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

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.