Cosmological and lunar laser ranging constraints on evolving dark energy in a nonminimally coupled curvature-matter gravity model

TL;DR

This work investigates a curvature–matter nonminimally coupled gravity model in the Jordan frame, where a nonminimal coupling induces an evolving dark energy behavior atop a Λ-dominated expansion. By introducing a tracking solution for the scalar field η, the authors derive conditions for a minimum of the effective potential and analyze the resulting dark-energy equation of state, linking cosmological growth to a chameleon-like mechanism that also affects Earth–Moon dynamics. They constrain the model using DESY5, Pantheon+, and DESI BAO data, and confront it with Lunar Laser Ranging bounds on the weak equivalence principle, finding that models with |m| ≳ 4 can fit the expansion data while remaining compatible with LLR. The results indicate a preference for dynamical dark energy in this NMC framework and highlight a viable region of parameter space where cosmology and solar-system tests coexist, with future measurements anticipated to sharpen the constraints.

Abstract

We analyze a cosmological solution to the field equations of a modified gravity model where curvature and matter are nonminimally coupled. The current Universe's accelerated expansion is driven by a cosmological constant while the impact of the nonminimal coupling on the expansion history is recast as an effective equation of state for evolving dark energy. The model is analyzed under a tracking solution that follows the minimum of the effective potential for a scalar field that captures the modified theory's effects. We determine the conditions for the existence of this minimum and for the validity of the tracking solution. Cosmological constraints on the parameters of the model are obtained by resorting to recent outcomes of data from the DESI collaboration in combination with the Pantheon+ and Dark Energy Survey supernovae compilations, which give compatible results that point to the presence of a dynamical behavior for dark energy. The gravity model violates the equivalence principle since it gives rise to a fifth force that implies the Earth and Moon fall differently towards the Sun. The cosmological constraints are intersected with limits resulting from a test of the equivalence principle in the Earth-Moon system based on lunar laser ranging data. We find that a variety of model parameters are consistent with both of these constraints, all while producing a dynamical evolution of dark energy with similarities to that found in recent DESI results.

Figures (7)

• Figure 1: The properties of the critical points of the effective potential are shown through the auxiliary function $g(R)$ introduced in Eq. \ref{['g(R)-definition']}. The function obeys the expected low and high curvature limits. Here we show the case $b>g(R^*)$, such that there exist two critical points, with $R_1$ corresponding to a maximum and $R_2$ to a minimum of the effective potential.
• Figure 2: Effective potential of the scalar field $\eta$ for various densities of non-relativistic matter $\rho$ (or equivalent redshifts) in the $m=-3$ NMC model with $\mu^{1/|m|}=-4R_0$, $R_0$ being the curvature due to matter at present time. The cosmological constant is taken to be such that $\Omega_\Lambda=0.7$ and the potentials are shown in arbitrary units to focus on their relative magnitude. The location of the minimum of each potential is shown by a dashed line of the corresponding color.
• Figure 3: Allowed $\{|m|,|\mu|^{1/|m|}\}$ parameter space for typical values of matter ($\Omega_m=0.3$) and dark energy ($\Omega_\Lambda=0.7$) content in a Universe with $H_0=70 \ \rm km/s/Mpc$ and having fixed $\varepsilon=10^{-2}$. The tracking condition is always more stringent than the existence of minimum condition for the effective potential.
• Figure 4: Allowed $\{\rho_0,\Lambda\}$ parameter space for a fixed exponent $m=-3$, NMC scale $|\mu|^{1/|m|}=7500 \ (\text{km/s/Mpc})^2$ and $\varepsilon=10^{-2}$, with $H_0=70 \ \rm km/s/Mpc$ having been fixed for this plot. By increasing $|\mu|$, the disallowed (red) region is increased, as expected. The $H(0)=H_0$ constraint for the NMC model is shown in blue, showing its deviation from $\Lambda$CDM (dashed) as the Universe becomes more dynamical with an increasing dominance of matter content.
• Figure 5: Constraints on cosmological parameters for the NMC models with different values of exponent $m$ in $f^2(R)$. All models agree on identical values of $\Omega_m$ and $H_0$, with the latter being related to the choice of fixing the sound horizon, with which it is degenerate. This has no effect on the NMC coupling, which grows with increasing $|m|$, as expected from the suppression of NMC effects associated with larger exponents.