Scale-Invariant Bounce Cosmology in Weyl f(Q) Gravity with Quintom Signature

TL;DR

This work investigates a nonsingular bouncing cosmology within Weyl-type $f(Q)$ gravity using a power-law form $f(Q)=\alpha Q^{\xi}$ and a Weyl vector with mass, analyzed in a flat FLRW background. By adopting the ansatz $\psi(t)=H(t)$ and reconstructing a bounce-appropriate scale factor $a(t)= (\beta \sinh^{2} t + \gamma)^{n/3}$, the authors derive modified Friedmann equations yielding a contracting phase, a smooth bounce at $t\approx 0$, and a post-bounce acceleration, with NEC violation localized near the bounce. The model exhibits quintom behavior ($\omega$ crosses $-1$) and a corresponding effective scalar-field reconstruction showing a quintessence-like negative kinetic energy and a phantom-like positive kinetic energy near the bounce, while ensuring finite energy density and symmetric Hubble-radius evolution around the bounce. Stability analysis reveals a transient gradient instability near the bounce and a bounded adiabatic index, indicating short-lived perturbative challenges that warrant a full linear perturbation study. Overall, the results support Weyl-type $f(Q)$ gravity as a ghost-free, geometrically motivated framework for nonsingular bouncing cosmologies and offer insights into early-universe dynamics and dark-energy phenomenology, with future work focusing on perturbations and observational constraints.

Abstract

We investigate a bouncing cosmological model within the Weyl-type $f(Q)$ gravity framework, employing a power-law form of the non-metricity scalar $Q$. The model successfully resolves the initial singularity problem by demonstrating a nonsingular bounce, where the universe transitions from a contracting phase $ \dot{a}(t)<0 $ to an expanding phase ($ \dot{a}(t)>0 $) at the bouncing point $t \approx 0.$ Key features include the violation of the null energy condition (NEC) near the bounce and the crossing of the phantom divide line ($ω=-1$) by the equation of state (EoS) parameter, indicating quintom-like behavior. The model exhibits accelerated expansion post-bounce, suggesting an inflationary phase. Stability analysis via the adiabatic index reveals instability near the bouncing point, while energy conditions highlight the dominance of dark energy. Additionally, the study explores scalar fields, showing that quintessence-like kinetic energy becomes negative and phantom-like kinetic energy peaks positively near the bounce, aligning with dark energy dynamics. The Hubble parameter, deceleration parameter, and Hubble radius further validate the bouncing scenario, with the latter displaying symmetric behaviour around the bounce. These results underscore the viability of Weyl-type $f(Q)$ gravity as a framework for nonsingular bouncing cosmologies, offering insights into early universe dynamics and dark energy behaviour.

Figures (5)

• Figure 1: The variation of $a$, $H$, $q$ and the Hubble radius $r_h$ for distinct model parameters.
• Figure 2: The evolution of the dynamical status of the model from the perspective of the bouncing scenario.
• Figure 3: The evolution of the energy conditions in the bouncing scenario around $t\approx0$.
• Figure 4: Evolution of stability parameters in the bouncing cosmology near $t\approx0$.
• Figure 5: The evolution of Scalar Fields in the bouncing scenario around $t=0$ for $\beta =0.3$, and $m=0.6$.