Cosmological Horizon Research Articles

Overview of thermodynamical properties for Reissner–Nordström–de Sitter spacetime in induced phase space

Since the black hole and cosmological horizons in the de Sitter (dS) spacetime with the Reissner–Nordström (RN) black hole are not independent with each other, which is caused by the gravitational effect, the interplay between two horizons should be considered. Based on this, by introducing the interactive entropy the RN–dS spacetime is analogous to a thermodynamic system with various thermodynamic quantities, in which the laws of thermodynamics still hold on. In our work, the thermodynamic properties of the RN–dS spacetime are mapped out in the induced phase space, which are similar to that in AdS black holes. The phase transition of the RN–dS spacetime between the high-potential and the low-potential black hole phases is observed. Compared with an ordinary thermodynamic system, the similar behaviors about the Joule–Thomson expansion and the critical exponents are also checked out. Finally, the scalar curvatures of two existent phases are presented to reveal the underlying microstructure and nature of phase transition in the RN–dS spacetime, which opens a new window to investigate the dS spacetime with black holes from an observational perspective.

Hidden conformal symmetries in Kerr–de Sitter spacetime revisited

We study the holographic picture for the Kerr–de Sitter spacetime with multiple horizons. Motivated by the studies of hidden conformal symmetry that associates to the black hole horizon, we show that such symmetry can also exist for the cosmological horizon that can lead us to the holographic calculation for the cosmological horizon entropy. To support the holography, we provide the scalar scattering calculation in the corresponding near region of each horizon by using the dual CFT formula. As one would expect, the cosmological horizon entropy and the associated scalar scattering can be understood by using a two dimensional conformal field theory.

A consistent approach to the path integral formalism of quantum mechanics based on the maximum length uncertainty

We have developed a proper path integral formalism consistent with the deformed version of the quantum mechanics that contains a maximum observable length scale at the order of the cosmological particle horizon, existing in cosmology. We have started by modifying the classical mechanics which shows non-minimal effects on the equation of motion of a particle. Next, we have provided representation of the deformed quantum mechanical algebra. With this algebra in hand, we have calculated the general form of the path integral propagator in this deformed background. Thereafter, as a most simple case, we have built up the explicit form of the free particle propagator. The modifications to the free particle propagator show some non-trivial effects in this case. Our formalism can be applied to analyze the quantum properties and observations emerging in the context of cosmology.

Cosmology in Painlevé-Gullstrand coordinates

Cosmology is most typically analyzed using standard co-moving coordinates, in which the galaxies are (on average, up to presumably small peculiar velocities) “at rest”, while “space” is expanding. But this is merely a specific coordinate choice; and it is important to realise that for certain purposes other, (sometimes radically, different) coordinate choices might also prove useful and informative, but without changing the underlying physics. Specifically, herein we shall consider the k= 0 spatially flat FLRW cosmology but in Painlevé-Gullstrand coordinates — these coordinates are very explicitly not co-moving: “space” is now no longer expanding, although the distance between galaxies is still certainly increasing. Working in these Painlevé-Gullstrand coordinates provides an alternate viewpoint on standard cosmology, and the symmetries thereof, and also makes it somewhat easier to handle cosmological horizons. With a longer view, we hope that investigating these Painlevé-Gullstrand coordinates might eventually provide a better framework for understanding large deviations from idealized FLRW spacetimes. We illustrate these issues with a careful look at the Kottler and McVittie spacetimes.

Thermodynamics of the Reissner–Nordström-de Sitter spacetime with quintessence

For Anti-de Sitte (AdS) black holes, the isochoric heat capacity of system is vanished, while the isobaric heat capacity is not. However, this situation does not hold on for de Sitter (dS) black holes. In this work, by introducing the interaction between the black hole horizon and the cosmological horizon of the Reissner–Nordström-de Sitter (RNdS) spacetime with quintessence, we discuss the phase transition of this system. The results show that the spacetime not only has the similar phase transition behavior to that of Van der Waals (VdW) system, and the non-vanishing isochoric heat capacity fulfills the whole thermodynamics system. Through the discussion of the entropic force between two horizons, we find out the role of entropic force in the evolution of spacetime. In addition, we also study the influence of various parameters on the phase transition and entropic force, which will provide a new method for exploring the interaction among black hole molecules from a micro perspective.

Generalization of the quadrupole formula for the energy of gravitational radiation in de Sitter spacetime

We study gravitational radiation produced by time changing matter source in de Sitter spacetime. We consider a cosmological Killing horizon instead of the conformal boundary used in the radiation theory in the Minkowski spacetime. The energy of the radiation passing through the horizon is derived. Our result takes the form of a generalized quadruple formula expressed in terms of the mass and pressure quadruple moments and is written explicitly up to the first order in $\sqrt{\Lambda}$. The zeroth order term recovers the famous Einstein's quadruple formula obtained for the perturbed Minkowski spacetime, whereas the first order term is a new correction.

Motion of the charged test particle in the spinning nonlinear electromagnetic black hole

In this paper the motion of charged and uncharged test particles in the rotating nonlinearly charged black hole (BH) is examined. Its asymptotics can be de Sitter or anti--de Sitter, depending on the value of the nonlinear parameter; consequently this BH can present one, two or three horizons, the third one being the cosmological horizon in the de Sitter case. Angular and radial test particle motions are analyzed and compared with its linear electromagnetic counterpart, the Kerr-Newman black hole (KN-BH). Several differences arise with the KN-BH, namely, the equatorial asymmetry is enhanced by the nonlinear electrodynamics field and for charged particles the access to one of the poles is forbidden; besides, a second circular orbit in the neighborhood of the external horizon appears, and the presence of the nonlinear electromagnetic field increases the curvature producing bounded orbits closer to the horizon.

Islands in Kerr–de Sitter spacetime and their flat limit

We use quantum extremal island method to study the information paradox on certain cosmological setups known as three dimensional Kerr-de Sitter spacetimes. To do so, we couple an auxiliary flat bath system to this spacetime in timelike singularity and measure entropy of hawking radiation in its asymptotic regions where the gravity is weak. We show that adding island regions to the entanglement wedge of radiation causes its entropy to obey Page curve. The boundary of island i.e. quantum extremal surface is located outside the cosmological horizon in the region connected directly to the bath. Taking the flat-space limit from the location of island and its related calculation in the Kerr-de Sitter sapcetime results in the flat-space cosmology (FSC) island, scrambling time and also Page time that were obtained in our previous paper. We repeat the same calculation for the pure de Sitter spacetime and show that our setup which neglects the effect of backreaction, leads also to a quantum extremal surface outside the cosmological horizon. We calculate the scrambling time and confirm the idea that pure de Sitter spacetime is a fast scrambler.

Entanglement entropy in a four-dimensional cosmological background

We compute the holographic entanglement entropy of a thermalized CFT on a time-dependent background in four dimensions. We consider a slab configuration extending beyond the cosmological horizon of a Friedmann-Lemaitre-Robertson-Walker metric. We identify a volume term that corresponds to the thermal entropy of the CFT, as well as terms proportional to the proper area of the entangling surface which are associated with strongly entangled degrees of freedom in the vicinity of this surface or with the expansion.

AdS-Taub-NUT spacetimes and exact black bounces with scalar hair

We present a new family of exact four-dimensional Taub-NUT spacetimes in Einstein-$\Lambda$ theory supplemented with a conformally coupled scalar field exhibiting a power-counting super-renormalizable potential. The construction proceeds as follows: A solution of a conformally coupled theory with a conformal potential, henceforth the seed $(g_{\mu\nu},\phi)$, is transformed by the action of a specific change of frame in addition with a simultaneous shift of the seed scalar. The new configuration, $(\bar{g}_{\mu\nu},\bar{\phi})$, solves the field equations of a conformally coupled theory with the aforementioned super-renormalizable potential. The solution spectrum of the seed is notoriously enhanced. We highlight the existence of two types of exact black bounces given by de Sitter and anti-de Sitter geometries that transit across three different configurations each. The de Sitter geometries transit from a regular black hole with event and cosmological horizons to a bouncing cosmology connecting two de Sitter Universes with different values of the asymptotic cosmological constant. An intermediate phase represented by a de Sitter wormhole or by a bouncing cosmology that connects two de Sitter Universes is shown, this under the presence of a cosmological horizon. On the other hand, the anti-de Sitter geometries transit from a regular black hole with inner and event horizons to a wormhole that connects two asymptotic boundaries with different constant curvatures. The intermediate phase is given by an anti-de Sitter regular black hole with a single event horizon that appears in two different settings. As a regular anti-de Sitter black hole inside of an anti-de Sitter wormhole or as an anti-de Sitter regular black hole with an internal cosmological bounce. These geometries are smoothly connected by the mass parameter only. Other black holes, bouncing cosmologies and wormholes are also found.

Holographic β Function in de Sitter Space

The scale invariance of the universe is slightly broken by slow roll parameters. It is likely the slow roll is dual to the random walk. We investigate the distribution function of the conformal zeromode. We identify de Sitter entropy $S_{dS}$ with the distribution entropy of the conformal zeromode $\rho(\omega)$. We have collected convincing support on our postulate. The semiclassical evidence is that the both are given by the gravitational coupling $1/g=\log N/2$ where $g=G_NH^2/\pi$ and $N$ is the e-folding number. We show the renormalized distribution function obeys gravitational Fokker-Planck equation (GFP) and Langevin equations . Under the Gaussian approximation, they boil down to a simple first order partial differential equation. The identical equation is derived by the thermodynamic arguments in the inflationary space-time. GFP determines the evolution of de Sitter entropy of the universe. It coincides with $\beta$ function of $g$. We find two types of the solutions of GFP:(1) UV complete spacetime and (2) inflationary spacetime with power potentials. The maximum entropy principle favors the scenario: (a) born small $\epsilon$ and (b) grow large by inflation. We like to convey the emerging notion of de Sitter duality. The inflationary universe: (bulk/geometrical) is dual to the stochastic space-time on the boundary (cosmological horizon ) as the both are the solutions of GFP.

On the perturbative formalism and a possible quantum Discrete spectrum for the Regge–Wheeler equation of a De Sitter spacetime

In this paper, we study the perturbative regime in the static patch of de Sitter metric in the Regge–Wheeler formalism. After realizing that perturbative regime in a de Sitter spacetime depicted in terms of usual spherical coordinates cannot be extended up to the cosmological horizon, we study perturbative equations, in particular the axial ones, in terms of the tortoise coordinate [Formula: see text]. We show that perturbative regime can be extended up to the cosmological horizon, provided that suitable boundary conditions are chosen. As an application, we explore the Regge–Wheeler equation at short distances by performing a Taylor expansion. In order to study some possible quantum effects at short distances, we impose to the equation so-obtained the same boundary conditions suitable for a quantum 3D harmonic oscillator. As a result, a discrete spectrum can be obtained. The aforementioned spectrum is analyzed and a relation with possible effects denoting quantum behavior of gravitons is suggested.

Thermodynamic ensembles with cosmological horizons

The entropy of a de Sitter horizon was derived long ago by Gibbons and Hawking via a gravitational partition function. Since there is no boundary at which to define the temperature or energy of the ensemble, the statistical foundation of their approach has remained obscure. To place the statistical ensemble on a firm footing we introduce an artificial “York boundary”, with either canonical or microcanonical boundary conditions, as has been done previously for black hole ensembles. The partition function and the density of states are expressed as integrals over paths in the constrained, spherically reduced phase space of pure 3+1 dimensional gravity with a positive cosmological constant. Issues related to the domain and contour of integration are analyzed, and the adopted choices for those are justified as far as possible. The canonical ensemble includes a patch of spacetime without horizon, as well as configurations containing a black hole or a cosmological horizon. We study thermodynamic phases and (in)stability, and discuss an evolving reservoir model that can stabilize the cosmological horizon in the canonical ensemble. Finally, we explain how the Gibbons-Hawking partition function on the 4-sphere can be derived as a limit of well-defined thermodynamic ensembles and, from this viewpoint, why it computes the dimension of the Hilbert space of states within a cosmological horizon.

Euclidean de Sitter black holes and microcanonical equilibrium

Schwarzschild-de Sitter (SdS) black holes do not admit a completely smooth Euclidean continuation. We discuss some modifications of the gravitational path integral that give Euclidean SdS a semiclassical equilibrium interpretation. First we consider "gravity in a cavity," defining the canonical ensemble in a box that excises one horizon. However, this standard approach does not work for positive cosmological constant: the solution of lowest free energy has a negative heat capacity, which is inconsistent if it is to provide the leading semiclassical contribution to a canonical partition function. Instead we modify the boundary conditions in the path integral to construct the microcanonical partition function, which appears to be well-defined. We then bring two ensembles into contact and remove the boundary, producing states of a larger microcanonical ensemble that contain, for example, both a black hole and a cosmological horizon at once. These systems are closed and have no boundary, but they must possess some form of mild metric discontinuity. We discuss the case where the discontinuity is equivalent to the insertion of a thin, rigid membrane, separating two systems that can exchange energy and are at local equilibrium. Equilibrium configurations obtained in this way are found to be thermodynamically unstable if they contain a black hole.

Unruh-DeWitt detectors in cosmological spacetimes

We analyze the response and thermal behavior of an Unruh-DeWitt detector as it travels through cosmological spacetimes, with special reference to the question of how to define surface gravity and temperature in dynamical spacetimes. Working within the quantum field theory on curved spacetime approximation, we consider a detector as it travels along geodesic and accelerated Kodama trajectories in de Sitter and asymptotically de Sitter FLRW spacetimes. By modelling the temperature of the detector using the detailed-balance form of the Kubo-Martin-Schwinger (KMS) conditions as it thermalizes, we can better understand the thermal behavior of the detector as it interacts with the quantum field, and use this to compare competing definitions of surface gravity and temperature that persist in the literature. These include the approaches of Kodama [Prog. Theor. Phys. 63, 1217 (1980).], Ashtekar and Krishnan [Living Rev. Relativity 7, 10 (2004).], Fodor et al. [Phys. Rev. D 54, 3882 (1996).], and Nielsen [Classical Quantum Gravity 23, 4637 (2006).]. While these are most often examined within the context of a dynamical black hole, here we shift focus to surface gravity on the evolving cosmological horizon.

Existence of Zero-Damped Quasinormal Frequencies for Nearly Extremal Black Holes

It has been observed that many spacetimes which feature a near-extremal horizon exhibit the phenomenon of zero-damped modes. This is characterised by the existence of a sequence of quasinormal frequencies which all converge to some purely imaginary number ialpha in the extremal limit and cluster in a neighbourhood of the line {{,mathrm{Im},}}s=alpha . In this paper, we establish that this property is present for the conformal Klein–Gordon equation on a Reissner–Nordström–de Sitter background. This follows from a similar result that we prove for a class of spherically symmetric black hole spacetimes with a cosmological horizon. We also show that the phenomenon of zero-damped modes is stable to perturbations that arise through adding a potential.

Possible signature of entanglement in null-energy-condition-violating inflation

In recent years, the classical version of the null energy condition (NEC) has been enhanced into its quantum generalization, the quantum null energy condition (QNEC). The right-hand side of the QNEC inequality is non-zero; it is multiplied by a factor of ћ and recovers the standard NEC in the classical limit. Moreover, the second derivative of entanglement entropy also plays a role in determining the right-hand side. In this work, we study several examples of theories of inflation that violate the standard NEC, yet still, possibly obey the QNEC. This suggests that the deviation of the standard NEC arises due to the existence of entanglement between regions inside and outside of the cosmological horizon. Possible connection to quantum fluctuations of de Sitter spacetime is also studied.

Special cosmological models derived from the semiclassical Einstein equation on flat FLRW space-times

This article presents numerical work on a special case of the cosmological semiclassical Einstein equation (SCE). The SCE describes the interaction of relativistic quantum matter by the expected value of the renormalized stress–energy tensor of a quantum field with classical gravity. Here, we consider a free, massless scalar field with general (not necessarily conformal) coupling to curvature. In a cosmological scenario with flat spatial sections for special choices of the initial conditions, we observe a separation of the dynamics of the quantum degrees of freedom from the dynamics of the scale factor, which extends a classical result by Starobinski (1980 Phys. Lett. B 91 99–102) to general coupling. For this new equation of fourth order governing the dynamics of the scale factor, we study numerical solutions. Typical solutions show a radiation-like Big Bang for the early Universe and de Sitter-like expansion for the late Universe. We discuss a specific solution to the cosmological horizon problem that can be produced by tuning parameters in the given equation. Although the model proposed here only contains massless matter, we give a preliminary comparison of the obtained cosmology with the ΛCDM standard model of cosmology and investigate parameter ranges in which the new models, to a certain extent, is capable of assimilating standard cosmology.

Observable effect of quantized cylindrical gravitational waves

We investigate the response of a model gravitational wave detector consisting of two particles to the quantized cylindrical gravitational waves and obtain a relation between the standard deviation of the distance between two particles and the distance from the source to the detector. It is found that the quantum effect carried by the cylindrical gravitational wave can be observed above Planck scale even though the source is as far as the cosmological horizon. The equation of motion for the change of the distance between two particles is obtained when the cylindrical gravitational waves pass. It is surprising that the dissipative term does not exist up to the first order approximation due to cylindrical symmetry of the gravitational wave.

Greybody factor for a static spherically symmetric black hole with non-linear electrodynamics

In this paper, we study the greybody factor for static spherically symmetric black hole with non-linear electrodynamics. For this purpose, we assume minimal coupling of the scalar field and find the radial equation by using the Klein–Gordon equation. We then apply tortoise coordinate to convert this equation into Schrodinger wave equation which helps to find the effective potential. The behavior of effective potential is checked for different values of the coupling and charge parameters. We find two solutions in two horizons named as event and cosmological horizons by using the radial equation. We consider the intermediate regime and match these two solutions to obtain the greybody factor and examine its behavior graphically. It is found that the greybody factor has an inverse relation with the coupling constant, mass, charge as well as the radius of the black hole and has a direct relation with angular momentum.