One-loop effective action for non-local modified Gauss–Bonnet gravity in de Sitter space

We discuss the classical and quantum properties of non-local modified Gauss–Bonnet gravity in de Sitter space, using its equivalent representation via string-inspired local scalar-Gauss–Bonnet gravity with a scalar potential. A classical, multiple de Sitter universe solution is found where one of the de Sitter phases corresponds to the primordial inflationary epoch, while the other de Sitter space solution—the one with the smallest Hubble rate—describes the late-time acceleration of our universe. A Chameleon scenario for the theory under investigation is developed, and it is successfully used to show that the theory complies with gravitational tests. An explicit expression for the one-loop effective action for this non-local modified Gauss–Bonnet gravity in the de Sitter space is obtained. It is argued that this effective action might be an important step towards the solution of the cosmological constant problem.     

Secular effects on inflation from one-loop quantum gravity

In this Letter we revisit and extend a previous analysis where the possible relevance of quantum gravity effects in a cosmological setup was studied. The object of interest are non-local (logarithmic) terms generated in the effective action of gravity due to the exchange in loops of massless modes (such as photons or the gravitons themselves). We correct one mistake existing in the previous work and discuss the issue in a more general setting in different cosmological scenarios. We obtain the one-loop quantum-corrected evolution equations for the cosmological scale factor up to a given order in a derivative expansion in two particular cases: a matter dominated universe with vanishing cosmological constant, and in a de Sitter universe. We show that the quantum corrections, albeit tiny, may have a secular effect that eventually modifies the expansion rate. For a de Sitter universe they tend to slow down the rate of the expansion, while the effect may be the opposite in a matter dominated universe.     

Gibbons-Hawking effect in the sonic de Sitter space-time of an expanding Bose-Einstein-condensed gas

We propose an experimental scheme to observe the Gibbons-Hawking effect in the acoustic analog of a (1+1)-dimensional de Sitter universe, produced in an expanding, cigar-shaped Bose-Einstein condensate. It is shown that a two-level system created at the center of the trap, an atomic quantum dot interacting with phonons, observes a thermal Bose distribution at the de Sitter temperature.     

The elliptic interpretation of black holes and quantum mechanics

The old “elliptic interpretation” of the Kruskal manifold is reviewed in the light of quantum mechanics. It is argued that its adoption would require giving up the complex structure of quantum mechanics and working with real Hilbert spaces. This may also be needed in cosmological theories in which the universe is CPT invariant. The cases of de Sitter and anti-de Sitter space are also discussed.     

Cosmological term in the general theory of relativity and localization of the de Sitter and Einstein groups

The theory of a gauge gravitational field with localization of the de Sitter group is formulated. Starting from the tetradic components of the de Sitter universe, a relationship is established between the Riemannian metric and the de Sitter gauge field. It is shown that the general theory of relativity with the cosmological term is the simplest variant of the de Sitter gauge theory of gravitation, which transforms in the limit of an infinite radius of curvature of the de Sitter universe into the Poincaré-invariant GTR without the cosmological term. A theory of a gauge gravitational field with localization of Einstein's group of motions of the uniform static universe (the Einstein group R × S0 (4)) is formulated in an analogous manner.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 86–90, August, 1984.     

A mesoscopic quantum gravity effect

We explore the symmetry reduced form of a non-perturbative solution to the constraints of quantum gravity corresponding to quantum de Sitter space. The system has a remarkably precise analogy with the non-relativistic formulation of a particle falling in a constant gravitational field that we exploit in our analysis. We find that the solution reduces to de Sitter space in the semi-classical limit, but the uniquely quantum features of the solution have peculiar property. Namely, the unambiguous quantum structures are neither of Planck scale nor of cosmological scale. Instead, we find a periodicity in the volume of the universe whose period, using the observed value of the cosmological constant, is on the order of the volume of the proton.     

Geometry of the quantum universe

A quantum universe with the global shape of a (Euclidean) de Sitter spacetime appears as dynamically generated background geometry in the causal dynamical triangulation (CDT) regularisation of quantum gravity. We investigate the micro- and macro-geometry of this universe, using geodesic shell decompositions of spacetime. More specifically, we focus on evidence of fractality and global anisotropy, and on how they depend on the bare coupling constants of the theory.     

Matching radiation-dominated and matter-dominated Einstein–de Sitter universes and an application for primordial black holes in evolving cosmological backgrounds

By matching across a surface of constant time, it is demonstrated that the spacetime for a radiation-dominated Einstein–de Sitter universe can be directly matched to the spacetime for a matter-dominated Einstein–de Sitter universe. Thus, this can serve as a model of a universe filled with radiation that suddenly is converted to matter and antimatter, or a universe filled with matter and antimatter that suddenly annihilates to leave radiation. This matching is shown to hold for asymptotically Einstein–de Sitter cosmological black hole spacetimes, yielding simplistic models of primordial black holes that evolve between being in radiation-dominated universes and matter-dominated universes.     

The euclidean vacuum: Justification from quantum cosmology

We evaluate the wave function of the universe for a de Sitter minisuperspace with inhomogeneous matter perturbations from a massive scalar field. From the Wheeler-DeWitt equation, we derive Schrödinger equations for the matter modes. We show that the matter part of the Hartle-Hawking wave function is the euclidean vacuum state of quantum field theory in curved spacetime.     

The semiclassical limit of causal dynamical triangulations

Previous work has shown that the macroscopic structure of the theory of quantum gravity defined by causal dynamical triangulations (CDT) is compatible with that of a de Sitter universe. After emphasizing the strictly nonperturbative nature of this semiclassical limit we present a detailed study of the three-volume data, which allows us to re-confirm the de Sitter structure, exhibit short-distance discretization effects, and make a first detailed investigation of the presence of higher-order curvature terms in the effective action for the scale factor. Technically, we make use of a novel way of fixing the total four-volume in the simulations.     

Holography and Non-Locality in a Closed Vacuum-Dominated Universe

A closed vacuum-dominated Friedmann universe is asymptotic to a de Sitter space with a cosmological event horizon for any observer. The holographic principle says the area of the horizon in Planck units determines the maximum number of bits of information about the universe that will ever be available to any observer. The wavefunction describing the probability distribution of mass quanta associated with bits of information on the horizon is the boundary condition for the wavefunction specifying the probability distribution of mass quanta throughout the universe. Local interactions between mass quanta in the universe cause quantum transitions in the wavefunction specifying the distribution of mass throughout the universe, with instantaneous non-local effects throughout the universe.     

Quantum Black Hole

Creation of a black hole in quantum cosmology is the third way of black hole formation. In contrast to the gravitational collapse from a massive body in astrophysics or from the quantum fluctuation of matter fields in the very early universe, in the quantum cosmology scenario the black hole is essentially created from nothing. The black hole originates from a constrained gravitational instanton. The probability of creation for all kinds of single black holes in the Kerr-Newman family, at the semiclassical level, is the exponential of the total entropy of the universe, or one quarter of the sum of both the black hole and the cosmological horizon areas. The de Sitter spacetime is the most probable evolution at the Planckian era.     

Cosmological perturbations and quantum fields in curved space

We identify the quantum theory of cosmological perturbations with the quantum field theory in curved spacetime with emphasis on its field concept. We materialize this idea by using a coherent state as a quantum analogue of a nontrivial classical field configuration. We present analytic results in a de Sitter universe for the massless and massive minimal free scalar fields. Some new features on the spectrum of perturbations are obtained for the massive case. We also show how such quantum field theories can be derived from quantum gravity using the semiclassical approximation. A physical degree of freedom is picked up from three scalar perturbations in the quantum gravity scalar system and its Schrödinger equation is derived. Peculiar features of quantum fields at imaginary time and its possible implications on boundary conditions for the wave function of the universe are also discussed.     

Triangular Invariants, Three-Point Functions and Particle Stability on the de Sitter Universe

We study a class of three-point functions on the de Sitter universe and on the asymptotic cone. A blending of geometrical ideas and analytic methods is used to compute some remarkable integrals, on the basis of a generalized star-triangle identity living on the cone and on the complex de Sitter manifold. We discuss an application of the general results to the study of the stability of scalar particles on the de Sitter universe.     

Quantum mechanics of the early universe

Quantum tunneling of the universe from nothing into a de Sitter vacuum, interpreted as the birth of the universe from a vacuum, is considered. Vilenkin's results are generalized by allowing for strings, domain walls, and various kinds of compressed matter that contribute to the potential through which the tunneling occurs. The energy spectrum of the universe in the quantum pre-de Sitter stage, the coefficient of passage through the potential barrier, which describes the probability of birth of the universe, and the conditions of applicability of the quasi-classical approximation in the calculation of these quantities are found.Brainstorm MNTP, Moscow. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 78–82, April, 1995.     

Neutrinos in a spherical de sitter universe: Exclusive properties of isotropic geodesics

The behavior of neutrinos as particles with spin 1/2 and with a strictly zero rest mass is studied. The qualitative differences between the case in which a particle's mass is small and that in which it is strictly zero are considered. In the former, a spin-1/2 particle must be described by a spinor, while in the latter, it can be described by a semispinor. These differences are manifested not only at the quantum but also at the classical level. It is essential that the case of a particle with a zero rest mass must be treated as strictly relativistic at any level. The exclusive properties of isotropic geodesic lines are considered. The chief one is their inherent conformal invariance. Because of it, the conformal angular momentum of a particle with zero rest mass is conserved in a Riemann universe that admits of a continuous group of conformal transformations. This is a 15-parameter group in a spherical de Sitter universe. Accordingly, 15 linearly independent, conformal momenta are conserved in it. The exclusive properties of isotropic geodesics in a spherical de Sitter universe are also manifested in the fact that they are straight in a five-dimensional, pseudo-Euclidean space enveloping that universe. Joint Institute for Nuclear Research. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 114–119, October, 1998.     

Is the compactified vacuum semiclassically unstable?

It is shown, by applying the positive-energy theorem, that the present vacuum (M⁴×K^D) in some higher-dimensional theories (e.g. the Candelas-Weinberg model) is stable against decay by quantum tunnelling without change of topology. Frieman and Kolb have found a quantum tunnelling instability of the present vacuum in the same models. But they did not take into account the gravitational effect, which is important and prevents the universe from decaying into the higher-dimensional de Sitter phase.     

The possible role of event-horizons in Quantum gravity

In this paper we extend to the de Sitter universe Bekenstein's result for the minimum variation of the black hole event-horizon area due to the absorption of an extended (classical) particle. Based on these equations we argue that at macroscopic scales the classical and quantum results should be in correspondence with each other (correspondence principle) and conclude that the event-horizon area is quantized in units of Planck's length squared. Consequences are discussed.     

Quantum instabilities and the cosmological constant

Several recent studies have found that the stress-energy of quantum fields in de Sitter space will take the form of a growing effective cosmological constant (Λ) with sign opposite to that of the background spacetime. This leads, in self-consistent scheme, to the spontaneous decay of the effective value of Λ, and has been proposed as a possible solution to the “problem of the cosmological constant”. By modeling the back-reaction of the spacetime to the quantum-stress-energy, it is shown that it is unlikely that such quantum instabilities can lower the value of Λ by a large factor and yield a universe even remotely like our own.     

The entangled accelerating universe

Using the known result that the nucleation of baby universes in correlated pairs is equivalent to spacetime squeezing, we show in this Letter that there exists a T-duality symmetry between two-dimensional warp drives, which are physically expressible as localized de Sitter little universes, and two-dimensional Tolman–Hawking and Gidding–Strominger baby universes respectively correlated in pairs, so that the creation of warp drives is also equivalent to spacetime squeezing. Perhaps more importantly, it has been also seen that the nucleation of warp drives entails a violation of the Bell's inequalities, and hence the phenomena of quantum entanglement, complementarity and wave function collapse. These results are generalized to the case of any dynamically accelerating universe filled with dark or phantom energy whose creation is also physically equivalent to spacetime squeezing and to the violation of the Bell's inequalities, so that the universe we are living in should be governed by essential sharp quantum theory laws and must be a quantum entangled system.