$f(Q)$ gravitational theory and its structure via red-shift

TL;DR

This paper introduces a new method for reconstructing $f(Q)$ gravity models using deceleration parameter parameterizations, enabling the development of cosmologically consistent modified gravity scenarios that can replace the cosmological constant.

Contribution

The paper presents a novel reconstruction approach for $f(Q)$ gravity based on deceleration parameter models, expanding the toolkit for modified gravity theories aligned with observations.

Findings

Viable $f(Q)$ models can produce dynamic dark energy scenarios.

Modified gravity models can mimic $ ext{Lambda}$CDM behavior.

Slight modifications lead to qualitatively distinct cosmic evolutions.

Abstract

We present a novel approach for reconstructing the $f(Q)$ gravitational theory using parameterizations of the deceleration parameter or alternative options. This method enables the development of modified gravity scenarios that align with cosmological observations. We analyze two deceleration parameter models and one effective equation of state model from the literature. By leveraging the matter density parameter's asymptotic behaviour, we further refine the viable parameter space for these models. One tested model demonstrates that even slight modifications can yield viable cosmic scenarios, where the dark energy (DE) sector becomes dynamic and is entirely described instead of using a cosmological constant, we use modified gravity. These scenarios are qualitatively distinct yet quantitatively consistent with $\Lambda$CDM.