On the Casimir energy for a massive quantum scalar field and the Cosmological constant

Abstract

We present a rigorous, regularization independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass $\mu\ne0$ which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field at fixed cosmic time, in which the expectation value of the renormalized energy-momentum tensor is independent of the space coordinate and is of the perfect fluid form $g_{\mu,\nu}\rho_{vac}$ with $\rho_{vac}>0$, thus providing a quantum field theoretic foundation of the Cosmological constant. Using some values of $\mu$ suggested in the literature for the hypothetical axion particle, there results a model for dark energy which is consistent with past and future evolution and is also in good agreement with experimental data.