Late-time cosmic dynamics in $f(R,L_{m})$ gravity with recent observations

TL;DR

This work analyzes late-time cosmic dynamics in a nonlinear f(R,L_m) gravity with f(R,L_m)=\frac{R}{2}+L_m^2 and an oscillatory equation of state ω(z)=ω_0+b\sin[\log(1+z)]. An analytic Hubble function H(z)=H_0(1+z)^{1+ω_0}e^{-b\cos(\log(1+z))} is derived under L_m=ρ, and the model is constrained via a joint MCMC on CC, DESI DR2 BAO, and three SN Ia compilations, yielding H_0≈67.2, ω_0≈-0.5, b≈0.95. The results show a transition from deceleration to acceleration at z_{tr}≈0.7–0.8, NEC and DEC holding while SEC is violated, and ω(z) approaching -1 at late times, reproducing ΛCDM-like expansion while allowing mild dynamical features. Statefinder analysis places the model in the quintessence region, with trajectories converging to the ΛCDM point (r,s)=(1,0); the inferred Universe age t_0≈13.3–13.4 Gyr is consistent with Planck and stellar chronometers. Information criteria indicate ΔAIC<2 (comparable to ΛCDM) but ΔBIC≈11 (strongly favoring ΛCDM when penalizing extra parameters), highlighting that the model is a viable yet more complex alternative to standard cosmology. Overall, the oscillatory f(R,L_m) framework provides an observationally consistent description of late-time acceleration and motivates further exploration of geometric-matter couplings in cosmology.

Abstract

In this work, we investigate the late-time cosmic dynamics in the framework of non-linear $f(R, L_m)$ gravity, adopting the functional form $f(R,L_m)=\frac{R}{2}+L_m^2$. To explore the dark energy behavior, we assume an oscillatory parametric equation of state, $ω(z) = ω_0 + b \sin[\log(1+z)]$, which allows smooth deviations from the cosmological constant. Using a joint MCMC analysis with the latest Hubble 31 chronometer data, DESI DR2 BAO measurements, and Type Ia supernova samples (Pantheon+, DES-SN5Y and Union 3), we obtain well-constrained parameters around $H_0 \simeq 67.2~\text{km s}^{-1}\text{Mpc}^{-1}$ and $ω_0\approx-0.5$, consistent with Planck 2018 and other current observations. The model exhibits a clear transition from deceleration to acceleration with $z_{\rm tr} \sim 0.7$--$0.8$, satisfies the NEC and DEC while violating the SEC and yields present EoS values close to $-1$, reproducing $Λ$CDM behavior at late times. The derived Universe ages ($t_0 \approx 13.3~\text{Gyr}$) agree well with CMB and stellar constraints, confirming that the proposed oscillatory $f(R, L_m)$ model provides an observationally consistent and dynamically viable alternative to $Λ$CDM cosmology.

Figures (7)

• Figure 1: Marginalized one- and two-dimensional posterior distributions of the model parameters $(H_0, \omega_0, b)$ derived from the joint MCMC analysis using (a) CC+BAO+Pantheon+, (b) CC+BAO+DES-SN5Y and (c) CC+BAO+Union 3 datasets. The inner, middle and outer contours represent the $1\sigma$, $2\sigma$, and $3\sigma$ confidence intervals, respectively, illustrating the consistency and complementarity among the combined cosmological probes.
• Figure 2: Variation of the deceleration parameter $q(z)$ with redshift $z$ for the $f(R, L_{m})$ model, using the CC+BAO+Pantheon+, CC+BAO+DES-SN5Y and CC+BAO+Union 3 datasets.
• Figure 3: Behavior of the energy density $\rho(z)$ and pressure $p(z)$ versus redshift $z$ for the $f(R, L_{m})$ gravity model, reconstructed from the joint dataset combinations.
• Figure 4: The redshift-dependent behavior of the $\omega(z)$ for the $f(R, L_{m})$ model, analyzed using the combined observational datasets: CC+BAO+Pantheon+, CC+BAO+DES-SN5Y and CC+BAO+Union 3 datasets.
• Figure 5: Evolution with redshift of the energy conditions (NEC, DEC and SEC) for the $f(R, L_{m})$ model, constrained using the CC+BAO+Pantheon+, CC+BAO+DES-SN5Y and CC+BAO+Union 3 datasets.