Avoidance of Big Crunch Singularity in the Q-SC-CDM model via nonminimal coupling: Theory and Data Analyses

TL;DR

We address whether a non-minimally coupled scalar field with a descending dark energy potential can avoid a Big Crunch while matching late-time data. We apply a dynamical-systems analysis to a NMC scalar field with $V(φ)=V_{0} e^{- κ α φ}-V_{1} e^{ κ β φ}$ and $F(φ)=1-ξ φ^2$, deriving autonomous equations and identifying de Sitter attractors. We constrain the model with Cosmic Chronometers, Pantheon Plus, DES-SN5YR, and DESI DR2 BAO, finding $Ω_{0m}$, $H_0$, and $r_d$ compatible with ΛCDM at 68% CL and a mild Pantheon+ tension; Om$(z)$ is close to ΛCDM for $z<2$, and information criteria indicate moderate support relative to ΛCDM. The results demonstrate a viable, phantom-free alternative to ΛCDM that can reproduce current acceleration and modifies future fate depending on $ξ$.

Abstract

We investigate a class of scalar field dark energy models non-minimally coupled to gravity, characterized by a double exponential potential and parameterized coupling $ξ$. We study the cosmological dynamics for a recently proposed descending dark energy model, namely, Q-SC-CDM. Initially, we choose distinct values of coupling parameter. For some values of $ξ$, the evolution of the universe is split up into three different phases: {\it decelerated expansion (early time), accelerated expansion (late-time) and slow-contraction (future era)}, and provide Big Crunch Singularity at distant future. In other scenario, the phase of slow-contraction vanishes, cosmic acceleration is obtained at current epoch, and the universe gets de-Sitter expansion at distant future. It is remarkable to see that the Big Crunch Singularity is redundant in the later case. Next, we investigate the phase space analysis for the model under consideration. Our investigation brings new asymptotic regimes and finds stable de-Sitter solution. Eventually, we perform a comprehensive Bayesian analysis using recent cosmological observations, including Cosmic Chronometers, Type Ia Supernovae (Pantheon+ and DES-SN5YR), and Baryon Acoustic Oscillation (DESI DR2) data. The results demonstrate that the present model yield constraints on key cosmological parameters Ω_{0m}, H_0 and the sound horizon r_d that are consistent with ΛCDM within 68\% confidence level, yet exhibit mild tension with Pantheon+ measurements. Additionally, we employ the Om(z) diagnostic test, Akaike and Bayesian Information Criteria to distinguish our model from ΛCDM. The Statistical comparison reveals moderate support for the current model.

Figures (9)

• Figure 1: The figure shows the evolution of potential (\ref{['eq:pot']}) vs field. Initially, the potential is positive for negative values of scalar field. As field evolves, the universe expands with cosmic acceleration and remains so untill $\phi_{dec}$. On further evolution of field, the potential becomes more negative. To this effect, the expansion factor $a(t)$ collapses at $\phi_{con}$, and correspondingly Hubble parameter $H(t)$ becomes zero, see Fig. \ref{['fig:NMC1']}.
• Figure 2: The figure shows the numerical evolution of expansion factor $a(t)$, Hubble parameter $H(t)$, energy density $\rho(t)$ deceleration parameter $q(t)$, equation of state $w(t)$ and density parameter $\Omega(t)$ versus $H_0t$ for NMC model with $\xi=0.1$, $\alpha=\beta=1$, $V_0=3.01$, $V_1=0.33$ and $\Omega_{0m} = 0.3$. The Unshaded, light gray shaded and dark shaded regions represent the periods of decelerated expansion, accelerated expansion $(H > 0)$ and slow contraction $(H < 0$ at $t = t_{con})$, respectively.
• Figure 3: The figure is similar to Fig. \ref{['fig:NMC1']} except $\xi=0.5$. In this case, we get $q=-0.53$, $w_{eff}=-0.72$, $w_{\phi}=-0.98$ and $\Omega_{\phi}=0.70$ at current epoch. Moreover, the phase of slow-contraction vanishes, and we obtain cosmic acceleration at current epoch and de-Sitter expansion in distant future.
• Figure 4: The figure represents the stable fixed points $A_3$ (left panel) and $A_4$ (right panel) for $\alpha=\beta=\xi=1$ and $w_m=0$. The black dots represent stable attractor points.
• Figure 5: The corner plot of decay dark energy model for $x_0 = 10^{-4}$.