Abstract
We show that, in warm inflation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phase-space distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller effective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm inflation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm inflation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
A.A. Starobinsky, A New Type of Isotropic Cosmological Models Without Singularity, Phys. Lett. B 91 (1980) 99 [INSPIRE].
K. Sato, First Order Phase Transition of a Vacuum and Expansion of the Universe, Mon. Not. Roy. Astron. Soc. 195 (1981) 467 [INSPIRE].
A.H. Guth, The Inflationary Universe: A Possible Solution to the Horizon and Flatness Problems, Phys. Rev. D 23 (1981) 347 [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.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. Berera and L.-Z. Fang, Thermally induced density perturbations in the inflation era, Phys. Rev. Lett. 74 (1995) 1912 [astro-ph/9501024] [INSPIRE].
A. Berera, Warm inflation, Phys. Rev. Lett. 75 (1995) 3218 [astro-ph/9509049] [INSPIRE].
A. Berera, I.G. Moss and R.O. Ramos, Warm Inflation and its Microphysical Basis, Rept. Prog. Phys. 72 (2009) 026901 [arXiv:0808.1855] [INSPIRE].
M. Bastero-Gil and A. Berera, Warm inflation model building, Int. J. Mod. Phys. A 24 (2009) 2207 [arXiv:0902.0521] [INSPIRE].
A. Berera, Interpolating the stage of exponential expansion in the early universe: A possible alternative with no reheating, Phys. Rev. D 55 (1997) 3346 [hep-ph/9612239] [INSPIRE].
A. Berera, Warm inflation at arbitrary adiabaticity: A Model, an existence proof for inflationary dynamics in quantum field theory, Nucl. Phys. B 585 (2000) 666 [hep-ph/9904409] [INSPIRE].
L.M.H. Hall, I.G. Moss and A. Berera, Scalar perturbation spectra from warm inflation, Phys. Rev. D 69 (2004) 083525 [astro-ph/0305015] [INSPIRE].
I.G. Moss and C. Xiong, Non-Gaussianity in fluctuations from warm inflation, JCAP 04 (2007) 007 [astro-ph/0701302] [INSPIRE].
C. Graham and I.G. Moss, Density fluctuations from warm inflation, JCAP 07 (2009) 013 [arXiv:0905.3500] [INSPIRE].
R.O. Ramos and L.A. da Silva, Power spectrum for inflation models with quantum and thermal noises, JCAP 03 (2013) 032 [arXiv:1302.3544] [INSPIRE].
S. Bartrum, A. Berera and J.G. Rosa, Warming up for Planck, JCAP 06 (2013) 025 [arXiv:1303.3508] [INSPIRE].
S. Bartrum, M. Bastero-Gil, A. Berera, R. Cerezo, R.O. Ramos and J.G. Rosa, The importance of being warm (during inflation), Phys. Lett. B 732 (2014) 116 [arXiv:1307.5868] [INSPIRE].
M. Bastero-Gil, A. Berera, I.G. Moss and R.O. Ramos, Theory of non-Gaussianity in warm inflation, JCAP 12 (2014) 008 [arXiv:1408.4391] [INSPIRE].
M. Bastero-Gil, A. Berera, R.O. Ramos and J.G. Rosa, Warm Little Inflaton, Phys. Rev. Lett. 117 (2016) 151301 [arXiv:1604.08838] [INSPIRE].
A. Berera, M. Gleiser and R.O. Ramos, A First principles warm inflation model that solves the cosmological horizon/flatness problems, Phys. Rev. Lett. 83 (1999) 264 [hep-ph/9809583] [INSPIRE].
A. Berera and R.O. Ramos, Construction of a robust warm inflation mechanism, Phys. Lett. B 567 (2003) 294 [hep-ph/0210301] [INSPIRE].
I.G. Moss and C. Xiong, Dissipation coefficients for supersymmetric inflatonary models, hep-ph/0603266 [INSPIRE].
M. Bastero-Gil, A. Berera and R.O. Ramos, Dissipation coefficients from scalar and fermion quantum field interactions, JCAP 09 (2011) 033 [arXiv:1008.1929] [INSPIRE].
M. Bastero-Gil, A. Berera and J.G. Rosa, Warming up brane-antibrane inflation, Phys. Rev. D 84 (2011) 103503 [arXiv:1103.5623] [INSPIRE].
M. Bastero-Gil, A. Berera, R.O. Ramos and J.G. Rosa, General dissipation coefficient in low-temperature warm inflation, JCAP 01 (2013) 016 [arXiv:1207.0445] [INSPIRE].
R. Cerezo and J.G. Rosa, Warm Inflection, JHEP 01 (2013) 024 [arXiv:1210.7975] [INSPIRE].
E.W. Kolb and M.S. Turner, The Early Universe, Front. Phys. 69 (1990) 1 [INSPIRE].
D. Lyth and A. Liddle, The Primordial Density Perturbation: Cosmology, Inflation and the Origin of Structure, Cambridge University Press, Cambridge (2009).
D. Bazow, G.S. Denicol, U. Heinz, M. Martinez and J. Noronha, Analytic solution of the Boltzmann equation in an expanding system, Phys. Rev. Lett. 116 (2016) 022301 [arXiv:1507.07834] [INSPIRE].
D. Bazow, G.S. Denicol, U. Heinz, M. Martinez and J. Noronha, Nonlinear dynamics from the relativistic Boltzmann equation in the Friedmann-Lemaître-Robertson-Walker spacetime, Phys. Rev. D 94 (2016) 125006 [arXiv:1607.05245] [INSPIRE].
J.M. Cline, Baryogenesis, hep-ph/0609145 [INSPIRE].
A.D. Sakharov, Violation of CP Invariance, c Asymmetry and Baryon Asymmetry of the Universe, Pisma Zh. Eksp. Teor. Fiz. 5 (1967) 32 [INSPIRE].
F.R. Klinkhamer and N.S. Manton, A Saddle Point Solution in the Weinberg-Salam Theory, Phys. Rev. D 30 (1984) 2212 [INSPIRE].
M. Fukugita and T. Yanagida, Baryogenesis Without Grand Unification, Phys. Lett. B 174 (1986) 45 [INSPIRE].
B. Fields and S. Sarkar, Big-Bang nucleosynthesis (2006 Particle Data Group mini-review), astro-ph/0601514 [INSPIRE].
D.V. Nanopoulos and S. Weinberg, Mechanisms for Cosmological Baryon Production, Phys. Rev. D 20 (1979) 2484 [INSPIRE].
M. Bastero-Gil, A. Berera, R.O. Ramos and J.G. Rosa, Warm baryogenesis, Phys. Lett. B 712 (2012) 425 [arXiv:1110.3971] [INSPIRE].
M.S. Turner, A.G. Cohen and D.B. Kaplan, Isocurvature Baryon Number Fluctuations in an Inflationary Universe, Phys. Lett. B 216 (1989) 20 [INSPIRE].
J. Yokoyama and Y. Suto, Baryon isocurvature scenario in inflationary cosmology: A particle physics model and its astrophysical implications, Astrophys. J. 379 (1991) 427 [INSPIRE].
S. Mollerach, On the Primordial Origin of Isocurvature Perturbations, Phys. Lett. B 242 (1990) 158 [INSPIRE].
M. Sasaki and J. Yokoyama, Initial condition for the minimal isocurvature scenario, Phys. Rev. D 44 (1991) 970 [INSPIRE].
J. Yokoyama, Formation of baryon number fluctuation in supersymmetric inflationary cosmology, Astropart. Phys. 2 (1994) 291 [INSPIRE].
K. Koyama and J. Soda, Baryon isocurvature perturbation in the Affleck-Dine baryogenesis, Phys. Rev. Lett. 82 (1999) 2632 [astro-ph/9810006] [INSPIRE].
D.H. Lyth, C. Ungarelli and D. Wands, The Primordial density perturbation in the curvaton scenario, Phys. Rev. D 67 (2003) 023503 [astro-ph/0208055] [INSPIRE].
D. Grin, D. Hanson, G.P. Holder, O. Doré and M. Kamionkowski, Baryons do trace dark matter 380,000 years after the big bang: Search for compensated isocurvature perturbations with WMAP 9-year data, Phys. Rev. D 89 (2014) 023006 [arXiv:1306.4319] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XX. Constraints on inflation, Astron. Astrophys. 594 (2016) A20 [arXiv:1502.02114] [INSPIRE].
Planck collaboration, P.A.R. Ade et al., Planck 2015 results. XIII. Cosmological parameters, Astron. Astrophys. 594 (2016) A13 [arXiv:1502.01589] [INSPIRE].
M. Benetti and R.O. Ramos, Warm inflation dissipative effects: predictions and constraints from the Planck data, Phys. Rev. D 95 (2017) 023517 [arXiv:1610.08758] [INSPIRE].
M. Bastero-Gil, S. Bhattacharya, K. Dutta and M.R. Gangopadhyay, Constraining Warm Inflation with CMB data, arXiv:1710.10008 [INSPIRE].
R. Arya, A. Dasgupta, G. Goswami, J. Prasad and R. Rangarajan, Revisiting CMB constraints on Warm Inflation, arXiv:1710.11109 [INSPIRE].
S. Bartrum, A. Berera and J.G. Rosa, Fluctuation-dissipation dynamics of cosmological scalar fields, Phys. Rev. D 91 (2015) 083540 [arXiv:1412.5489] [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: 1711.09023
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Bastero-Gil, M., Berera, A., Ramos, R.O. et al. Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation. J. High Energ. Phys. 2018, 63 (2018). https://doi.org/10.1007/JHEP02(2018)063
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2018)063