Warm Inflation Beyond the Markovian Limit

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.