Patch Of De Sitter Spacetime Research Articles

Entropy-Area Law and Temperature of de Sitter Horizons from Modular Theory

Abstract We derive an entropy-area law for the future horizon of an observer in diamonds inside a static patch of de Sitter space-time, taking into account the back reaction of quantum matter fields. We prove the positivity and convexity of the relative entropy for coherent states using Tomita–Takesaki modular theory, from which the quantum null energy condition for diamonds follows. Furthermore, we show that the generalized entropy conjecture holds. Finally, we reveal that the local temperature that is measured by an observer at rest exhibits subleading quantum corrections with respect to the well known cosmological horizon temperature H/(2π).

Gravitational thermodynamics of causal diamonds in (A)dS

The static patch of de Sitter spacetime and the Rindler wedge of Minkowski spacetime are causal diamonds admitting a true Killing field, and they behave as thermodynamic equilibrium states under gravitational perturbations. We explore the extension of this gravitational thermodynamics to all causal diamonds in maximally symmetric spacetimes. Although such diamonds generally admit only a conformal Killing vector, that seems in all respects to be sufficient. We establish a Smarr formula for such diamonds and a ``first law" for variations to nearby solutions. The latter relates the variations of the bounding area, spatial volume of the maximal slice, cosmological constant, and matter Hamiltonian. The total Hamiltonian is the generator of evolution along the conformal Killing vector that preserves the diamond. To interpret the first law as a thermodynamic relation, it appears necessary to attribute a negative temperature to the diamond, as has been previously suggested for the special case of the static patch of de Sitter spacetime. With quantum corrections included, for small diamonds we recover the ``entanglement equilibrium'' result that the generalized entropy is stationary at the maximally symmetric vacuum at fixed volume, and we reformulate this as the stationarity of free conformal energy with the volume not fixed.

Gibbons-Hawking radiation of gravitons in the Poincaré and static patches of de Sitter spacetime

We discuss the quantization of linearized gravity in the background de Sitter spacetime using a gauge-invariant formalism to write the perturbed gravitational field in the static patch. This field is quantized after fixing the gauge completely. The response rate of this field to monochromatic multipole sources is then computed in the thermal equilibrium state with the well known Gibbons-Hawking temperature. We compare this response rate with the one obtained in the Bunch-Davies-like vacuum state defined in the Poincar\'e patch. These response rates are found to be the same as expected. This agreement serves as a verification of the infrared finite graviton two-point function in the static patch of de Sitter spacetime found previously.

On propagation of energy flux in de Sitter spacetime

In this paper, we explore propagation of energy flux in the future Poincar\'e patch of de Sitter spacetime. We present two results. First, we compute the flux integral of energy using the symplectic current density of the covariant phase space approach on hypersurfaces of constant radial physical distance. Using this computation we show that in the tt-projection, the integrand in the energy flux expression on the cosmological horizon is same as that on the future null infinity. This suggests that propagation of energy flux in de Sitter spacetime is sharp. Second, we relate our energy flux expression in tt-projection to a previously obtained expression using the Isaacson stress-tensor approach. We also comment on the energy flux computation in TT-gauge on hypersurfaces of constant radial physical distance.

Memory in de Sitter space and Bondi-Metzner-Sachs-like supertranslations

It is well known that the memory effect in flat spacetime is parametrized by the BMS supertranslation. We investigate the relation between the memory effect and diffeomorphism in de Sitter spacetime. We find that gravitational memory is parametrized by a BMS-like supertranslation in the static patch of de Sitter spacetime. We also show a diffeomorphism that corresponds to gravitational memory in the Poincare/cosmological patch. Our method does not need to assume the separation between the source and the detector to be small compared with the Hubble radius, and can potentially be applicable to other FLRW universes, as well as "ordinary memory" mediated by massive messenger particles.

Graviton two-point function in 3 + 1 static de Sitter spacetime

In [R. P. Bernar, L. C. B. Crispino and A. Higuchi, Phys. Rev. D 90 (2014) 024045.] we investigated gravitational perturbations in the background of de Sitter spacetime in arbitrary dimensions. More specifically, we used a gauge-invariant formalism to describe the perturbations inside the cosmological horizon, i.e. in the static patch of de Sitter spacetime. After a gauge-fixed quantization procedure, the two-point function in the Bunch–Davies-like vacuum state was shown to be infrared finite and invariant under time-translation. In this work, we give details of the calculations to obtain the graviton two-point function in 3 + 1 dimensions.

Static patch solipsism: conformal symmetry of the de Sitter worldline

We show that the propagators of gravitons and scalar fields seen by a static patch observer in de Sitter spacetime are controlled by hidden symmetries at all frequencies. The retarded Green's function is determined by an action generated by conformal Killing vectors of de Sitter spacetime times a line. This observation uses the fact that the static patch of dS is conformal to the hyperbolic patch of AdS3 × Sd − 1. The poles of the propagators, the quasinormal frequencies, are generated by associated actions. The quasinormal mode-generating algebras capture the conformal weights more usually read off from the fields at future and past infinity. For conformally coupled scalar fields, and for gravitons in four dimensions, this algebra has an enhanced supersymmetric structure and is generated by particular conformal Killing vectors of de Sitter spacetime. We show how the worldline de Sitter propagators can be reproduced from a ‘level matched’ left- and right-moving conformal quantum mechanics with an appropriate spectrum of primary operators. Our observations are consistent with the notion that the static patch of de Sitter spacetime is dually described by a (level matched) large N worldline conformal quantum mechanics.