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Warm Inflation Beyond the Markovian Limit

Mayukh R. Gangopadhyay, Nilanjana Kumar

Abstract

Warm inflation is commonly studied under the assumption that the stochastic force sourcing inflaton fluctuations is Markovian. Realistic thermal systems, however, possess finite relaxation times and can therefore generate colored noise with non-zero correlation time. In this work, we investigate warm inflation beyond the Markovian limit and determine how finite correlation time modifies the primordial scalar power spectrum. We show that memory effects suppress the scalar spectrum relative to the standard white-noise result and derive a simple expression for this correction in terms of the background thermal dynamics. In particular, we relate the size of the non-Markovian effect directly to the thermal ratio between the bath temperature and the Hubble scale, thereby establishing a transparent link between warm-inflation background quantities and the validity of the Markovian approximation. We also derive the corresponding modification of the tensor-to-scalar ratio and the induced shifts in the scalar spectral index and the running of the scalar spectral index. Our results provide a simple and practical diagnostic for identifying when finite correlation-time effects become relevant in warm-inflation model building.

Warm Inflation Beyond the Markovian Limit

Abstract

Warm inflation is commonly studied under the assumption that the stochastic force sourcing inflaton fluctuations is Markovian. Realistic thermal systems, however, possess finite relaxation times and can therefore generate colored noise with non-zero correlation time. In this work, we investigate warm inflation beyond the Markovian limit and determine how finite correlation time modifies the primordial scalar power spectrum. We show that memory effects suppress the scalar spectrum relative to the standard white-noise result and derive a simple expression for this correction in terms of the background thermal dynamics. In particular, we relate the size of the non-Markovian effect directly to the thermal ratio between the bath temperature and the Hubble scale, thereby establishing a transparent link between warm-inflation background quantities and the validity of the Markovian approximation. We also derive the corresponding modification of the tensor-to-scalar ratio and the induced shifts in the scalar spectral index and the running of the scalar spectral index. Our results provide a simple and practical diagnostic for identifying when finite correlation-time effects become relevant in warm-inflation model building.
Paper Structure (10 sections, 58 equations, 7 figures)

This paper contains 10 sections, 58 equations, 7 figures.

Table of Contents

  1. Introduction
  2. Warm inflation background and the thermal ratio $T/H$
  3. Stochastic dynamics beyond the Markovian limit
  4. Langevin equation
  5. Colored-noise parameter
  6. Detailed derivation of the scalar suppression factor
  7. Consequences for cosmological observables
  8. Regimes of validity and physical interpretation
  9. Numerical summary and parameter-space interpretation
  10. Conclusions

Figures (7)

  • Figure 1: Thermal ratio $T/H$ as a function of the dissipative ratio $Q$ obtained from Eq. \ref{['eq:TH']}.
  • Figure 2: Colored-noise parameter $\eta_c(Q)$ computed from Eq. \ref{['eq:etacQ']}.
  • Figure 3: Scalar suppression ratio $P_{\rm col}/P_{\rm white}=\delta(Q)$ obtained from Eq. \ref{['eq:deltaQ']}.
  • Figure 4: Enhancement of the tensor-to-scalar ratio due to colored noise, $r_{\rm col}/r_{\rm white}=1/\delta(Q)$.
  • Figure 5: Colored-noise contribution to the spectral index, $\Delta n_s(Q)=d\ln\delta/d\ln k$, evaluated using the mild scale dependence of Eq. \ref{['eq:Qk']}.
  • ...and 2 more figures