Weighing the vacuum energy.

We discuss the weight of vacuum energy in various contexts. First, we compute the vacuum energy for flat spacetimes of the form T³×R, where T³ stands for a general 3-torus. We discover a quite simple relationship between energy at radius R and energy at radius l2/R. Then we consider quantum gravity effects in the vacuum energy of a scalar field in M 3×S¹ where M 3 is a general curved spacetime, and the circle S 1 refers to a spacelike coordinate. We compute it for general relativity and generic transverse diffeomorphisms theories. In the particular case of unimodular gravity vacuum energy does not gravitate. [ABSTRACT FROM AUTHOR]