Non-Singular Bouncing cosmology from Phantom Scalar-Gauss-Bonnet Coupling: Reconstruction with Observational Insights

TL;DR

The paper investigates non-singular bouncing cosmology in a phantom scalar field coupled to Gauss–Bonnet gravity, considering both non-viscous and bulk-viscous fluids. Using the scale factor $a(t)=\left(\frac{\alpha}{\eta}+t^2\right)^{\frac{1}{2\eta}}$, the authors reconstruct the phantom potential $V(t)$ and analyze energy conditions, stability, and the post-bounce evolution, highlighting NEC violation as essential for the bounce. Viscosity is shown to regulate the dynamics, yielding a positive, subluminal squared sound speed and stabilizing the post-bounce phase, while the non-viscous case exhibits NEC/SEC violations and gradient instabilities near the bounce. Observational viability is demonstrated via Bayesian MCMC against Pantheon+ SN data, with best-fit $(\alpha,\eta)$ giving $\chi^2_{\rm red}\approx0.995$, and the reconstructed inflationary observables $(n_s,r)$ lying within Planck 2018 68% CL contours, supporting the model as a viable pre-inflationary scenario and illustrating the stabilizing role of viscosity.

Abstract

We examine non-singular bounce cosmology within the framework of a phantom scalar field coupled to the Gauss-Bonnet term in both non-viscous and bulk-viscous cases. Using the scale factor ansatz $α(t)=\left(\fracαη+t^2\right)^{\frac{1}{2 η}}$, we reconstruct the scalar field potential $V(t)$, and observe a smooth potential well centered at the bounce point. The resulting energy density, pressure, and equation-of-state parameter show NEC violation necessary for successful bounce, while viscosity controls post-bounce dynamics with a positive and smooth squared speed of sound. In contrast, for the non-viscous model, sharp divergences occur just at the bounce and continues to be negative in the expanding phase, which in turn emphasises the stabilising role of dissipative effects. The energy condition analysis indicates a temporary NEC and SEC violation in the viscous scenario, whereas its persistent violation within the non-viscous model suggests a continuous accelerated expansion. Observational viability is found through Bayesian MCMC fitting in regards to the Pantheon+ supernova data, with best-fit parameters providing a reduced chi-squared of $χ_{red}^2 =0.995$ while the inflation observables derived from the reconstructed potential place our model predictions inside $68\%$ CL Planck 2018 confidence contours. Our findings suggest that bounce cosmologies could offer a physically reasonable and observationally acceptable alternative or pre-inflationary scenario, while highlighting the role that viscosity could play for a stable and smooth cosmological evolution.

Figures (9)

• Figure 1: Evolution of $a$, $H$ and $q$ against cosmic time $t$ for different values of $\alpha$.
• Figure 2: Behaviour of the reconstructed $V(t)$ plotted against cosmic time $t$. We have taken $\phi_{0} = 0.07$, $n= 2$, $f_{0}= 0.04$, $h= 0.06$, $\rho_{m_0}= 0.45$, $\alpha=0.2506, \eta=1.0924$, $m= 0.08$, $C_{1}= 10.6$, $\lambda=0.008$, $B=1.006$ and $\rho_{c}= 0.05$.
• Figure 3: Behaviour of the reconstructed density and EoS parameter($w$) plotted against cosmic time $t$ for model-I.
• Figure 4: The reconstructed pressure and the EoS parameter($\omega$) plotted against cosmic time $t$ in case of a bouncing model while considering bulk viscosity. In this case, our chosen values of the parameters are $\phi_{0}=0.107, m=2, f_{0}=1.04, h=0.06, \rho_{m}=0.45, \alpha= 0.2506, \eta= 1.0924, m=1.08, C_{1}=1.92, \rho_{c}=2.95, \beta=2.89, \gamma=1.0057, \tau=0.005, \xi=3.004, \sigma=3.067$
• Figure 5: Energy conditions plotted against cosmic time $t$ while considering the bouncing models with and without bulk viscosity.