Slow-roll inflation in (dual) Kaniadakis cosmology
We investigate slow-roll inflation within the framework of Kaniadakis and dual Kaniadakis cosmology, where the usual entropy formalism is generalized through a deformation parameter $κ$. By deriving the modified Friedmann equations and the corresponding inflationary dynamics induced by Kaniadakis entropy, we analyze the deviations from standard inflation arising from $κ$-corrections.To test the viability of these models, we evaluate two representative inflationary potentials: the power-law and the Mexican-hat (symmetry breaking) potentials. We compute the scalar and tensor spectral indices, the tensor-to-scalar ratio, and the primordial power spectrum, comparing them against the latest Planck and BICEP observational constraints. Our results show that in the standard Kaniadakis formulation, viable slow-roll inflationary scenarios compatible with observations can be obtained, although the allowed values of the deformation parameter are suppressed, yielding bounds of $κ\sim \mathcal{O}(10^{-9})$ and $κ\sim \mathcal{O}(10^{-37})$ for the power-law and Mexican-hat potentials, respectively. Conversely, for the dual Kaniadakis formulation, we find no physical parameter space that simultaneously satisfies the observational bounds for these potentials, rendering this formulation phenomenologically disfavored. These findings suggest that while standard Kaniadakis cosmology can leave potentially observable imprints on primordial perturbations, the constraints on $κ$ during inflation are significantly weaker than those from late-time cosmological bounds, hinting at a possible energy-scale dependence of the non-extensive deformation parameter.