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation, Astrophys. J. Suppl. 192 (2011) 18 [arXiv:1001.4538] [INSPIRE].
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [INSPIRE].
A.D. Linde, A New Inflationary Universe Scenario: A Possible Solution of the Horizon, Flatness, Homogeneity, Isotropy and Primordial Monopole Problems, Phys. Lett. B 108 (1982) 389 [INSPIRE].
A. Albrecht and P.J. Steinhardt, Cosmology for Grand Unified Theories with Radiatively Induced Symmetry Breaking, Phys. Rev. Lett. 48 (1982) 1220 [INSPIRE].
A. Vilenkin, The Birth of Inflationary Universes, Phys. Rev. D 27 (1983) 2848 [INSPIRE].
A.D. Linde, Eternally Existing Selfreproducing Chaotic Inflationary Universe, Phys. Lett. B 175 (1986) 395 [INSPIRE].
A.D. Linde, Eternal chaotic inflation, Mod. Phys. Lett. A 1 (1986) 81 [INSPIRE].
P. Creminelli, S. Dubovsky, A. Nicolis, L. Senatore and M. Zaldarriaga, The phase transition to slow-roll eternal inflation, JHEP 09 (2008) 036 [arXiv:0802.1067] [INSPIRE].
A.H. Guth and E.J. Weinberg, Could the Universe Have Recovered from a Slow First Order Phase Transition?, Nucl. Phys. B 212 (1983) 321 [INSPIRE].
Y. Sekino, S. Shenker and L. Susskind, On the Topological Phases of Eternal Inflation, Phys. Rev. D 81 (2010) 123515 [arXiv:1003.1347] [INSPIRE].
S. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
N. Arkani-Hamed, S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, A measure of de Sitter entropy and eternal inflation, JHEP 05 (2007) 055 [arXiv:0704.1814] [INSPIRE].
S. Dubovsky, L. Senatore and G. Villadoro, The Volume of the Universe after Inflation and de Sitter Entropy, JHEP 04 (2009) 118 [arXiv:0812.2246] [INSPIRE].
C. Jarzynski, Nonequilibrium Equality for Free Energy Differences, Phys. Rev. Lett. 78 (1997) 2690 .
A.V. Frolov and L. Kofman, Inflation and de Sitter thermodynamics, JCAP 05 (2003) 009 [hep-th/0212327] [INSPIRE].
T. Jacobson, Thermodynamics of space-time: The Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260 [gr-qc/9504004] [INSPIRE].
S. Winitzki, Reheating-volume measure in the landscape, Phys. Rev. D 78 (2008) 123518 [arXiv:0810.1517] [INSPIRE].
M. Alishahiha, E. Silverstein and D. Tong, DBI in the sky, Phys. Rev. D 70 (2004) 123505 [hep-th/0404084] [INSPIRE].
N. Arkani-Hamed, P. Creminelli, S. Mukohyama and M. Zaldarriaga, Ghost inflation, JCAP 04 (2004) 001 [hep-th/0312100] [INSPIRE].
S. Dubovsky and S. Sibiryakov, Spontaneous breaking of Lorentz invariance, black holes and perpetuum mobile of the 2nd kind, Phys. Lett. B 638 (2006) 509 [hep-th/0603158] [INSPIRE].
R.M. Wald, Black hole entropy is the Noether charge, Phys. Rev. D 48 (1993) 3427 [gr-qc/9307038] [INSPIRE].
V. Iyer and R.M. Wald, Some properties of Noether charge and a proposal for dynamical black hole entropy, Phys. Rev. D 50 (1994) 846 [gr-qc/9403028] [INSPIRE].
M.K. Parikh and S. Sarkar, Beyond the Einstein Equation of State: Wald Entropy and Thermodynamical Gravity, arXiv:0903.1176 [INSPIRE].