Statefinder Analysis of Symmetric Teleparallel Cosmology

TL;DR

This paper uses the statefinder diagnostic to analyze and differentiate two $f(Q)$ gravity models in symmetric teleparallel cosmology, revealing their implications for the universe's accelerated expansion and dark energy behavior.

Contribution

It introduces and evaluates two specific $f(Q)$ models using statefinder and Om diagnostics, providing new insights into their cosmological behaviors.

Findings

Both models predict an accelerating universe due to dark energy.

Model I exhibits phantom-like behavior, while Model II follows quintessence.

The models' trajectories in the $r-s$ plane help distinguish their nature.

Abstract

Statefinder diagnostic is a convenient method that can differentiate between the various dark energy models. In this article, we analyze the statefinder parameters in symmetric teleparallel cosmology. The $f(Q)$ gravity theory is an alternative theory to GR, where gravitational interactions attribute to the non-metricity scalar $Q$. In the present work, we consider two $f(Q)$ models which contains a linear and a non-linear form of non-metricity scalar, specifically, $f(Q)=\alpha Q + \frac{\beta}{Q}$ and $f(Q)=\alpha Q + \beta Q^2$, where $\alpha$ and $\beta$ are free parameters and then statefinder parameters $(r,s)$ are evaluated. We plot the trajectory of our models in the $r-s$ plane. In addition, we analyze the physical behavior of different cosmological parameters such as density, deceleration, and the EoS parameters. Further, we use Om diagnostic to differentiate the behavior of both $f(Q)$ models. We found that both $f(Q)$ models predicts that the present universe is accelerating due to the dark energy component evolving due to non-metricity. Moreover, model I represents phantom type behavior while model II follows quintessence scenario.