Back(reaction) to the Future in the Unruh-de Sitter State

TL;DR

The paper introduces the Unruh-de Sitter state as the de Sitter analogue of the black hole Unruh state, constructing it to have incoming BD-like and outgoing static-like fluxes, thereby breaking de Sitter isometries while remaining well-defined on planar patches. Using a 2D reduction and Christensen–Fulling consistency conditions, the authors compute the vacuum expectation value of the energy-momentum tensor, finding a net incoming energy flux and negative outgoing flux that violate the null energy condition, with the 2D results extended to the s-wave sector of 4D near the horizon. Inserting the renormalized EMT into the semiclassical Einstein equations yields a backreaction that slowly shrinks the de Sitter horizon, with the rate suppressed by $(H/M_{p})^{2}$ and a lifetime of order $M_{p}^{2}/H^{2}$, suggesting instability only on very long timescales set by the de Sitter entropy. The work argues that Unruh-de Sitter may be a natural initial state for inflationary patches, with limited impact on standard slow-roll predictions but potential implications for eternal inflation and swampland considerations, and highlights the need for further studies of full cosmological perturbations and global consistency.

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.

Figures (2)

• Figure 1: The de Sitter Penrose diagram, including the static ($u,v$) and global ($U,V$) lightcone coordinates, as defined. The planar patch is shaded gray.
• Figure 2: Illustration of the finite region (dark shaded) in the de Sitter Penrose diagram where we can analyze the approximately homogeneous backreaction effect due to the stress-energy in the Unruh state. Here $|r_0/\eta_0| \gtrsim 1$ and $\eta_1$ corresponds to the time where the effect becomes order one.