Abstract
We present a 4-dimensional back reaction analysis of de Sitter space for a conformally coupled scalar field in the presence of vacuum energy initialized in the Bunch–Davies vacuum. In contrast to the usual semi-classical prescription, as the source term in the Friedmann equations we use expectation values where the unobservable information hidden by the cosmological event horizon has been neglected i.e. coarse grained over. It is shown that in this approach the energy-momentum is precisely thermal with constant temperature despite the dilution from the expansion of space due to a flux of energy radiated from the horizon. This leads to a self-consistent solution for the Hubble rate, which is gradually evolving and at late times deviates significantly from de Sitter. Our results hence imply de Sitter space to be unstable in this prescription. The solution also suggests dynamical vacuum energy: the continuous flux of energy is balanced by the generation of negative vacuum energy, which accumulatively decreases the overall contribution. Finally, we show that our results admit a thermodynamic interpretation which provides a simple alternate derivation of the mechanism. For very long times the solutions coincide with flat space.
Highlights
The de Sitter spacetime is one of the most analytically tractable examples of a genuinely curved solution to Einstein’s field equation
As a continuation of the work [36] here we explore the gravitational implications from a particular coarse grained density matrix: the cosmological event horizon of de Sitter space splits the Universe into observable and unobservable patches essentially identically to a black hole, which motivates us to disregard all information contained beyond the horizon
For clarity we summarize the arguments of this section here once more: in de Sitter space as described by the expanding FLRW coordinates (18) initialized to the Bunch–Davies vacuum the energy-momentum of a quantum field has a thermal character when in the density matrix one includes only the observable states inside the horizon
Summary
The de Sitter spacetime is one of the most analytically tractable examples of a genuinely curved solution to Einstein’s field equation. If de Sitter space were unstable to quantum corrections and could decay, this could provide an important mechanism for alleviating the cosmological constant problem and perhaps the fine-tuning issues encountered in the extremely flat inflationary potentials that are required by observations. A de Sitter instability would have a profound impact on the fate of the Universe since it rules out the possibility of an eternally exponentially expanding de Sitter space as classically implied by the CDM concordance model. The thermodynamics of spacetime horizons is established as a mature, well-studied subject [13,43,44,45,46,47,48,49]. By invoking thermodynamic concepts in the impactful work [13] it was argued that the de Sitter horizon does evaporate.
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