Linear cosmological perturbations in $f(Q)$ -gravity model using the $1 + 3$ covariant formalism

In this manuscript, the evolution of scalar perturbations in f(Q) gravity mode using the 1 + 3 covariant formalism is studied. After reviewing f(Q) cosmology, the first-order evolution equations are derived, and the scalar and harmonic decomposition techniques are applied. We then solve the system of equations to find the density fluctuations through redshift and then apply the quasi-static approximation. The numerical results of density fluctuations are presented in dust and radiation-dominated epochs of the universe, and both wavelength modes: long- and short-wavelength modes are considered for the case of radiation dominated universe. From the results of density fluctuations, we clearly observe the contribution of nonmetricity gravity to the formation of large-scale structures. We use the power-law nonmetricity gravity model which is f(Q) = Q + αQn for numerical analysis.