Modified entropy cosmology tightly constrained by Planck inflation data

Kaniadakis entropy generalizes standard thermodynamics via a single deformation parameter κ, and applying it to the early universe modifies the Friedmann equations and inflationary dynamics. Computing the scalar spectral index and tensor-to-scalar ratio for slow-roll inflation under both the standard and 'dual' Kaniadakis formulations, the authors find that agreement with Planck constraints requires κ to be strongly suppressed — meaning only small departures from conventional cosmology are allowed. The dual formulation offers somewhat more room in parameter space. The results confirm that non-extensive thermodynamic corrections can survive observational tests, but only barely.