We show that the Hartle-Hawking vacuum for any theory of interacting massive scalars on a fixed de Sitter background is both perturbatively well-defined and stable in the IR. Correlation functions in this state may be computed on the Euclidean section and Wick-rotated to Lorentz-signature. The results are manifestly de Sitter-invariant and contain only the familiar UV singularities. More importantly, the connected parts of all Lorentz-signature correlators decay at large separations of their arguments. Our results apply to all cases in which the free Euclidean vacuum is well defined, including scalars with masses belonging to both the complementary and principal series of SO (D, 1). This suggests that interacting QFTs in de Sitter -including higher spin fields -are perturbatively IR-stable at least when i) the Euclidean vacuum of the zero-coupling theory exists and ii) corresponding Lorentz-signature zero-coupling correlators decay at large separations. This work has significant overlap with a paper by Stefan Hollands, which is being released simultaneously.

We compute 1-loop corrections to Lorentz-signature de Sitter-invariant 2-point functions defined by the interacting Euclidean vacuum for massive scalar quantum fields with cubic and quartic interactions. Our results apply to all masses for which the free Euclidean de Sitter vacuum is well-defined, including values in both the complimentary and the principal series of SO(D, 1). In dimensions where the interactions are renormalizeable we provide absolutely convergent integral representations of the corrections. These representations suffice to analytically extract the leading behavior of the 2-point functions at large separations and may also be used for numerical computations. The interacting propagators decay at long distances at least as fast as one would naively expect, suggesting that such interacting de Sitter invariant vacuua are well-defined and are wellbehaved in the IR. In fact, in some cases the interacting propagators decay faster than any free propagator with any value of M 2 > 0.and define representations of the (connected) de Sitter group SO 0 (D, 1). It is useful to define the dimensionless mass parameter σ by −σ(σ + d) := M 2 2 . Throughout most of our work, the ambiguity σ → −(σ + d) will be a redundancy of our description, and symmetry σ → −(σ + d) will provide a useful check on our calculations. However, for the moment   J + 2α, J − L + α, J − M + α, J − N + α J + α + 1, J − L + 1, J − M + 1, J − N + 1   , (A10) when J := (L+M +N )/2 ∈ N 0 , and L, M , and N satisfy the triangle inequalities; otherwise D(α, L, M, N ) = 0.

The merger of binary neutron stars is likely to lead to differentially rotating remnants. In this paper, we survey several cold nuclear equations of state (EOSs) and numerically construct models of differentially rotating neutron stars in general relativity. For each EOS we tabulate maximum allowed masses as a function of the degree of differential rotation. We also determine effective polytropic indices and compare the maximum allowed masses with those for the corresponding polytropes. We consistently find larger mass increases for the polytropes, but even for the nuclear EOSs we typically find maximum masses 50% higher than the corresponding values for nonrotating (Tolman-Oppenheimer-Volkoff ) stars. We evaluate our findings for the six observed binary neutron star (pulsar) systems, including the recently discovered binary pulsar J0737À3039. For each EOS we determine whether their merger could automatically lead to prompt collapse to a black hole, or whether the remnant can be supported against collapse by uniform rotation (possibly as a supramassive star) or differential rotation (possibly as a hypermassive star). For hypermassive stars, delayed collapse to a black hole is likely. For the most recent EOSs we survey the merger remnants can all be supported by rotation against prompt collapse, but their actual fate will depend on the nonequilibrium dynamics of the coalescence event. Gravitational wave observations of coalescing binary neutron stars may be able to distinguish these outcomes-no, delayed, or prompt collapseand thereby constrain possible EOSs.

In order to better understand how AdS holography works for sub-regions, we formulate a holographic version of the Reeh-Schlieder theorem for the simple case of an AdS Klein-Gordon field. This theorem asserts that the set of states constructed by acting on a suitable vacuum state with boundary observables contained within any subset of the boundary is dense in the Hilbert space of the bulk theory. To prove this theorem we need two ingredients which are themselves of interest. First, we prove a purely bulk version of Reeh-Schlieder theorem for an AdS Klein-Gordon field. This theorem relies on the analyticity properties of certain vacuum states. Our second ingredient is a boundaryto-bulk map for local observables on an AdS causal wedge. This mapping is achieved by simple integral kernels which construct bulk observables from convolutions with boundary operators. Our analysis improves on previous constructions of AdS boundary-to-bulk maps in that it is formulated entirely in Lorentz signature without the need for large analytic continuation of spatial coordinates. Both our Reeh-Schlieder theorem and boundary-tobulk maps may be applied to globally well-defined states constructed from the usual AdS vacuum as well more singular states such as the local vacuum of an AdS causal wedge which is singular on the horizon.

The two-point function of linearized gravitons on de Sitter space is infrared divergent in the standard transverse traceless synchronous gauge defined by k = 0 cosmological coordinates (also called conformal or Poincaré coordinates). We show that this divergence can be removed by adding a linearized diffeomorphism to each mode function; i.e., by an explicit change of gauge. It follows that the graviton vacuum state is well-defined and de Sitter invariant in agreement with various earlier arguments.