Crossing phantom divide in $f(Q)$ gravity

TL;DR

This paper explores how certain modified gravity theories, specifically $f(Q)$ gravity, can naturally allow the universe's dark energy equation of state to cross the phantom divide line, with implications for cosmic evolution.

Contribution

It demonstrates that $f(Q)$ gravity models can inherently realize crossing the phantom divide and provides a method to reconstruct these models from observational data.

Findings

Exponential $f(Q)$ models behave like $\\Lambda$CDM at high redshift.

Combined $f(Q)$ models can cross the phantom divide line.

Future crossings of the phantom line are a generic feature of feasible $f(Q)$ models.

Abstract

We investigate the possibility of crossing a phantom divide line in the extension of symmetric teleparallel gravity or the $f(Q)$ gravity, where $Q$ is the non-metricity. We study the cosmic evolution of the effective equation of state parameter for dark energy considering exponential, logarithmic, and combined $f(Q)$ theories. Moreover, the exponential model behaves like the $\Lambda$CDM at high redshifts before deviating to $\omega_{eff}<-1$ or $\omega_{eff}>-1$, respectively, depending on the value of model parameter. It also approaches a de-sitter phase asymptotically. However, the crossing of the phantom divide line, i.e., $\omega= -1$, is realized in the combined $f(Q)$ theory. Furthermore, statefinder diagnostics are studied in order to differentiate between several dark energy models. To ensure the three model's stability, we employ the stability analysis using linear perturbations. We demonstrate how to reassemble $f(Q)$ via a numerical inversion approach based on existing observational constraints on cosmographic parameters and the potential of bridging the phantom divide in the resulting model. It explicitly demonstrates that future crossings of the phantom dividing line are a generic feature of feasible $f(Q)$ gravity models.