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

Abstract

In this paper we continue the investigations in [1] concerning the origin of the cosmological constant. First of all, we generalise the results in [1,2] 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 Λ 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 ∼ 10 −5 meters. This implies that the actual observed value of the cosmological constant is fixed (frozen) at this new physical scale.

The Cosmological Constant From Planckian Fluctuations and the Averaging Procedure

“…Abstract In this paper I continue the investigation in [1,2] concerning my proposal on the nature of the cosmological constant. In particular, I study both mathematically and physically the quantum Planckian context and I provide, in order to depict quantum fluctuations and in absence of a complete quantum gravity theory, a semiclassical solution where an effective inhomogeneous metric at Planckian scales or above is averaged.…”

Einstein, Planck and Vera Rubin: Relevant Encounters Between the Cosmological and the Quantum Worlds

“…Remarkably, a completely new point of view, regarding the origin of Λ has been recently put forward [221][222][223] The main idea relies on the nature of Λ and its very small observed value and states that quantum fluctuations can explain the equation of state of the cosmological constant. In fact, a radiation field sufficiently close to the Planck scale can allow quantum fluctuations so strong to permit the transformation of this radiation field into one with the equation of state that Λ shows.…”

“…where L P is the Planck length and the constant π A comparison with the Casimir effect is outlined in ref. 222. In this regard, it should be noticed that an expression for a quantum modification of the Misner-Sharp mass, introduced in ref.…”

The physical nature of the cosmological constant and the decoherence scale in a renormalization-group approach

“…The scale L D fixes the observed value of Λ. In this paper we continue the investigations in [13,14,15]. In particular, after adopting a suitable physically reasonable expression for the renormalization scale µ, we analyse the possible relation between our semiclassical expression for ρ Λ and the one extrapolated in literature by using a renormalization group approach [16,17,18,19,20,21].…”

“…In [11] the cosmological constant is supposed to be effectively given by Λ ∼ 1 L 2 P at Planckian scales, but effective inhomogeneities at Planckian scales inhibit a huge cosmological constant and as a consequence a small cosmological constant emerges at macroscopic scales. In [13,14,15], we presented a new model. The new idea is that a huge cosmological constant is effectively created at Planckian scales, where Planckian fluctuations are expected to be very strong, but vacuum fluctuations must be averaged on bigger and bigger scales.…”