Non-singular Bouncing Cosmology in $f(R,G,T)$--Quintom model

TL;DR

The paper develops a non-singular bouncing cosmology by coupling a quintom scalar sector to an extended gravity framework $f(R,G,T)$ in a flat FLRW background. It demonstrates how higher-derivative terms can be rendered ghost-free via FLRW degeneracy conditions and a comprehensive stability analysis, including the Hamiltonian formulation and scalar perturbations with $\mathcal G_S>0$ and $\mathcal F_S>0$, ensuring $c_s^2=\mathcal F_S/\mathcal G_S\ge0$ through the bounce. A central result is the novel double crossing of the phantom divide line $\omega_{\text{eff}}=-1$ during the bounce, driven by curvature–matter coupling and quintom dynamics, while the models remain NEC-violating only transiently near the bounce. The work provides five explicit reconstructed models (linear, exponential-curvature, power-law, teleparallel, and non-minimal coupling) that realize non-singular bounces and connect early universe dynamics to late-time acceleration, with clear criteria for ghost freedom and stability. These findings offer a viable alternative to inflation for early-universe cosmology and yield testable predictions in the perturbation sector and late-time behavior.

Abstract

We present a unified framework for non-singular bouncing cosmologies in modified gravity, combining $f(R,G,T)$ geometry with quintom scalar dynamics in a flat FLRW universe. While single-field models achieve phantom divide line (PDL) crossing and stable bounces, our $f(R,G,T)$-quintom coupling provides a novel implementation of a \textit{double} PDL crossing of $ω_{\text{eff}}$ during the bounce. We address stability concerns through Hamiltonian analysis, showing that FLRW symmetry constraints suppress Ostrogradsky instabilities by reducing higher-derivative terms to metric invariant. The scalar field equation of motion is explicitly derived, confirming cancellation of pathological modes. Numerical reconstruction of five $f(R,G,T)$ models confirms non-singular bounces with $ρ_{\text{eff}}>0$ and $c_s^2 \geq 0$, alongside parametric control over energy condition violations. Our work extends prior studies by: (1) unifying early-time bounce dynamics with late-time dark energy, (2) demonstrating a novel double-PDL crossing signature compatible with FLRW stability, and (3) establishing explicit ghost-free criteria for higher-derivative terms.

Figures (21)

• Figure 1: Evolution of (a) scale factor $a(t)$ and (b) Hubble parameter $H(t)$ for different equations of state ($\omega=-1$: black, $-1/3$: red, $1/3$: blue) in the linear coupling model. A successful bounce, characterized by $a(t)$ reaching a minimum and $H(t)$ crossing zero, is evident for the dark energy cases ($\omega \leq -1/3$).
• Figure 2: Effective equation of state $\omega_{\text{eff}}(t)$ showing (a) evolution for $\omega = -1$ (black line) and (b) evolution for $\omega = -1/3$ (red line). The phantom divide line (PDL) at $\omega_{\text{eff}} = -1$ is shown as a dashed line. Both cases show PDL crossing behavior near the bounce point.
• Figure 3: (a) Effective equation of state $\omega_{\text{eff}}(t)$ for $\omega = 1/3$ (blue line) and (b) composite view comparing all cases: $\omega = -1$ (black), $\omega = -1/3$ (red), and $\omega = 1/3$ (blue). The radiation-dominated case ($\omega=1/3$) shows no PDL crossing, remaining in the quintessence regime throughout.
• Figure 4: Stability analysis for the linear coupling model ($\omega = -1$). (a) The kinetic term remains positive $\mathcal{G}_S > 0$ throughout the evolution, confirming the absence of ghosts. (b) The squared sound speed $c_s^2$ remains non-negative, indicating no gradient instabilities. The brief period where $c_s^2 = 0$ at $t \approx \pm 0.25$ corresponds to a momentary freezing of perturbations rather than an instability.
• Figure 5: Evolution of (a) scale factor $a(t)$ and (b) Hubble parameter $H(t)$ for different equations of state ($\omega=-1$: black, $-1/3$: red, $1/3$: blue). The $\omega=-1$ case shows optimal bounce behavior with a clear minimum in $a(t)$ and smooth transition of $H(t)$ through zero.