Cosmology with explicit and spontaneous background fields

We study a general class of effective backgrounds that break diffeomorphism invariance and their potential roles in cosmology. Specifically, we examine both explicit and spontaneous background fields which display distinct transformation properties and are characterized with different dynamics. For explicit breaking, we focus on the $t$-sector of the minimal gravitational Standard-Model Extension (SME) and for spontaneous breaking on a vector field called the bumblebee model. In both cases, we derive the modified Friedmann equations and find a configuration of the background fields that preserve isotropy and homogeneity. We show that the explicit $t$-sector admits phases of accelerated expansion of the universe with standard matter.