Viable f(R) Scenarios Unifying Inflation with Realistic Dynamical Dark Energy

TL;DR

This work assesses two viable $F(R)$ gravity scenarios that aim to unify early-time inflation with late-time dynamical dark energy. By solving the cosmological dynamics and enforcing viability conditions, the authors fit the models to Pantheon+ SNe Ia, DESI BAO, H(z), and Planck data, demonstrating that both models can reproduce a dynamical dark energy equation of state $\omega_{DE}(z)$ with a phantom-to-quintessence transition and outperform ΛCDM in $\chi^2$, AIC, and BIC. The logarithmic model and an exponential $F(R)$ variant show robust fits with best-fit parameters lying away from anti-gravity regions, while remaining viable across cosmic history. A narrowed exponential form with $\beta=1$ yields a particularly favorable, parsimonious description that reinforces the potential of $F(R)$ gravity to describe both inflation and current acceleration within a single framework.

Abstract

Two $F(R)$ gravity models are tested on the basis of their viability during all stages of cosmological evolution. It is shown that these models can describe both the early-time inflationary epoch and the dark energy epoch. The models are confronted with the latest observational data, including the Pantheon+ catalogue with Type Ia supernovae, the Dark Energy Spectroscopic Instrument measurements of baryon acoustic oscillations, the Hubble parameter estimations and data from cosmic microwave background radiation. Investigation of the viability conditions for these models, in particular, the condition $\frac{dF}{dR}>0$ required a deep analysis. Both models appeared to be viable during the early-time era, but for the late-time evolution the viability conditions are not fulfilled in definite domains in the parameter spaces of these models. However the best fitted parameters, determined in confrontation with the mentioned observational data, lie far from the forbidden domains for both models. These $F(R)$ gravity models describe the observations with the large advantage over the $Λ$-Cold-Dark-Matter model, not only in $χ^2$ statistics, but also with Akaike and Bayesian information criteria. This success of the two $F(R)$ gravity scenarios is connected with their capability to mimic dynamical dark energy, similarly to models with variable equation of state, that is necessary for describing the latest Pantheon+ and DESI observational data.

Figures (4)

• Figure 1: Contour plots of $\chi^2$ with $1\sigma$, $2\sigma$ CL in the $\alpha-\gamma$ plane for the logarithmic model (\ref{['ModLog']}) (the top panels); evolution of $F_R$, $F_{RR}^*=2\Lambda F_{RR}$, $y$ and $x$ az functions of redshift $z$ (late-time) and the Ricci scalar ${\cal R}=R/(2\Lambda)$ (early-time dynamics) in the middle panels; the dark energy density and EoS parameters in the bottom panels.
• Figure 2: Contour plots of $\chi^2$ with $1\sigma$, $2\sigma$ CL, likelihood functions ${\cal L}(\theta_i)$ and one-parameter distributions $\chi^2(H_0)$ for the logarithmic model (\ref{['ModLog']}) in comparison with the exponential (\ref{['FRexpon']}) and $\Lambda$CDM (\ref{['HLCDM']}) models for SNe Ia, CC, CMB and BAO DESI data.
• Figure 3: Contour plots of $\chi^2$ with $1\sigma$, $2\sigma$ CL and $F_R=0$ in the $\beta-\log\varepsilon$ plane for the model (\ref{['ModExp']}) with $e^{\varepsilon{\cal R}^{-\beta}}$ (the top-left panel); evolution of $F_R$, $F_{RR}^*=2\Lambda F_{RR}$, $y$ and $x$ az functions of redshift $z$ (late-time) and the Ricci scalar ${\cal R}=R/(2\Lambda)$ (early-time dynamics) in the top-right panels; the dark energy density and EoS parameters in the bottom panels.
• Figure 4: For the model (\ref{['ModExp']}) with $e^{\varepsilon{\cal R}^{-\beta}}$ the contour plots at $1\sigma$, $2\sigma$ CL, likelihood functions ${\cal L}(\theta_i)$ and one-parameter distributions $\chi^2(H_0)$ are shown in comparison with the logarithmic (\ref{['ModLog']}) and $\Lambda$CDM (\ref{['HLCDM']}) models for SNe Ia, CC, CMB and BAO DESI data.