Abstract
Motivated by black hole physics, we define the Unruh state for a scalar field in de Sitter space. Like the Bunch-Davies state, the Unruh-de Sitter state appears thermal to a static observer. However, it breaks some of the symmetries of de Sitter space. We calculate the expectation value of the energy-momentum tensor in the Unruh-de Sitter state in two dimensions and find a non-vanishing flux of outgoing negative energy. Extrapolating the result to four dimensions, we argue that this backreacts on the initial de Sitter geometry semi-classically. Notably, we estimate that de Sitter space is destabilized on a timescale set by the gravitational entropy; analogous to black hole evaporation, the endpoint of this instability is a singular geometry outside the regime of effective field theory. Finally, we suggest that the Unruh-de Sitter state may be a natural initial state for patches of de Sitter space, and discuss the implications for slow-roll and eternal inflation, and for de Sitter thermodynamics.
Highlights
We estimate that de Sitter space is destabilized on a timescale set by the gravitational entropy; analogous to black hole evaporation, the endpoint of this instability is a singular geometry outside the regime of effective field theory
The Unruh state is accepted as a physically viable state because it is regular on the future horizon; the putative singularity on the past horizon is occluded by the collapsing matter forming the black hole
For the Bunch-Davies state, we find the well-known result that the vacuum expectation value of the energy-momentum tensor is proportional to the metric, as it must be in order to preserve the de Sitter isometries
Summary
Let us begin with a brief review of two-dimensional Rindler space. In Rindler coordinates the line element reads ds2 = e2aξ −dτ 2 + dξ. Annihilated by the aoperators, while the ingoing (V ) vacuum is chosen to be annihilated by theb operators This state is singular on the past horizon but regular everywhere else. In the context of a black hole that forms from a collapsing star, the Schwarzschild geometry is replaced at early times by the geometry of the collapsing star This covers up the past horizon so that the would-be singularity there is of no physical relevance. The de Sitter counterpart of the black hole Unruh state is well-defined on an entire planar patch and might even be a natural alternative to the commonly used Bunch-Davies state These results are summarized in table 1. We have included the time-reversed Unruh state, for which the singularity occurs on the black hole future horizon; this, is not a physically reasonable state if one assumes that the equivalence principle holds and that nothing special happens at the future event horizon
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