Fitting NANOGrav 15-year data and ACT data with modified inflation in entropic cosmology

Recent evidences of stochastic gravitational wave background (SGWB) through Pulsar Time Array (PTA) observations hint towards an alternative inflationary scenario, compared to the usual inflation, for describing the early stage of the universe in order to be compatible with the PTA data. Moreover, currently the Atacama Cosmology Telescope (combined with the Planck 2018 and BAO) refines the constraint on inflationary observables, compared to the only-Planck 2018 measurements. In the present work, we simultaneously address these two issues by incorporating certain modification during inflation over the usual inflationary scenario. Such modification amplifies the primordial tensor perturbation over the modes that are sensitive to the NANOGrav frequency region. For this purpose, we take the thermodynamic route of cosmology where the entropy of the apparent horizon is given by a generalized form of entropy that is able to generalize the other known form of horizon entropies for suitable representations. The constraints on the model parameters coming from the ACT data also fit the NANOGrav 15-year data (based on numerical analysis), which reveal the model's compatibility with both the ACT and the PTA data.