Towards a quantum theory of de Sitter space

In this work we investigate the quantum theory of light propagating in $D-$dimensional de Sitter spacetimes. To do so, we use the method of dynamic invariants to obtain the solution of the time-dependent Schr\"odinger equation. The quantum behavior of the electromagnetic field in this background is analyzed. As the electromagnetism loses its conformality in $D\neq4$, we point that there will be particle production and comoving objects will feel a Bunch-Davies thermal bath. Th...

Semiclassical gravity predicts that de Sitter space has a finite entropy. We suggest a picture for Euclidean de Sitter space in string theory, and use the AdS/CFT correspondence to argue that de Sitter entropy can be understood as the number of degrees of freedom in a quantum mechanical dual.

Two important problems in studying the quantum black hole, namely the construction of the Hilbert space and the definition of the time evolution operator on such Hilbert space, are discussed using the de Sitter background field method for an observer far from the black hole. This is achieved through the ambient space formalism. Remarkably, in this approximation (distant observer), the theory preserves unitarity and analyticity, it is free from any infrared divergence, and it ...

Before we ask what is the theory of quantum gravity, it is a legitimate quest to formulate a robust quantum field theory in curved spacetime (QFTCS). Several conceptual problems have raised concerns over several decades, mainly because no S-matrix formulation is yet found in QFTCS. We argue that the institutional thinking of fixing a spacetime geometry, observers, light-cones and then quantizing the fields in that "intuitively", or "classically", fixed spacetime is the origin...

Experimental evidences and theoretical motivations lead to consider the curved space-time relativity based on the de Sitter group $SO_0(1,4)$ or $Sp(2,2)$ as an appealing substitute to the flat space-time Poincare relativity. Quantum elementary systems are then associated to unitary irreducible representations of that simple Lie group. At the lowest limit of the discrete series lies a remarkable family of scalar representations involving Krein structures and related undecompo...

We study de Sitter JT gravity in the canonical formulation to illustrate constructions of Hilbert spaces in quantum gravity, which is challenging due to the Hamiltonian constraints. The key ideas include representing states as "invariants" (solutions to the Wheeler-DeWitt equation) or dual "co-invariants" (equivalence classes under gauge transformations), defining a physical inner product by group averaging, and relating this to Klein-Gordon inner products via gauge-fixing co...

In 1975 Figari, H{\o}egh-Krohn and Nappi constructed the P(phi)_2 model on the de Sitter space. Here we complement their work with new results, as well as by connecting this model to various areas of mathematics. In particular, i.) we discuss the causal structure of de Sitter space and the induces representations of the Lorentz group. We show that the UIRs of SO_0(1,2) for both the principal and the complementary series can be formulated on Hilbert spaces whose functions are ...

We investigate the quantum aspects of three-dimensional gravity with a positive cosmological constant. The reduced phase space of the three-dimensional de Sitter gravity is obtained as the space which consists of the Kerr-de Sitter space-times and their Virasoro deformations. A quantization of the phase space is carried out by the geometric quantization of the coadjoint orbits of the asymptotic Virasoro symmetries. The Virasoro algebras with real central charges are obtained ...

The Kodama state is unique in being an exact solution to all the constraints of quantum gravity that also has a well defined semi-classical interpretation as the quantum version of a classical spacetime, namely de Sitter or anti-de sitter space. Despite this, the state fails to pass some of the key tests of a physically realistic quantum state. In an attempt to resolve this problem, we track down the root of the problem to a choice for a particular parameter: the Immirzi para...

We discuss and extend some aspects pertaining to the canonical quantisation of JT gravity in de Sitter space, including the problem of time and the construction of a Hilbert space. We then extend this discussion to other two dimensional models obtained by changing the dilaton potential and show that the canonical quantisation procedure can be carried out for a large class of such models. Some discussion leading towards a path integral understanding for states, other than the ...