On the effective Stefan-Boltzmann law and the thermodynamic origin of the initial radiation density in warm inflation

Yongwan Gim,Wontae Kim,B Gwak,H.-C Kim,W Lee,C Kim,G Kang,J Lee,S Lee,C.-H Lee

doi:10.1051/epjconf/201816806004

Yongwan Gim, Wontae Kim + Show 8 more

Open Access

https://doi.org/10.1051/epjconf/201816806004

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Abstract

In this presentation, we are going to explain the thermodynamic origin of warm inflation scenarios by using the effetive Stefan-Boltzmann law. In the warm inflation scenarios, radiation always exists to avoid the graceful exit problem, for which the radiation energy density should be assumed to be finite at the starting point of the warm inflation. To find out the origin of the non-vanishing initial radiation energy density, we derive an effective Stefan-Boltzmann law by considering the non-vanishing trace of the total energy-momentum tensors. The effective Stefan-Boltzmann law successfully shows where the initial radiation energy density is thermodynamically originated from. And by using the above effective Stefan-Boltzmann law, we also study the cosmological scalar perturbation, and obtain the sufficient radiation energy density in order for GUT baryogenesis at the end of inflation. This proceeding is based on Ref. [1]

Highlights

Inflation is an elegant solution to the interesting problems such as the horizon and flatness problems in the big bang cosmology [2,3,4], during which the rapid expansion lays the universe in a supercooled phase
Motivated by the non-zero initial radiation energy density in warm inflation scenario, we performed thermodynamic analysis for the warm inflation model by using the definitions for the inflaton and radiation energy density presented in Ref. [11]
By using the effective Stefan-Boltzmann law for the radiation energy density, we studied the number of e-folds and the spectral index of the scalar perturbation under the slow-roll approximations in the power-law potential and damping terms, so that the temperature (16) at the end of warm inflation was successfully calculated, and it satisfies the upper bound lower than the GUT scale [11], and lower bound of the big bang nucleosynthesis [19, 20] by the CMB data [21]

Summary

Introduction

Inflation is an elegant solution to the interesting problems such as the horizon and flatness problems in the big bang cosmology [2,3,4], during which the rapid expansion lays the universe in a supercooled phase. Thereafter the reheating process should be assumed for the graceful exit problem. In contrast to the assumption of the supercooled universe after inflation, another way to approach this issue without reheating process has been studied in Ref. First one is a damping term during warm inflation. Second one is the large-scale initial radiation energy density. It can be naturally assumed to be nonzero, ρr(ti) 0 [7], which is compatible with the Stefan-Boltzmann law of ρr = 3γT 4 in the hot thermal bath at the initial point of inflation, t = ti. One might wonder how to exist the large-scale initial radiation energy density and what is the origin of it in the warm inflation scenario

Effective Stefan-Boltzmann law in warm inflation

Temperatures at the horizon crossing and at the end of inflation

Conclusion