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Gravitational reheating formulas and bounds in oscillating backgrounds

Jaume de Haro, Llibert Aresté Saló, Supriya Pan

Abstract

In this article we calculate the reheating temperature in the cosmological scenarios where heavy scalar particles are gravitationally produced, due to a conformally coupled interaction between a massive scalar quantum field and the Ricci scalar, during the oscillations of the inflaton field. We explore two distinct cases, namely the one in which these particles decay during the domination of the inflaton's energy density and the other one where the decay occurs after this phase. For each scenario, we have derived formulas to calculate the reheating temperatures based on the energy density of the produced particles and their decay rate. We establish bounds for the maximum reheating temperature, defined as the temperature reached by the universe when the decay of gravitationally produced particles concludes at the onset of the radiation-dominated epoch. Finally, we use the Born approximation to find analytic formulas for the reheating temperature.

Gravitational reheating formulas and bounds in oscillating backgrounds

Abstract

In this article we calculate the reheating temperature in the cosmological scenarios where heavy scalar particles are gravitationally produced, due to a conformally coupled interaction between a massive scalar quantum field and the Ricci scalar, during the oscillations of the inflaton field. We explore two distinct cases, namely the one in which these particles decay during the domination of the inflaton's energy density and the other one where the decay occurs after this phase. For each scenario, we have derived formulas to calculate the reheating temperatures based on the energy density of the produced particles and their decay rate. We establish bounds for the maximum reheating temperature, defined as the temperature reached by the universe when the decay of gravitationally produced particles concludes at the onset of the radiation-dominated epoch. Finally, we use the Born approximation to find analytic formulas for the reheating temperature.

Paper Structure

This paper contains 13 sections, 125 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Reheating via gravitational production of heavy particles
  3. Decay before the end of the background domination
  4. Decay after the end of the background domination
  5. Bounds on the maximum reheating temperature
  6. Analytic formulas for the particle production and the corresponding bounds
  7. Case: $n=3$
  8. Case: $n\rightarrow \infty$
  9. Application to $\alpha$-attractors
  10. Qualitative study and Numerical calculations
  11. Numerical results
  12. Analytic results: Born approximation
  13. Conclusions

Figures (1)

  • Figure 1: Stabilisation of the value of $|\beta_k|^2$ for $m_{\chi}=10^{-2}H_{\rm END}$ in function of the number of $e$-folds after the end of inflation for different modes.

Theorems & Definitions (4)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 5.1