  In this manuscript, we studied the accelerated expansion history of the
universe and the formations of large-scale structures using $f(Q)$ gravity
model. The expansion rate of the universe within distance modulus and redshift
has been performed in $f(Q)$ gravity. This work is also devoted to
investigating the linear cosmological perturbations in the $f(Q)$ gravity model
using the $1 + 3$ covariant formalism. The scalar and harmonic decomposition
techniques are applied to find the evolution equation. The growth of matter
density contrasts is analyzed with redshift $z$. Using the nonmetricity
modified gravity model which is $f (Q) = Q+\alpha Q^n$, the accelerating
expanding universe and the formations of the large-scale structures have been
explained. The quasi-static approximation technique is applied to analyze the
growth of matter contrasts. The growth of density contrast is studied within
the dust and radiation-dominated universe in the presence of nonmetricity
gravity.
