Generalizing the Bogoliubov vs Boltzmann approaches in gravitational production
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2025
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| author | Chakraborty, Ayan Clery, Simon Haque, Md Riajul Maity, Debaprasad Mambrini, Yann |
| author_facet | Chakraborty, Ayan Clery, Simon Haque, Md Riajul Maity, Debaprasad Mambrini, Yann |
| contents | We investigate the spectral behavior of scalar fluctuations generated by gravity during inflation and the subsequent reheating phase. We consider a non-perturbative 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 post-inflationary equation of state (EoS), $0\leq w_ϕ\leq1$. Furthermore, we study the mass-breaking effect of the IR spectrum by including finite mass, $m_χ$, of the daughter scalar field. We show that for $m_χ/H_{\rm e} \gtrsim 3/2$, where $H_{\rm e}$ is the Hubble parameter during inflation, the IR spectrum of scalar fluctuations experiences exponential mass suppression, while for smaller masses, $m_χ/H_{\rm e}<3/2$, the spectrum remains flat in the IR regime regardless of the post-inflationary EoS. For any general EoS, we also compute a specific IR scale, $k_m$, 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, $1/9 \lesssim w_ϕ\lesssim 1$, 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, $0 \lesssim w_ϕ\lesssim 1$. We also explore the relationship between the gravitational reheating temperature and the reheating EoS employing the non-perturbative analytic approach, finding that reheating can occur for $w_ϕ\gtrsim 0.6$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_21877 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalizing the Bogoliubov vs Boltzmann approaches in gravitational production Chakraborty, Ayan Clery, Simon Haque, Md Riajul Maity, Debaprasad Mambrini, Yann General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology High Energy Physics - Theory We investigate the spectral behavior of scalar fluctuations generated by gravity during inflation and the subsequent reheating phase. We consider a non-perturbative 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 post-inflationary equation of state (EoS), $0\leq w_ϕ\leq1$. Furthermore, we study the mass-breaking effect of the IR spectrum by including finite mass, $m_χ$, of the daughter scalar field. We show that for $m_χ/H_{\rm e} \gtrsim 3/2$, where $H_{\rm e}$ is the Hubble parameter during inflation, the IR spectrum of scalar fluctuations experiences exponential mass suppression, while for smaller masses, $m_χ/H_{\rm e}<3/2$, the spectrum remains flat in the IR regime regardless of the post-inflationary EoS. For any general EoS, we also compute a specific IR scale, $k_m$, 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, $1/9 \lesssim w_ϕ\lesssim 1$, 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, $0 \lesssim w_ϕ\lesssim 1$. We also explore the relationship between the gravitational reheating temperature and the reheating EoS employing the non-perturbative analytic approach, finding that reheating can occur for $w_ϕ\gtrsim 0.6$. |
| title | Generalizing the Bogoliubov vs Boltzmann approaches in gravitational production |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.21877 |