https://doi.org/10.1140/epjc/s10052-023-12112-7
Regular Article – Theoretical Physics
Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology
1
Dipartimento di Fisica, Università degli Studi di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
2
INFN Gruppo Collegato di Salerno-Sezione di Napoli c/o Dipartimento di Fisica, Università di Salerno, Fisciano, Italy
3
Applied Physics Section of Environmental Science Department, Escola Politècnica Superior, Universitat de Lleida, Av. Jaume II, 69, 25001, Lleida, Spain
4
Department of Physics, College of Sciences, Shiraz University, 71454, Shiraz, Iran
5
Biruni Observatory, College of Sciences, Shiraz University, 71454, Shiraz, Iran
b
giuseppegaetano.luciano@udl.cat
Received:
17
July
2023
Accepted:
5
October
2023
Published online:
17
October
2023
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 BICEP and Planck data allows us to constrain Kaniadakis parameter to 
, which is discussed in relation to other observational bounds in the 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 
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.
© The Author(s) 2023
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