Gravity In De Sitter Spacetime Research Articles

The graviton four-point function in de Sitter space

We compute the tree-level late-time graviton four-point correlation function, and the related quartic wavefunction coefficient, for Einstein gravity in de Sitter spacetime. We derive this result in several ways: by direct calculation, using the in-in formalism and the wavefunction of the universe; by a heuristic derivation leveraging the flat space wave-function coefficient; and by using the boostless cosmological bootstrap, in particular the combination of the cosmological optical theorem, the amplitude limit, and the manifestly local test. We find agreement among the different methods.

Holographic networks for ( 1+1 )-dimensional de Sitter space-time

Holographic tensor networks associated to tilings of (1+1)-dimensional de Sitter spacetime are introduced. Basic features of these networks are discussed, compared, and contrasted with conjectured properties of quantum gravity in de Sitter spacetime. Notably, we highlight a correspondence between the quantum information capacity of the network and the cosmological constant.

Infrared problem in the Faddeev-Popov ghost propagator in perturbative quantum gravity in de Sitter spacetime

The propagators for the Faddeev-Popov (FP) ghosts in Yang-Mills theory and perturbative gravity in the covariant gauge are infrared (IR) divergent in de Sitter spacetime. An IR cutoff in the momentum space to regularize these divergences breaks the de Sitter invariance. These IR divergences are due to the spatially constant modes in the Yang-Mills case and the modes proportional to the Killing vectors in the case of perturbative gravity. It has been proposed that these IR divergences can be removed, with the de Sitter invariance preserved, by first regularizing them with an additional mass term for the FP ghosts and then taking the massless limit. In the Yang-Mills case, this procedure has been shown to correspond to requiring that the physical states, and the vacuum state in particular, be annihilated by some conserved charges in the Landau gauge. In this paper we show that there are similar conserved charges in perturbative gravity in the covariant Landau gauge in de Sitter spacetime and that the IR-regularization procedure described above also correspond to requiring that the vacuum state be annihilated by these charges with a natural definition of the interacting vacuum state.

Islands in cosmology

A quantum extremal island suggests that a region of spacetime is encoded in the quantum state of another system, like the encoding of the black hole interior in Hawking radiation. We study conditions for islands to appear in general spacetimes, with or without black holes. They must violate Bekenstein’s area bound in a precise sense, and the boundary of an island must satisfy several other information-theoretic inequalities. These conditions combine to impose very strong restrictions, which we apply to cosmological models. We find several examples of islands in crunching universes. In particular, in the four-dimensional FRW cosmology with radiation and a negative cosmological constant, there is an island near the turning point when the geometry begins to recollapse. In a two-dimensional model of JT gravity in de Sitter spacetime, there are islands inside crunches that are encoded at future infinity or inside bubbles of Minkowski spacetime. Finally, we discuss simple tensor network toy models for islands in cosmology and black holes.

Gupta-Bleuler quantization for linearized gravity in de Sitter spacetime

In a recent Letter, we have pointed out that the linearized Einstein gravity in de Sitter (dS) spacetime besides the spacetime symmetries generated by the Killing vectors and the evident gauge symmetry also possesses a hitherto `hidden' local (gauge-like) symmetry which becomes anomalous on the quantum level. This gauge-like anomaly makes the theory inconsistent and must be canceled at all costs. In this companion paper, we first review our argument and discuss it in more detail. We argue that the cancelation of this anomaly makes it impossible to preserve dS symmetry in linearized quantum gravity through the usual canonical quantization in a consistent manner. Then, demanding that all the classical symmetries to survive in the quantized theory, we set up a coordinate-independent formalism \`{a} \emph{la} Gupta-Bleuler which allows for preserving the (manifest) dS covariance in the presence of the gauge and the gauge-like invariance of the theory. On this basis, considering a new representation of the canonical commutation relations, we present a graviton quantum field on dS space, transforming correctly under isometries, gauge transformations, and gauge-like transformations, which acts on a state space containing a vacuum invariant under all of them. Despite the appearance of negative norm states in this quantization scheme, the energy operator is positive in all physical states, and vanishes in the vacuum.

Semi-classical gravity in de Sitter spacetime and the cosmological constant

We show that there exist solutions to the semi-classical gravity equations in de Sitter spacetime sourced by the renormalised stress-energy tensor of a free Klein-Gordon field. For the massless scalar, solutions exist for every possible value of the cosmological constant, provided that the curvature coupling parameter is chosen appropriately. In the massive case, imposing Wald's axioms for the renormalised stress-energy tensor, the mass of the field and the curvature coupling constraint the allowed values of Λ. For a massive, minimally coupled field, a “small Λ” solution is found, fixed by the relation m2≃4.89707×1012Λ. We emphasise that in this framework, the old cosmological constant problem in its standard formulation plays no rôle, in the sense that there are no bare-vs-physical values of Λ, for only the physical Λ appears in the semi-classical equations, and the value that it is allowed to take is fixed or restricted by the equations themselves. We explain that there is an important relation between the cosmological constant problem and the violation of Wald's stress-energy renormalisation axioms.

Effective Lagrangian in de Sitter spacetime

Scale invariant fluctuations of metric are universal feature of quantum gravity in de Sitter spacetime. We construct an effective Lagrangian which summarizes their implications on local physics by integrating super-horizon metric fluctuations. It shows infrared quantum effects are local and render fundamental couplings time dependent. We impose Lorenz invariance on the effective Lagrangian as it is required by the principle of general covariance. We show that such a requirement leads to unique physical predictions by fixing the quantization ambiguities. We explain how the gauge parameter dependence of observables is canceled. In particular the relative evolution speed of the couplings are shown to be gauge invariant.

Quantum Linear Gravity in de Sitter Universe on Gupta-Bleuler Vacuum State

Application of Krein space quantization to the linear gravity in de Sitter space-time have constructed on Gupta-Bleuler vacuum state, resulting in removal of infrared divergence and preserving de Sitter covariant. By pursuing this path, the non uniqueness of vacuum expectation value of the product of field operators in curved space-time disappears as well. Then the vacuum expectation value of the product of field operators can be defined properly and uniquely.

Weyl gauging of topologically massive gravity

We construct a Weyl-invariant extension of topologically massive gravity which, remarkably, turns out to include topologically massive electrodynamics, with a Proca mass term, conformally coupled to a scalar field. The action has no dimensionful parameters, therefore, the masses are generated via symmetry breaking either radiatively in flat backgrounds or spontaneously in constant curvature backgrounds. The broken phase of the theory, generically, has a single massive spin-2 and a massive spin-1 excitation. Chiral gravity in asymptotically anti-de Sitter spacetimes does not arise as a low energy theory, while chiral gravity in de Sitter spacetime is not ruled out.

Krein space quantization of linear gravity in de Sitter spacetime and generalization to QFT

It has been shown that the negative-norm states or negative-frequency solutions of the field equation are indispensable for a fully covariant quantization (Krein space quantization) of the minimally coupled free scalar field in de Sitter spacetime. The new method of quantization has been applied for the free boson and spinor fields in Minkowski spacetime, and the basic structure of quantum field theory is reformulated in Krein space. It is seen that the presence of unphysical negative-frequency states plays the role of an automatic renormalization tool for the theory.

How to use retarded Green’s functions in de Sitter spacetime

We demonstrate in examples that the covariant retarded Green's functions in electromagnetism and linearized gravity work as expected in de Sitter spacetime. We first clarify how retarded Green's functions should be used in spacetimes with spacelike past infinity such as de Sitter spacetime. In particular, we remind the reader of a general formula which gives the field for given initial data on a Cauchy surface and a given source (a charge or stress-energy tensor distribution) in its future. We then apply this formula to three examples: (i) electromagnetism in the future of a Cauchy surface in Minkowski spacetime, (ii) electromagnetism in de Sitter spacetime, and (iii) linearized gravity in de Sitter spacetime. In each example the field is reproduced correctly as predicted by the general argument. In the third example we construct a linearized gravitational field from two equal point masses located at the "North and South Poles" which is non-singular on the cosmological horizon and satisfies a covariant gauge condition and show that this field is reproduced by the retarded Green's function with corresponding gauge parameters.

Quantum linearization instabilities of de Sitter spacetime. I

It is known that all the physical states in linearized gravity are required to be invariant under the continuous isometries of the background spacetime if it is spatially compact. For example, all the physical states in linearized gravity in de Sitter spacetime are required to be SO(4, 1) invariant. A detailed derivation of SO(4, 1) invariance of the physical state is presented. Also, it is found that normal ordering of operators is unnecessary in the constraints which demand SO(4, 1) invariance. Then it is proved that there are no normalizable SO(4, 1)-invariant states other than the vacuum state in the Fock space. This appears to suggest that there would be no dynamics in de Sitter spacetime. A step towards a possible resolution of this paradox will be presented in the sequel to this article.

Linearized gravity in de Sitter spacetime as a representation of SO(4, 1)

The solutions to the linearized Einstein equation in de Sitter spacetime are explicitly written down. Their group-theoretical properties are examined with an emphasis on the way these solutions form a unitary representation of the de Sitter group, SO(4, 1). For this purpose of duality operator acting on them is defined. This operator is analogous to the helicity operator on gravitons in Minkowski spacetime. It is found that the self-dual solutions and the anti-self-dual solutions separately form unitary irreducible representations. The work presented is a preliminary for the study of quantum linearization instabilities, which will be reported elsewhere.

Quantum linearization instabilities of de Sitter spacetime. II

For pt.I see ibid., vol.8, no.11, p.1961 (1991). The requirement of de Sitter invariance of physical states in linearized gravity in de Sitter spacetime leads to an apparent paradox. That is, it appears that the vacuum would be the only allowed physical state. The first step toward resolving this paradox is to construct a new Hilbert space of de Sitter-invariant states. First, de Sitter-invariant states with infinite norm are constructed by smearing the states in the original Fock space of linearized gravity over the de Sitter group. Next, a new finite inner product of these states is defined by dividing the original inner product by the infinite volume of the de Sitter group. Then an orthonormal basis for de Sitter-invariant states is given. (The construction of this orthonormal basis provides a proof of the positive-definiteness of the new inner product.) The Hilbert space of de Sitter-invariant states thus obtained is hoped to serve as a starting point towards defining a meaningful perturbative gravity (at the tree level) in de Sitter spacetime.

Magnetic field induced by vacuum polarization in de Sitter spacetime.

We derive the effective Lagrangian of a magnetic field in the context of a massless scalar QED coupled to gravity in de Sitter spacetime. It is found that the magnetic field is produced at the beginning of the inflation in a minimally coupled scalar QED, and that the intensity B is proportional to ${\mathrm{eH}}^{2}$ (H is the Hubble constant). When H${=10}^{15}$ GeV, B\ensuremath{\sim}1.3\ifmmode\times\else\texttimes\fi{}${10}^{47}$ G.