Validation of NANOGrav 15-year data and ACT data by modified inflation in entropic cosmology

TL;DR

This work argues that current PTA hints from NANOGrav 15-year data and CMB-informed ACT constraints can be reconciled within an entropic cosmology framework derived from a 4-parameter generalized entropy of the apparent horizon. By allowing a brief modification of the inflationary dynamics—codified through a negative slow-roll phase in a three-stage inflation sequence—the model yields a blue-tilted primordial tensor spectrum in the NANOGrav band while preserving the ACT-compatible, nearly scale-invariant spectrum on CMB scales. The tensor evolution is computed via piecewise transfer functions across inflationary stages and the radiation era, yielding explicit expressions for present-day GW energy density in three k-ranges, with the middle range displaying the tilt controlled by $\omega$. A joint analysis with NG15 data, using ACT-consistent entropic parameters and fixed high-frequency cutoffs, finds good compatibility across ACT and PTA observations, predicting detectable signals for upcoming GW observatories and providing a concrete testbed for generalized horizon-entropy cosmology in the early universe.

Abstract

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.

Figures (7)

• Figure 1: $\epsilon(N)$ vs. $N$ for the considered form of $\sigma(N)$ in Eq. (\ref{['sigma function']}) with $N_\mathrm{f} = 60$.
• Figure 2: Simultaneous compatibility of $n_s$ and $r$ according to Eq. (\ref{['ns final form']}) and Eq. (\ref{['r final form']}). The left and right plots correspond to $N_\mathrm{f}=55$ and $N_\mathrm{f}=60$ respectively.
• Figure 3: $\epsilon_\mathrm{m}(N)$ vs. $N$. for $C=-0.4$, $D=10$ and $N_\mathrm{f} = 60$. Moreover, we take $N_\mathrm{1}=6$ and $N_\mathrm{2}=14$ (later we will see that such values of $N_\mathrm{1}$ and $N_\mathrm{2}$ are compatible with the best fitted values of the parameters).
• Figure 4: $H(N)$ (in the unit of $\mathrm{GeV}$) vs. $N$. for $C=-0.4$, $D=10$ and $N_\mathrm{f} = 60$. Moreover, we take $N_\mathrm{1}=6$ and $N_\mathrm{2}=14$.
• Figure 5: Corner plot for the entropic model sampling over the inflationary parameters $f_\mathrm{1}$ and $\nu$. The frequency $f_\mathrm{1}$ is given in Hz.