Exponential $f(R)$ cosmology with massive neutrinos as a dynamical dark energy framework

TL;DR

This work assesses an exponential $f(R)$ gravity model, augmented by massive neutrinos, as a dynamical dark-energy framework. Using Bayesian MCMC with data from Cosmic Chronometers, DESI DR2 BAO, Planck-CMB, and Pantheon+ SNe Ia, the authors map the $f(R)$ parameters to corresponding $\Lambda$CDM equivalents and solve a stiff system for the background expansion. The exponential $f(R)$ scenario remains compatible with current observations, modestly alleviating the $H_0$ tension and neutrino-mass tension relative to $\Lambda$CDM, and is statistically competitive with CPL when SNe data are included. The results highlight a nontrivial interplay between modified gravity and neutrino physics in late-time cosmology and motivate further exploration of dynamical dark-energy implementations within MG theories.

Abstract

The exponential $f(R)$ gravity model provides a theoretically well-motivated extension of General Relativity, introducing a modified gravitational dynamics at late times consistent with a dynamical dark energy scenario, while recovering the $Λ$CDM-like regime at high redshifts with a smooth transition. Using a Bayesian Markov Chain Monte Carlo (MCMC) analysis, we constrain the parameters of the exponential $f(R)$ model in combination with the total neutrino mass $\sum m_ν$, employing the latest measurements from cosmic chronometers, the DESI DR2 BAO data, the CMB acoustic scale, and the Pantheon+ supernovae compilation, comparing the results with the $Λ$CDM and the $w_0w_a$CDM models. Our results show that the exponential $f(R)$ model remains consistent with current observations while slightly alleviating the Hubble tension and the neutrino mass problem relative to $Λ$CDM, although the constraints on $\sum m_ν$ are tighter than those obtained for the phenomenological $w_0w_a$CDM scenario. These results indicate that the interplay between modified gravity and neutrino physics in the late Universe may offer a viable framework for further investigation of cosmological tensions.

Figures (11)

• Figure 1: Plot of the function $E(z)$ defined in Eq. \ref{['eq:expression-E(z)']} (red curve) compared with the respective dimensionless Hubble function in the $\Lambda$CDM model (dashed black curve). The vertical black dotted line indicates the initial redshift $z_i$, defined in Eq. \ref{['eq:initial-redshift']}, below which ($z<z_i$) the deviations between the exponential $f(R)$ cosmology and the $\Lambda$CDM model become non-negligible. In this plot we used the best fit parameters of the full analysis given in Table \ref{['table:Best_Fit_Table']}.
• Figure 2: Corner plot showing the constraints on the cosmological parameters $(H_0, \alpha,\beta,\Omega_\text{m},\sum m_\nu)$ of the exponential $f(R)$ model, obtained from the MCMC analysis using the full combination of datasets (CC, DESI DR2, CMB-$\theta_\ast$, and Pan+). The contours correspond to the $1\sigma$ ($\sim68\%$ C.L.) and $2\sigma$ ($\sim95\%$ C.L.) confidence regions, while the diagonal panels display the one-dimensional posterior distributions. After deriving the posteriors for $(H^\ast_0, \alpha,\beta,\omega_\text{b}^\ast,\omega_\text{bc}^\ast,\omega_\nu^\ast)$, the physical parameters of the $f(R)$ model $(H_0, \alpha,\beta,\omega_\text{b},\omega_\text{bc},\omega_\nu)$ are recovered through the mapping relations in Eq. \ref{['eq:mapping-relations']}.
• Figure 3: Marginalized 1$\sigma$ posterior distribution for the parameter $\sum m_\nu$ for different cosmological models and combination of datasets. Red, blue, and black curves are referred to the exponential $f(R)$ gravity, $\Lambda$CDM, and $w_0w_a$CDM models, respectively. A dashed curve is obtained from the analysis using the combination of CC, DESI, and CMB datasets, while a continuous curve is relative to the same datasets but including the Pan+ sample.
• Figure 4: Numerical evaluation of the Fermi-Dirac integral \ref{['eq:fermi-dirac']} for fixed $\sum m_\nu = 0.06$ eV. The vertical line represents the transition redshift from relativistic to non-relativistic neutrinos. The energy density behaves as the one for a non-relativistic (blue) specie at low redshift and as a relativistic (red) one at high redshifts.
• Figure 5: Corner plot for the parameters $(H_0,\Omega_\text{m},\Omega_\Lambda,\sum m_\nu)$ in the joint datasets without the SNe catalog.