Cosmological solutions in f(Q) gravity via Noether symmetry approach

Symmetry plays a crucial role in theoretical physics, especially Noether symmetry, which is a powerful approach for identifying the models at the fundamental level. The exact solution is provided within the point-like Lagrangian framework. In this work, we study one of the alternative theories of gravity based on the non-metricity scalar [Formula: see text], namely [Formula: see text] gravity, via Noether symmetry. We utilize Noether symmetry within the framework of [Formula: see text] gravity to derive the functional expression for [Formula: see text], which is given by [Formula: see text]. To confirm the exact solution of the model through Noether symmetry, we continue to consider the Friedmann–Robertson–Walker (FRW) cosmology with the dynamical solution of the system using dimensionless variables and show that the accelerated expansion of the universe follows a power law scale factor. In the following, we show that the quantities corresponding to the exact solution for [Formula: see text] lead to an accelerated expansion universe. Finally, in the framework of [Formula: see text] scalar–tensor cosmology, we apply the Noether symmetry approach to find the cosmological models consistent with the Noether symmetry.