Complete dark energy scenario in $f(Q)$ gravity

In theoretical physics, the fundamental nature and evolution mechanism of dark energy is still an open question. In General Relativity Theory, the simplest explanation for dark energy is the cosmological constant $\Lambda$. However, the cosmological constant $\Lambda$ facing a sensitive problem called fine-tunning problem. In the present work, we follow a different approach where the gravitational sector is the responsible candidate for the evolution of dark energy instead of the matter source. The modified symmetric teleparallel gravity or $f(Q)$ gravity is a recently proposed theory of gravity where the gravitational interaction ruled by the non-metricity term $Q$. In this manuscript, we assume a $f(Q)$ model that contains a linear and a non-linear form of non-metricity scalar, particularly $f(Q)=\alpha Q + \beta Q^n$, where $\alpha$, $\beta$, and $n$ are free model parameters. Then we find the values of our model parameters that would be in agreement with the observed value of cosmographic parameters. We analyze the behavior of different cosmological parameters like deceleration parameter, density, and the equation of state parameter with the energy conditions for our cosmological model. We found that for higher positive values of $n$ specifically $n \geq 1$, dark energy fluid part evolving due to non-metricity behaves like quintessence type dark energy while for higher negative values of $n$ specifically $n \leq -1$ it follows phantom scenario. Further for $n=0$, our cosmological $f(Q)$ model behaves like $\Lambda$CDM model. Thus, we conclude that the geometrical generalization of GR can be a viable candidate for the description of origin of the dark energy.