Enhanced Gravitational Effects of Radiation and Cosmological Implications

TL;DR

This work investigates gravity coupled to the determinant of the matter energy-momentum tensor, introducing a generally covariant function $f(D)$ with $D=rac{| extbf{det}\,T|}{| extbf{det}\,g|}$. Focusing on power-law and scale-free realizations, it shows that modified gravity predominantly affects radiation, leaving nonrelativistic matter evolution intact; in the scale-free case ($n=1/4$) radiation gravitates with an effective coupling $G_{ ext{eff}}=(1+3^{1/4}\lambda_r)G$, while $ ho_r$ evolves as in standard cosmology. A full MCMC analysis against Planck, ACT/SPT-3G, DESI, and Pantheon+ data demonstrates that this Enhanced Gravitational Effect of Radiation (EGER) can modestly alleviate the Hubble tension, with best-fit photon and neutrino couplings $(\lambda_\gamma,\lambda_\nu)\approx(0.04,-0.03)$ and an equivalent $N_{ ext{eq}}\approx3.17$, but the degree of tension relief depends on the dataset and neutrino assumptions. Importantly, EGER yields distinct perturbation signatures in the small-scale CMB, differentiating it from standard $N_{ ext{eff}}$ or SIDR scenarios, and remains compatible with BBN constraints. The results point to a testable, gravity-based pathway to address early-universe discrepancies and motivate future CMB and BAO surveys to probe determinant-based couplings more precisely.

Abstract

In the momentarily comoving frame of a cosmological fluid, the determinant of the energy-momentum tensor (EMT) is highly sensitive to its pressure. This component is significant during radiation-dominated epochs and becomes naturally negligible as the universe transitions to the matter-dominated era. Here, we investigate the cosmological consequences of gravity sourced by the determinant of the EMT. Unlike Azri and Nasri, Phys. Lett. B 836, 137626 (2023), we consider the most general scenario in which the second order variation of the perfect-fluid Lagrangian does not vanish. We analyze the dynamics of the power-law case and explore the cosmological implications of the scale-free model characterized by dimensionless couplings to photons and neutrinos. We show that, unlike various theories based on the EMT, the present setup, which leads to enhanced gravitational effects of radiation (EGER), does not alter the time evolution of the energy density of particle species. Using current cosmological observations, we constrain the model parameters and show that EGER may offer a viable mechanism for alleviating the Hubble tension. Although it exhibits a phenomenological analogy to tightly-coupled relativistic fluid scenarios, EGER remains purely gravitational in origin and yields distinguishable signatures in the small-scale anisotropies of the cosmic microwave background. The radiation-gravity couplings we propose here are expected to yield testable cosmological and astrophysical signatures, probing whether gravity distinguishes between relativistic and nonrelativistic species in the early universe.

Figures (2)

• Figure 1: 68% and 95% contours for the $N_\text{eff}$ and EGER models. The grey bands denote the 68% and 95% contours for the SH0ES measurement of $H_0 = 73.17 \pm 0.86 \text{ km s}^{-1} \text{ Mpc}^{-1}$shoes2, while the grey dashed line represents the SM value of $N_\text{eff} = 3.044$.
• Figure 2: CMB TT power spectrum residuals with respect to the bestfit $\Lambda$CDM spectra. The blue residual is for the bestfit EGER model to dataset $\mathcal{D}_2$ while the other two residuals are for free-streaming and fluid-like dark radiation models with $N_\text{eff} =N_\text{eq}^{\text{bestfit}}$. All three models assume massive neutrinos and all other cosmological parameters are kept constant.