Modified cosmology through generalized mass-to-horizon entropy: implications for structure growth and primordial gravitational waves

TL;DR

This work develops a generalized mass-to-horizon entropy framework within entropic cosmology and derives modified Friedmann dynamics that introduce an effective dark-energy sector controlled by the entropic index $n$ and coupling $\gamma$. It then analyzes early-Universe signatures by computing the PGW spectrum and the linear growth of matter perturbations under a spherical Top-Hat collapse, showing that $n$ governs background expansion and structure growth, while $\Omega_{\rm GW}$ can be suppressed or enhanced relative to GR depending on $n$. The paper identifies observational prospects to test the model via PGWs with current and future detectors and discusses degeneracies with other non-extensive entropies, outlining future work on nonlinear evolution and running entropic parameters. Overall, the generalized MHR framework can mimic ΛCDM at late times but predicts distinctive early-Universe imprints and a tunable growth history that may address cosmological tensions and offer new tests of gravity–thermodynamics. The study highlights the importance of consistent thermodynamic-general-relativistic links and motivates further work to fully integrate perturbations in the entropic framework.

Abstract

In the framework of entropic cosmology, entropic forces arising at the cosmological horizon have been proposed as an alternative mechanism to explain the Universe's current accelerated phase. However, recent studies have shown that, under the Clausius relation and assuming a linear mass-to-horizon (MHR) relation, all entropic force models reduce to the original Bekenstein-Hawking formulation, regardless of the specific form of the horizon entropy. As a result, they inherit the same observational limitations in accounting for cosmic dynamics. To address this issue, a generalized MHR has been introduced, providing the foundation for a modified cosmological scenario rooted in the gravity-thermodynamics conjecture. In this work, we explore the implications of this generalized framework for early-Universe dynamics. Specifically, we analyze the growth of matter perturbations within the spherical Top-Hat formalism in the linear regime, showing that the density contrast profile is significantly influenced by the modified background dynamics predicted by the model. Moreover, considering the sensitivity of upcoming gravitational wave detectors in the sub-$10^3\,\mathrm{Hz}$ range, we examine the impact on the relic abundance of Primordial Gravitational Waves (PGWs), identifying parameter regions where deviations from standard cosmology may arise through an enhanced PGW spectrum.

Figures (3)

• Figure 1: Plot of the ratio $H(z)/H_{\Lambda \mathrm{CDM}}$ versus $z$, for different values of $n$. We used the modified expression of the Hubble rate in Eq. \ref{['ModHubrate']} and set $\Omega_{m,0}\simeq 0.3$, $\Omega_{r,0}\simeq 10^{-5}$.
• Figure 2: Plot of the PGW spectrum versus the frequency $f$ for $n_T=0$, $A_S\simeq2.1\times10^{-9}$ and different value of the entropic parameter $n$, while keeping $\gamma$ fixed to its value in the standard theory. The shaded regions represent the forecasted sensitivity ranges of various GW detectors Breitbach:2018ddu, which are listed on the right together with their expected launch years. In gray we show the regions excluded by PTA KAGRA:2021kbb and LIGO Shannon:2015ect.
• Figure 3: Plot of the matter density contrast $\delta_m$ versus $z$, for different values of $n$.