Cosmological implications and ghost dark energy model in f(Q,C) gravity

The primary purpose of this work is to examine the ghost dark energy model in the framework of $f(Q,C)$ gravity, where $Q$ denotes the non-metricity and $C$ defines the boundary term. For this objective, we examine a flat Friedmann–Robertson–Walker spacetime containing an ideal matter distribution. We investigate a scenario involving interacting fluids that include both dark energy and dark matter in this framework. Further, we reconstruct $f(Q,C)$ functional form to analyze the effects of this modified approach on the development of the cosmos. The reconstructed $f(Q,C)$ model reveals an increasing behavior for both non-metricity and redshift functions, indicating a viable cosmological model. We explore the behavior of various cosmic parameters with respect to different parametric values. The positive energy density and negative pressure suggest that the universe is in the accelerated expansion phase. The equation of state parameter falls in the phantom region, aligning with observational data. Additionally, the increasing behavior in the (${\omega }_D-{\omega }_D^{\prime }$)-plane indicates a freezing region, the $(r-s)$-plane behavior corresponds to the Chaplygin gas model, reinforcing the model’s compatibility with current cosmological observations. This work provides new insights into the relationship between dark energy models and modified gravity theory, enhancing our understanding of cosmic evolution. Our findings align with the existing observational data (Ade et al., 2016), demonstrating that $f(Q,C)$ model accurately describes the dark energy and cosmic evolution.