Cosmic inflation in the context of κ-deformed theories

This paper addresses a new inflationary scenario driven by a slowly-rolling homogeneous scalar field, assuming a generalized potential inspired by Kaniadakis' κ-deformed theory, defined as expκ⁡(x)=(1+κ2x2+κx)1/κ. We show that this kind of potential can arise in the context of brane cosmology, where the field describing the size of the extra-dimension, so-called radion, is interpreted as the inflaton. Within the slow-roll approximation, we obtain the main predictions of the model and compare them with current data from cosmic microwave background and large-scale structure observations. We show that this single scalar field model admits a wider set of solutions than usual exponential scenarios and predicts acceptable values for the spectral index, running of the spectral index, and tensor-to-scalar ratio for the remaining number of e-folds lying in the interval N=55±5 and an energy scale on which λ≥2. In particular, our findings suggest that the κ-parameter value depends on the analysis. For instance, the ns−κ and αs−ns planes point out to κ≲0.2, while the fNLlocal−κ analysis discards κ values very close to zero. Finally, combining these analyses, we conclude that 0.02≲κ≲0.2.