Modified $f(Q)$ gravity models and their cosmological consequences

TL;DR

This paper explores three modified $f(Q)$ gravity models—power-law, exponential, and logarithmic—to determine which best replicates the $ ext{Lambda}$CDM cosmological evolution by analyzing their solutions and parameter behaviors.

Contribution

It introduces and compares three specific $f(Q)$ models, solving their field equations and identifying parameter ranges that align with standard cosmological observations.

Findings

Power-law model matches $ ext{Lambda}$CDM$ for $ ext{lambda}=-1$ and $-2$.

Exponential model fits well for $5 extless eta extless 11$.

Logarithmic model aligns for $3.8 extless \gamma extless 4.4$.

Abstract

In this work, we consider three different $f(Q)$ models, such as power-law, exponential, and logarithmic, to study which model better mimics $\Lambda$CDM evolution theoretically. Henceforth, we determine solutions to the $f(Q)$ gravity field equations in the isotropic and homogeneous universe. Since all the models contain two model parameters, we reduce the degrees of freedom using the first Friedman equation at the present time. Further, we check the behavior of cosmological parameters using the obtained solution to the field equations and compare it with the $\Lambda$CDM model. As a result, the power-law model shows a good match with $\Lambda$CDM model for $\lambda=-1$ and $\lambda=-2$, while the exponential model behaves well for the range $5\le \beta<11$, and the logarithmic model matches for $3.8<\gamma<4.4$.