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

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 $3.8<\gamma<4.4$.