Warm Inflation Triggered by Entropies of Some Recent Dark Energy Models within $f(Q)$ Gravity

This manuscript aims to study cosmic warm inflation (WI) in the framework of $f(Q)$ gravity, where $Q$ represents the nonmetricity (NM) scalar. To accomplish this task, we introduce the Tsallis, Renyi, and Barrow holographic dark energy (HDE) entropies into the standard Friedmann equations. Utilizing the slow-roll (SR) approximation, we find exact analytic solutions for the inflaton field, the effective potential necessary to produce inflation, and the scale factor for both low and high-dissipative regimes. We calculate key parameters, including SR parameters, the number of e-folds, the scalar spectral index and its running, and finally tensor-to-scalar ratio to assess the accuracy of the chosen DE models in light of the published observational data. The allowed ranges of the involved free parameters are found from the limits on inflationary observables imposed by the Planck data. It is concluded that the obtained results are consistent with proposed theoretical predictions up to $2\sigma$ confidence level.