Warm Inflation in $f(Q)$ gravity

Abstract

We investigate warm inflation in the framework of $f(Q)$ gravity within a Friedmann-Robertson-Walker spacetime. Unlike cold inflation, where the inflaton evolves in isolation, warm inflation features continuous interaction between the inflaton field and radiation throughout the inflationary epoch, facilitating energy transfer through dissipative processes and maintaining thermal equilibrium. In our novel approach, we employ $f(Q)$ dark energy as the driving mechanism for warm inflation, leveraging the geometric degrees of freedom associated with non-metricity as dynamical variables. We derive the field equations using slow-roll approximations and analyze two specific $f(Q)$ models: a power-law form $f(Q) = Q + m Q^n$ and a logarithmic form $f(Q) = mQ\ln(nQ)$. Our analysis focuses on the high-dissipative regime, where thermal fluctuations dominate over quantum fluctuations. We compute key inflationary observables, including the scalar spectral index $n_s$, tensor-to-scalar ratio $r$, and slow-roll parameters. Our results demonstrate that $f(Q)$ dark energy successfully drives warm inflation while satisfying essential physical conditions: initial dominance of $f(Q)$ energy density over radiation density initially, and thermal fluctuations exceeding quantum fluctuations ($T > H$). As inflation progresses, energy transfers from the geometric $f(Q)$ sector to radiation, eventually bringing both densities to comparable levels near inflation's end. Importantly, our computed values align well with current observational constraints from Planck and BICEP/Keck: $n_s = 0.965 \pm 0.004$ and $r < 0.036$. This validates the viability of warm inflation in $f(Q)$ gravity and establishes a unified geometric framework for understanding both early universe inflation and late-time cosmic acceleration.