Generalizing the Bogoliubov vs Boltzmann approaches in gravitational production

Article Type

Research Article

Publication Title

Physical Review D

Abstract

We investigate the spectral behavior of scalar fluctuations generated by gravity during inflation and the subsequent reheating phase. We consider a nonperturbative Bogoliubov treatment within the context of pure gravitational reheating. We compute both long- and short-wavelength spectra, first for a massless scalar field, revealing that the spectral index in part of the infrared (IR) regime varies between −6 and −3, depending on the postinflationary equation of state (EoS), 0 ≤ wϕ ≤ 1. Furthermore, we study the massbreaking effect of the IR spectrum by including the finite mass, mχ, of the daughter scalar field. We show that for mχ=He ≳ 3=2, where He is the Hubble parameter during inflation, the IR spectrum of scalar fluctuations experiences exponential mass suppression, while for smaller masses, mχ=He < 3=2, the spectrum remains flat in the IR regime regardless of the postinflationary EoS. For any general EoS, we also compute a specific IR scale, km, of fluctuations below which the IR spectrum will suffer from this finite mass effect. In the UV regime, oscillations of the inflaton background lead to interference terms that explain the high-frequency oscillations in the spectrum. Interestingly, we find that for any EoS, 1=9 ≲ wϕ ≲ 1, the spectral behavior turns out to be independent of the EoS, with a spectral index −6. We have compared this Bogoliubov treatment for the UV regime to perturbative computations with solutions to the Boltzmann equation and found an agreement between the two approaches for any EoS, 0 ≲ wϕ ≲ 1. We also explore the relationship between the gravitational reheating temperature and the reheating EoS employing the nonperturbative analytic approach, finding that reheating can occur for wϕ ≳ 0.6.

First Page

43511

Last Page

43511

DOI

10.1103/1l7y-rdqr

Publication Date

8-12-2025

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