  In this study, we investigate the cosmological history within the framework
of modified $f(Q)$ gravity, which proposes an alternative theory of gravity
where the gravitational force is described by a non-metricity scalar. By
employing a parametrization scheme for the Hubble parameter, we obtain the
exact solution to the field equations in $f(Q)$ cosmology. To constrain our
model, we utilize external datasets, including 57 data points from the Hubble
dataset, 1048 data points from the SN dataset, and six data points from the BAO
dataset. This enables us to determine the best-fit values for the model
parameters involved in the parameterization scheme. We analyze the cosmic
evolution of various cosmological parameters, including the deceleration
parameter, which exhibits the expected behavior in late-time cosmology and
changes its signature with redshift. Further, we present the evolution of
energy density, EoS parameter, and other geometrical parameters with respect to
redshift. Furthermore, we discuss several cosmological tests and diagnostic
analyses. Our findings demonstrate that the late-time cosmic evolution can be
adequately described without the need for dark energy by employing a
parametrization scheme in modified gravity.

General Relativity and Quantum Cosmology