Symmetric teleparallel cosmology with boundary corrections

Abstract: We investigate the geometrodynamical effects of introducing the boundary term in symmetric teleparallel gravity. Specifically, we consider a homogeneous and isotropic universe in $f\left( Q, B \right) $, where $Q$ is the non-metricity scalar, and $B$ is the boundary term that relates the non-metricity and Ricci scalars. For the connection in the coincidence gauge, we find that the field equations are of fourth-order, and the fluid components introduced by the boundary are attributed to a scalar field. In the coincidence gauge, the cosmological field equations are equivalent to those of teleparallelism with a boundary term. Nevertheless, for the connection defined in the non-coincidence gauge, the geometrodynamical fluid consists of three scalar fields. We focus on the special case of $f\left( Q, B \right) = Q + F\left( B \right) $ theory, and we determine a new analytic cosmological solution that can explain the late-time acceleration of the universe and provide a geometric mechanism for the unification of dark energy with dark matter.