The physical origin of the cosmological constant: continuum limit and the analogy with the Casimir effect

In this paper we continue the investigations in (Viaggiu 2018 Class. Quantum Gray. 35 215011) concerning the origin of the cosmological constant. First of all, we generalize the results in (Viaggiu 2018 Class. Quantum Gray. 35 215011, Buchdahl 1970 Mon. Not. R. Astron. Soc. 1501) by considering a continuum approximation for a radiation field in a cosmological background. In this way, we clearly show that the bare cosmological constant is obtained with wanishing temperature T and that the specific heat C is zero at the decoherence scale L-D. Moreover, we address the issue to fix the parameters present in our model. In particular, we push forward the analogy between our expression for Lambda(L) at a given proper scale L and the one extrapolated by the Casimir effect. As a consequence, we can fix the decoherence scale L-D at which we have the crossover to classicality to be of the order of similar to 10(-5) m. This implies that the actual observed value of the cosmological constant is fixed (frozen) at this new physical scale.