Existence of Noether vector fields of Bianchi type-I spacetimes in modified symmetric teleparallel <i>f(Q)</i> gravity

The aim of this paper is to find Noether vector fields (NVFs) of Bianchi type-I spacetimes in the modified symmetric teleparallel gravity (STG). For this purpose, initially, we solve equations of motion of the STG in the background of Bianchi type-I spacetimes. In order to solve equations, we consider linear as well as quadratic forms of [Formula: see text], where [Formula: see text] is a generic function of the non-metricity scalar Q. We then calculate the NVFs for the formulated metrics. In most cases, there exist proper NVFs. In addition to the existence of proper NVFs, we also observe some additional symmetries that conserve linear as well as angular momentum. A thorough investigation reveals that in the STG, the overall dimensions of Noether symmetry algebra for the Bianchi type-I spacetimes are 5, 6, 7, 8, and 17.