Vacuum energy and the universe in special relativity

Abstract

The problem of the cosmological constant and vacuum energy is usually thought of as the subject of general relativity. However, vacuum energy is important for the Universe even in the absence of gravity, i.e., in the case when Newton’s constant G is exactly zero, G=0. We discuss the response of the vacuum energy to the perturbations of the quantum vacuum in special relativity and find that, as in general relativity, the vacuum energy density is on the order of the energy density of matter. In general relativity, the dependence of the vacuum energy on the equation of state of matter does not contain G and thus is valid in the limit G→0. However, the result obtained for the vacuum energy in a world without gravity, i.e., when G=0 exactly, is different.