Cosmology in symmetric teleparallel bumblebee gravity

Symmetric teleparallel gravity (STG) is an alternative description of the gravitational field as an effect of the nonmetricity rather than the curvature of the spacetime. For an specific choice of the symmetric teleparallel lagrangian, the STG dynamics is equivalent to the general relativity (GR), and it is called Symmetric teleparallel equivalent to general relativity (STEGR). We propose a local Lorentz violating dynamics in the gravitational sector in the STEGR framework. The Lorentz violation is trigged by the vacuum expectation value (vev) of the well-known bumblebee field, whose vev couples to the nonmetricity tensor. The effects of such couplings on the cosmological evolution is investigated.