We investigate the quantum Ricci curvature, which was introduced in earlier work, in full, four-dimensional quantum gravity, formulated nonperturbatively in terms of Causal Dynamical Triangulations (CDT). A key finding of the CDT approach is the emergence of a universe of de Sitter-type, as evidenced by the successful matching of Monte Carlo measurements of the quantum dynamics of the global scale factor with a semiclassical minisuperspace model. An important question is whether the quantum universe exhibits semiclassicality also with regard to its more local geometric properties. Using the new quantum curvature observable, we examine whether the (quasi-)local properties of the quantum geometry resemble those of a constantly curved space. We find evidence that on sufficiently large scales the curvature behaviour is compatible with that of a four-sphere, thus strengthening the interpretation of the dynamically generated quantum universe in terms of a de Sitter space.
The general plane wave solutions of the Proca field in conformal charts of the de Sitter expanding universe are derived for arbitrary polarizations showing how the frequencies can be separated in rest frames, defining thus the rest frame vacuum of this field.
We demonstrate that the static ground state atom, which interacts with a conformally coupled massless scalar field in the de Sitter invariant vacuum, can obtain a position-dependent energy-level shift and this shift could cause a Casimir-Polder-like force on it. Interestingly no such force arises on the inertial atom bathed in a thermal radiation in the Minkowski universe. Thus, although the energy-level shifts of the static atom for these two cases are structurally the same, whether the energy-level shift causes the Casimir-Polder-like force, in principle, could be as an indicator to distingu…
Motivated by the dark energy issue, the one-loop quantization approach for a class of relativistic higher order theories is discussed in some detail. A specific F(R,P,Q) gravity model at the one-loop level in a de Sitter universe is investigated, extending the similar program developed for the case of $F(R)$ gravity. The stability conditions under arbitrary perturbations are derived.
We investigate the global spacetime structure of torus de Sitter universe, which is exact de Sitter space with torus identification based on the flat chart. We show that past incomplete null geodesics in torus de Sitter universe are locally extendible. Then we give an extension of torus de Sitter universe so that at least one of the past incomplete null geodesics in the original spacetime becomes complete. However we find that extended torus de Sitter universe has two ill behaviors. The first one is a closed causal curve. The second one is so called quasi regular singularity, which means that …
By making use of the background field method, the one-loop quantization for Euclidean Einstein-Weyl quadratic gravity model on the de Sitter universe is investigated. Using generalized zeta function regularization, the on-shell and off-shell one-loop effective actions are explicitly obtained and one-loop renormalizability, as well as the corresponding one-loop renormalization group equations, are discussed. The so called critical gravity is also considered.
We consider the brane universe in the bulk background of the topological AdS-Schwarzschild black holes, where the brane tension takes larger value than the fine-tunned value. The resulting universe is radiation dominated and has positive cosmological constant. We obtain the associated cosmological Cardy formula and the Cardy-Verlinde formula. We also derive the Hubble and the Bekenstein entropy bounds from the conjectured holography bound on the Casimir entropy.
We construct explicit mode expansions of various tree-level propagators in the Rindler -- de Sitter universe, also known as the static (or compact) patch of the de Sitter spacetime. We construct in particular the Wightman functions for thermal states having a generic temperature $T$. We give a fresh simple proof that the only thermal Wightman propagator that respects the de Sitter isometry is the restriction to the Rindler -- de Sitter wedge of the propagator for the Bunch--Davies state. It is the thermal state with $T = (2 π)^{-1}$ in the units of de Sitter curvature. We show that propagators…
We propose to embed de Sitter space into five dimensional anti-de Sitter space to compute some physical quantities of interest, using the AdS/CFT correspondence. The static de Sitter can be considered as the conformal structure of the boundary of the hyperbolic AdS5 with a horizon, thus energy as well as entropy can be computed. The global dS can be embedded into a half-global AdS5, and the dS entropy can be regarded as entanglement entropy in this case. Finally, the inflationary dS can also be regarded as the boundary of AdS5, and this can be extended to include general cosmology with a posit…
We investigate main properties and mutual relations of the so-called A and B-metrics with any value of the cosmological constant. In particular, we explicitly show that both the AII and BI-metrics are, in fact, the famous Schwarzschild-(anti-)de Sitter spacetime (that is the AI-metric) boosted to superluminal speed. Together they form the complete gravitational field of a tachyon in Minkowski or (anti-)de Sitter universe. The boundary separating the AII and BI regions is the Mach-Cherenkov shockwave on which the curvature is unbounded. We analyze various geometric features of such spacetimes, …
The possibility of quantum creation of a dilatonic AdS Universe is discussed.Without dilaton it is known that quantum effects lead to the annihilation of AdS Universe. We consider the role of the form for the dilatonic potential in the quantum creation of a dilatonic AdS Universe. Using the conformal anomaly for dilaton coupled scalar, the anomaly induced action and the equations of motion are obtained. The anomaly induced action is added to classical dilaton gravity action. The solutions of the full theory which correspond to quantum-corrected AdS Universe are given for number of dilatonic po…
We provide a construction of a class of local and de Sitter covariant tachyonic quantum fields which exist for discrete negative values of the squared mass parameter and which have no Minkowskian counterpart. These quantum fields satisfy an anomalous non-homogeneous Klein-Gordon equation. The anomaly is a covariant field which can be used to select the physical subspace (of finite codimension) where the homogeneous tachyonic field equation holds in the usual form. We show that the model is local and de Sitter invariant on the physical space. Our construction also sheds new light on the massles…
We show that a simple sub-class of Horndeski theory can describe a time crystal Universe. The time crystal Universe can be regarded as a baby Universe nucleated from a flat space, which is mediated by an extension of Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory. Remarkably, when a cosmological constant is included, de Sitter Universe can be created by tunneling from the time crystal Universe. It gives rise to a past completion of an inflationary Universe.
We study bosonic Quantum Field Theory on the double covering $\widetilde{dS}_{2}$ of the 2-dimensional de Sitter universe, identified to a coset space of the group $SL(2,{\Bbb R})$. The latter acts effectively on $\widetilde{dS}_{2}$ and can be interpreted as it relativity group. The manifold is locally identical to the standard the Sitter spacetime ${dS}_2$; it is globally hyperbolic, geodesically complete and an inertial observer sees exactly the same bifurcate Killing horizons as in the standard one-sheeted case. The different global Lorentzian structure causes however drastic differences b…
We show that the quantum universe emerging from a nonperturbative, Lorentzian sum-over-geometries can be described with high accuracy by a four-dimensional de Sitter spacetime. By a scaling analysis involving Newton's constant, we establish that the linear size of the quantum universes under study is in between 17 and 28 Planck lengths. Somewhat surprisingly, the measured quantum fluctuations around the de Sitter universe in this regime are to good approximation still describable semiclassically. The numerical evidence presented comes from a regularization of quantum gravity in terms of causal…
We perform the resummation of the infrared logarithms in the inflationary universe. Applying the renormalization group, we derive the stochastic equations as the effective theory at the horizon. We focus on the conformal zero mode to respect local Lorentz symmetry. Under Gaussian approximation, we derive the fundamental equation for the Universe (EqU). We also derive the identical equation from the first law of thermodynamics in a dual geometric picture. We believe it is a convincing evidence for de Sitter duality between quantum stochastic physics on the boundary and classical thermodynamics …
Over the years, de Sitter spacetime has been a central focus, in studies involving quantum fields, for its importance in the early and late expansion stages of the universe. While de Sitter spacetime closely mimics characteristics of the inflationary and dark energy dominated universe it does not help to understand the radiation and matter dominated expansions. In this review, we revisit some recent works, involving the author, which study gravitational particle creation beyond the de Sitter stage. Specifically, we present novel aspects of particle creation in the radiation dominated universe,…
We describe a few unexpected features of de Sitter Quantum Field Theory that have no Minkowskian counterparts. These phenomena show that even when the cosmological constant is tiny a Minkowskian way of fast thinking about de Sitter can lead to mistakes and that de Sitter QFT is essentially different from standard relativistic (Minkowskian) QFT.
A semi-classical analysis of vacuum energy in the expanding spacetime suggests that the cosmological term decays with time, with a concomitant matter production. For early times we find, in Planck units, $Λ\approx H^4$, where H is the Hubble parameter. The corresponding cosmological solution has no initial singularity, existing since an infinite past. During an infinitely long period we have a quasi-de Sitter, inflationary universe, with $H \approx 1$. However, at a given time, the expansion undertakes a phase transition, with H and $Λ$ decreasing to nearly zero in a few Planck times, producin…
Radiative properties of gravitational and electromagnetic fields generated by uniformly accelerated charged black holes in asymptotically de Sitter spacetime are studied by analyzing the C-metric exact solution of the Einstein-Maxwell equations with a positive cosmological constant. Its global structure and physical properties are thoroughly discussed. We explicitly find and describe the specific pattern of radiation which exhibits the dependence of the fields on a null direction along which the (spacelike) conformal infinity is approached. This directional characteristic of radiation suppleme…
Poletti and Wiltshire have shown that, with the exception of a pure cosmological constant, the solution of a dilaton black hole in the background of de Sitter or anti-de Sitter universe, does not exist in the presence of one Liouville-type dilaton potential. Here with the combination of three Liouville-type dilaton potentials, we obtain the dilaton black hole solutions in the background of de Sitter or anti-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 Sitter universe.
We construct simple standing wave solutions in a 5D space-time with a ghost scalar field. The nodes of these standing waves are 'islands' of 4D Minkowski space-time. For the 5D model with increasing (decreasing) warp factor there are a finite (infinite) number of nodes and thus Minkowski island-universes having different parameters, such as gravitational and cosmological constants. This feature is similar to the assumptions of the landscape models, which postulate a large number of universes with different parameters. This standing wave solution also provides a new localization mechanism - mat…
We study gravitational and electromagnetic radiation generated by uniformly accelerated charged black holes in anti-de Sitter spacetime. This is described by the C-metric exact solution of the Einstein-Maxwell equations with a negative cosmological constant Lambda. We explicitly find and interpret the pattern of radiation that characterizes the dependence of the fields on a null direction from which the (timelike) conformal infinity is approached. This directional pattern exhibits specific properties which are more complicated if compared with recent analogous results obtained for asymptotic b…
We discuss the spectrum of the tensor metric perturbations and the stability of warped compactifications with the de Sitter spacetime in the higher-dimensional gravity. The spacetime structure is given in terms of the warped product of the non-compact direction, the spherical internal dimensions and the four-dimensional de Sitter spacetime. To realize a finite bulk volume, we construct the brane world model, using the cut-copy-paste method. Then, we compactify the spherical directions on the brane. In any case, we show the existence of the massless zero mode and the mass gap of it with massive…
In this note we investigate outcomes of a symplectic formula for the gravitational waves charges in the general relativity linearized around the de Sitter spacetime. We derive their explicit form at {\it scri} in the Bondi frame, compare with the connected Noether expression and analyze their gauge dependence which allows us to fix unambiguously boundary terms. We also discuss minimal requirements needed to impose on initial data to have finite values of charges. Furthermore, we analyze transformation laws of the energy upon the action of the de Sitter group and discuss its physical interpreta…
Observational evidence suggests that our universe is currently evolving towards an asymptotically de Sitter future. Unfortunately and in spite of much recent attention, various quantum, holographic and cosmological aspects of de Sitter space remain quite enigmatic. With such intrigue in mind, this paper considers the ``construction'' of a toy model that describes an asymptotically de Sitter universe. More specifically, we add fluid-like matter to an otherwise purely de Sitter spacetime, formulate the relevant solutions and then discuss the cosmological and holographic implications. If the obje…
Semiclassical Physics in gravitational scenario, in its first approximation (1st order) cares only for the expectation value of stress energy tensor and ignores the inherent quantum fluctuations thereof. In the approach of stochastic gravity, on the other hand, these matter fluctuations are supposed to work as the source of geometry fluctuations and have the potential to render the results from 1st order semiclassical physics irrelevant. We study the object of central significance in stochastic gravity, i.e. the noise kernel, for a wide class of Friedmann space-times. Through an equivalence of…
Fermion production in an external Coulomb field on de Sitter expanding universe is studied. The amplitude and probability of pair production in an external Coulomb field are computed and the cases of large/small values of the expansion factor comparatively with the particle mass are studied. We obtain from our calculations that the modulus of the momentum is no longer a conserved quantity. We find that in the de Sitter space there are probabilities for production processes where the helicity is no longer conserved. For a vanishing expansion factor we recover the Minkowski limit where the ampli…
In this paper we study the charged electro-weak interactions in the de Sitter geometry. We develop the reduction formalism for the Proca field with the help of the solutions for the interacting fields. Perturbation theory is used for obtaining the definition of the transition amplitudes in the first order. We apply our formalism to the study of spontaneous vacuum emission of fermions, anti-fermions and $W^{\pm}$ bosons in the expanding de Sitter universe. Our results are generalizations of the Weinberg-Salam electro-weak theory to curved space-time, in the case of $W^{\pm}$ boson interaction w…
The previous discussion \cite{ezawa} on reducing the phase space of the first order Einstein gravity in 2+1 dimensions is reconsidered. We construct a \lq\lq correct" physical phase space in the case of positive cosmological constant, taking into account the geometrical feature of SO(3,1) connections. A parametrization which unifies the two sectors of the physical phase space is also given.
The lowest order contribution of the amplitude of the Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given momentum and helicity. One studies the difficulties that arises when one passes from the amplitude to cross section.
The lowest order contribution of the amplitude of Dirac-Coulomb scattering in de Sitter spacetime is calculated assuming that the initial and final states of the Dirac field are described by exact solutions of the free Dirac equation on de Sitter spacetime with a given energy and helicity. We find that the total energy is conserved in the scattering process.
We study the proposal that a de Sitter (dS) universe with an Anti-de Sitter (AdS) bubble can be replaced by a dS universe with a boundary CFT. To explore this duality, we consider incident gravitons coming from the dS universe through the bubble wall into the AdS bubble in the original picture. In the dual picture, this process has to be identified with the absorption of gravitons by CFT matter. We have obtained a general formula for the absorption probability in general $d+1$ spacetime dimensions. The result shows the different behavior depending on whether spacetime dimensions are even or od…
We present a detailed analysis of a quantum model for Loop Quantum Cosmology based on strict application of the Thiemann regularization algorithm for the Hamiltonian in Loop Quantum Gravity, extending the results presented previously in our brief report. This construction leads to a qualitative modification of the bounce paradigm. Quantum gravity effects still lead to a quantum bounce connecting deterministically large classical Universes. However, the evolution features a large epoch of de Sitter Universe, with emergent cosmological constant of Planckian order, smoothly transiting into a spat…
We perform a foliation of a four dimensional Riemannian space-time with respect to a discrete time which is an integer multiple of the Planck time. We find that the quantum fluctuations of the metric have a discrete energy spectrum. The metric field is expanded in stationary eigenstates, and this leads to the description of a de Sitter-like universe. At the Planck scale the model describes a Planckian Euclidean black hole.
We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and causal properties, present details of the numerical set-up and explain how to extract "volume profiles". Extensive Monte Carlo measurements of the system show the emergence of a de Sitter universe on large scales from the underlying quantum ensemble, similar to what was observed previously in standard CDT quantum gravity. This provides evidence that the disting…
Casimir-Polder interaction arises from the vacuum fluctuations of quantum field that depend on spacetime curvature and thus is spacetime-dependent. Here we show how to use the resonance Casimir-Polder interaction (RCPI) between two entangled atoms to detect spacetime curvature. We find that the RCPI of two static entangled atoms in the de Sitter-invariant vacuum depends on the de Sitter spacetime curvature relevant to the temperature felt by the static observer. It is characterized by a $1/L^2$ power law decay when beyond a characteristic length scale associated to the breakdown of a local ine…
We discuss the role of conformal matter quantum effects (using large $N$ anomaly induced effective action) to creation-annihilation of an Anti-de Sitter Universe. The arbitrary GUT with conformally invariant content of fields is considered. On a purely gravitational (supersymmetric) AdS background, the quantum effects act against an (already existing) AdS Universe. The annihilation of such a Universe occurs, what is common for any conformal matter theory. On a dilaton-gravitational background, where there is dilatonic contribution to the induced effective action, the quantum creation of an AdS…
Motivated by the dark energy issue, the one-loop quantization approach for a family of relativistic cosmological theories is discussed in some detail. Specifically, general $f(R)$ gravity at the one-loop level in a de Sitter universe is investigated, extending a similar program developed for the case of pure Einstein gravity. Using generalized zeta regularization, the one-loop effective action is explicitly obtained off-shell, what allows to study in detail the possibility of (de)stabilization of the de Sitter background by quantum effects. The one-loop effective action maybe useful also for t…
Viable models of modified gravity which satisfy both local as well as cosmological tests are investigated. It is demonstrated that some versions of such highly non-linear models exhibit multiply de Sitter universe solutions, which often appear in pairs, being one of them stable and the other unstable. It is explicitly shown that, for some values of the parameters, it is possible to find several de Sitter spaces (as a rule, numerically); one of them may serve for the inflationary stage, while the other can be used for the description of the dark energy epoch. The numerical evolution of the effe…
We study the effect of a bubble wall on the entanglement entropy of a free massive scalar field between two causally disconnected open charts in de Sitter space. We assume there is a delta-functional wall between the open charts. This can be thought of as a model of pair creation of bubble universes in de Sitter space. We first derive the Euclidean vacuum mode functions of the scalar field in the presence of the wall in the coordinates that respect the open charts. We then derive the Bogoliubov transformation between the Euclidean vacuum and the open chart vacua that makes the reduced density …
The dynamical generation of a four-dimensional classical universe from nothing but fundamental quantum excitations at the Planck scale is a long-standing challenge to theoretical physicists. A candidate theory of quantum gravity which achieves this goal without invoking exotic ingredients or excessive fine-tuning is based on the nonperturbative and background-independent technique of Causal Dynamical Triangulations. We demonstrate in detail how in this approach a macroscopic de Sitter universe, accompanied by small quantum fluctuations, emerges from the full gravitational path integral, and ho…
I study the global structure of de Sitter space in the semi-classical and one-loop approximations to quantum gravity. The creation and evaporation of neutral black holes causes the fragmentation of de Sitter space into disconnected daughter universes. If the black holes are stabilized by a charge, I find that the decay leads to a necklace of de Sitter universes (`beads') joined by near-extremal black hole throats. For sufficient charge, more and more beads keep forming on the necklace, so that an unbounded number of universes will be produced. In any case, future infinity will not be connected…
We observe that the equation of motion for a free scalar field in a closed universe with radiation and a positive cosmological constant is given by Lamé's equation. Computing the exact power spectrum of scalar field perturbations, the presence of both curvature and radiation produces a red tilt weakly dependent on the amount of radiation.
Assuming both that our Universe is evolving into a de Sitter space and a vanishing cosmological constant, leaves only the option that the observed acceleration is provided by a "kinetic" energy of a scalar field. From an effective field theory point of view, the absence of Ostrogradsky instabilities restricts the choice to shift-symmetric Horndeski theories. Within these theories, we find the conditions for the existence of a de Sitter critical point in a universe filled by matter, radiation and a Horndeski scalar. Moreover, we show that this point is a universal attractor and we provide the t…
An accelerated boundary correspondence (ABC) is solved for the de Sitter moving mirror cosmology. The beta Bogoliubov coefficients reveal the particle spectrum is a Planck distribution with temperature inversely proportional to horizon radius. The quantum stress-tensor indicates a constant emission of energy flux consistent with eternal equilibrium, while the total energy carried by the particles remains finite. The curved spacetime transformation to flat spacetime with an accelerated boundary is illustrated, and also shown for Anti-de Sitter (AdS) spacetime.
A nonlocal gravity model, which does not assume the existence of a new dimensional parameter in the action and includes a function $f(\Box^{-1} R)$, with $\Box$ the d'Alembertian operator, is considered. The model is proven to have de Sitter solutions only if the function f satisfies a certain second-order linear differential equation. The de Sitter solutions corresponding to the simplest case, an exponential function f, are explored, without any restrictions on the parameters. If the value of the Hubble parameter is positive, the de Sitter solution is stable at late times, both for negative a…
We perform a minisuperspace analysis of an information-theoretic nonlinear Wheeler-deWitt (WDW) equation for de Sitter universes. The nonlinear WDW equation, which is in the form of a difference-differential equation, is transformed into a pure difference equation for the probability density by using the current conservation constraint. In the present study we observe some new features not seen in our previous approximate investigation, such as a nonzero minimum and maximum allowable size to the quantum universe: An examination of the effective classical dynamics supports the interpretation of…
In this paper we study the propagation in a de Sitter universe of gravitational waves generated by perturbating some unspecified spherical astrophysical object in the frequencies domain. We obtain the axial and polar perturbation equations in a cosmological de Sitter universe in the usual comoving coordinates, the coordinates we occupy in our galaxy. We write down the relevant equations in terms of Laplace transform with respect to the comoving time $t$ instead of the usual Fourier one that is no longer available in a cosmological context. Both axial and polar perturbation equations are expres…
We study particle decay in de Sitter space-time as given by first order perturbation theory in an interacting quantum field theory. We show that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur there. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. Particles with lower mass are even stranger: The masses of their decay products must obey quantification rules, and their lifetime is zero.
In this work, we investigate inflationary cosmology using scalar field theory deformed by the generalized uncertainty principle (GUP) containing a linear momentum term. Apart from being consistent with the existence of a minimum measurable length scale, this GUP is also consistent with doubly special relativity and hence with the existence of maximum measurable momentum. We use this deformed scalar field theory to analyze the tensor and scalar mode equations in a de Sitter background, and to calculate modifications to the tensor-to-scalar ratio. Finally, we compare our results for the tensor-t…
The scalar particle production from vacuum in the presence of electric field, on the de Sitter spacetime is studied. We use perturbation methods to define the transition amplitude. We obtain that the momentum is not conserved in this process. The probability of pair production is computed by squaring the transition amplitude. Our graphical representations shows that, the probability of scalar particle production was important only in early stage of the universe, when the Hubble's constant was very large in comparison with the mass of the particle. Also we propose here a criteria of particle-an…
