Vacuum Polarization Effects During the Reheating Epoch

TL;DR

The paper investigates vacuum polarization effects during the reheating epoch in the Starobinsky inflation framework by embedding quantum backreaction within semiclassical gravity using curvature-squared counterterms. It develops a trace-equation approach, introduces the vacuum-polarization tensor via ${}^{(1)}H_{\mu\nu}$ and ${}^{(3)}H_{\mu\nu}$, and derives the scalaron decay width with and without these quantum corrections. The main result is that vacuum polarization yields a small correction to the decay width, $\Gamma = \frac{M_R^3}{24 M_{Pl}^2} + \frac{256 \pi M_R^3}{27 M_{Pl}^2 \tau^3} k_3 e$, with the correction $\Delta\Gamma$ estimated to be about $0.01$ GeV at early reheating, thus preserving the dominance of the standard width. The work highlights a practical method to separate background damping from decay-induced damping and discusses the potential for future numerical validation and higher-precision cosmological tests.

Abstract

Quantum effects in the era of reheating of the universe after inflation are considered. A semiclassical approach to gravity theory is applied within Starobinsky's inflationary model with backreaction. Some subtleties associated with accounting for quantum effects in the one-loop approximation are clarified. An estimate of the contribution of vacuum polarization in the stress-energy tensor of matter fields to the cosmological particle creation due to the scalaron decay is presented.

Figures (2)

• Figure 1: Evolution of the dimensionless scalar curvature $r$ as a function of the dimensionless time $\tau$ for initial values $r(0)=-300$ and $h(0)=5$.
• Figure 2: Evolution of the dimensionless Hubble parameter $h$ as a function of the dimensionless time $\tau$ for initial values $r(0)=-300$ and $h(0)=5$.