Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology

TL;DR

This paper explores a modified cosmological model based on Kaniadakis entropy, analyzing its implications for slow-roll inflation, perturbation growth, and consistency with Planck data, revealing that Kaniadakis corrections influence early Universe dynamics.

Contribution

It introduces a new cosmological scenario using Kaniadakis entropy, deriving modified Friedmann equations, and investigates their effects on inflation and perturbation growth with observational constraints.

Findings

Kaniadakis parameter constrained to $ ext{kappa}\, extless ext{O}(10^{-12} ext{ to }10^{-11})$ by Planck data.

Kaniadakis correction accelerates the growth of density perturbations in the early Universe.

Modified equations produce a primordial power spectrum consistent with observational data.

Abstract

Kaniadakis entropy is a one-parameter deformation of the classical Boltzmann-Gibbs-Shannon entropy, arising from a self-consistent relativistic statistical theory. Assuming a Kaniadakis-type generalization of the entropy associated with the apparent horizon of Friedmann-Robertson-Walker (FRW) Universe and using the gravity-thermodynamics conjecture, a new cosmological scenario is obtained based on the modified Friedmann equations. By employing such modified equations, we analyze the slow-roll inflation, driven by a scalar field with power-law potential, at the early stages of the Universe. We explore the phenomenological consistency of this model by computation of the scalar spectral index and tensor-to-scalar ratio. Comparison with the latest Planck data allows us to constrain Kaniadakis parameter to $\kappa\lesssim\mathcal{O}(10^{-12}\div10^{-11})$, which is discussed in relation to other observational bounds in the past literature. We also disclose the effects of Kaniadakis correction term on the growth of perturbations at the early stages of the Universe by employing the spherically symmetric collapse formalism in the linear regime of density perturbations. We find out that the profile of density contrast is non-trivially affected in this scenario. Interestingly enough, we observe that increasing Kaniadakis parameter $\kappa$ corresponds to a faster growth of perturbations in a Universe governed by the corrected Friedmann equations. Finally, we comment on the consistency of the primordial power spectrum for scalar perturbations with the best data-fit provided by Planck.