Dark energy and a new realization of the matter Lagrangian

TL;DR

This work introduces a generalized matter Lagrangian L_m = f(rho,P) to realize dark energy as a non-standard combination of baryonic thermodynamics, while ensuring separate conservation of the baryonic and dark-energy sectors. In a FRW background the authors derive the form f(rho,P) = P - B(rho), yielding rho_eff = rho + B and P_eff = P - B + (rho + P) B_rho, and they show that L_m = -rho and L_m = P are not fully equivalent in this framework. They study two parameterizations of B, including a power-law and a logarithmic form (LogDE), and analyze energy conditions, linear perturbations with G_eff = (1 + B_rho) G, and observational constraints using cosmic chronometers, Pantheon+, and f sigma_8 data. The results indicate that LogDE behaves phantom-like yet remains very close to Lambda CDM at late times, with mild deviations in early-time expansion and growth of structure; this framework provides a unified, baryon-based route to DE and a concrete set of predictions to test with current and future data. Overall, the paper offers a novel, testable alternative to standard DE models by tying dark energy to the thermodynamics of baryonic matter through a conserved, environment-dependent Lagrangian.

Abstract

A new realization of the matter Lagrangian is introduced which models the dark energy component as a non-standard combination of thermodynamics quantities of the baryonic matter. We will prove that the present realization is independent of existing models with matter-geometry couplings and has a property that the energy-momentum tensor of both baryonic matter and dark energy is conserved separately. We further show that two possible choices of the matter Lagrangian in the $Λ$CDM model are not totally equivalent and investigate the background and perturbative constraints on the form of matter Lagrangian. We will also investigate cosmological implications of a test model with logarithmic DE and obtain the model parameters by confronting the model with observational data on the cosmic chronometers, Pantheon$^+$ and $fσ_8$ datasets. We will also explain in details the predictions of the model on the late time behavior of the universe and compare the result with $Λ$CDM model.

Figures (9)

• Figure 1: The behavior of the effective and DE eos parameters of the logarithmic DE model. The solid line represents the DE sector and the dashed line denotes the effective part. The dotted line represents the $\Lambda$CDM behavior. Transition energy is also shown.
• Figure 2: The corner plot of the values of $H_0$, $\Omega_{m0}$ and $\sigma_{8}$ parameters with their $1\sigma$ and $2\sigma$ confidence levels for the logarithmic DE model (left) and together with $\Lambda$CDM model (right).
• Figure 3: The behavior of $f\sigma_8$ as a function of $z$ for the LogDE model for the best fit values of the parameters as given by table \ref{['bestfit']}. The shaded area denotes the $1\sigma$ error. Dashed lines represent $\Lambda$CDM model. The error bars correspond to the observational data.
• Figure 4: The behavior of the rescaled Hubble parameter $H/(1+z)$ for the LogDE model (top panel) and the difference between the LogDE and $\Lambda$CDM models (bottom panel) as a function of the redshift for the best fit values of the parameters as given by table \ref{['bestfit']}. The shaded area denotes the $1\sigma$ error. Dashed lines represent $\Lambda$CDM model. The error bars correspond to the observational data of the cosmic chronometers dataset.
• Figure 5: The behavior of the deceleration parameter $q$ as a function of redshift $z$ for LogDE model for the best fit values of the parameters as given by table \ref{['bestfit']}. The shaded area denotes the $1\sigma$ error. Dashed lines represent $\Lambda$CDM model. The vertical dotted line denotes the deceleration to acceleration phase transition redshift.