Cosmological dynamics and thermodynamic behavior in f(Q,C) gravity: An analytical and observational approach

Abstract

In this study, we investigate a Friedmann–Robertson–Walker (FRW) cosmological model within the context of $f(Q,C)$ gravity, where $Q$ represents the non-metricity scalar and $C$ denotes a boundary term. We explore two specific forms of $f(Q,C)$: $f(Q,C)=Q+\alpha Q+\beta ClogC$ and $f(Q,C)=Q+\alpha Q+\frac{\beta }{C}$, with $\alpha$ and $\beta$ as free parameters. Utilizing a parametric form of the Hubble parameter, $H\left(z\right)=H_0{\left(\sigma {(1+z)}^3+\delta +(1-\sigma -\delta ){(1+z)}^2\right)}^{\frac{1}{2}}$, we fit the model by employing the MCMC technique to observational data, which includes Hubble, Hubble+BAO and Hubble+Pantheon datasets. Our findings show that the energy density increases over time and the deceleration parameter $q$ transitions from positive to $-1$, which indicates an accelerated expansion of Universe that is similar to $\Lambda$CDM. The equation of state parameter $\omega$ also approaches to $-1$ that confirms this behavior. We also examine energy conditions and it is observed that our model violates the strong energy condition. Statefinder diagnostics indicate a progression from quintessence to $\Lambda$CDM which is consistent with current observations. Furthermore, thermodynamic analysis demonstrates that entropy density increases with redshift that implies the validation of the second law of thermodynamics. Overall, our $f(Q,C)$ model provides a detailed description of cosmic evolution and fits well with observational data.