De Sitter Temperature Research Articles

Small Schwarzschild de Sitter black holes, the future boundary and islands

We continue the study of 4-dimensional Schwarzschild de Sitter black holes in the regime where the black hole mass is small compared with the de Sitter scale, following arXiv:2207.10724 [hep-th]. The de Sitter temperature is very low compared with that of the black hole. We consider the future boundary as the location where the black hole Hawking radiation is collected. Using 2-dimensional tools, we find unbounded growth of the entanglement entropy of radiation as the radiation region approaches the entire future boundary. Self-consistently including appropriate late time islands emerging just inside the black hole horizon leads to a reasonable Page curve. We also discuss other potential island solutions which show inconsistencies.

The minus sign in the first law of de Sitter horizons

Due to a well-known, but curious, minus sign in the Gibbons-Hawking first law for the static patch of de Sitter space, the entropy of the cosmological horizon is reduced by the addition of Killing energy. This minus sign raises the puzzling question how the thermodynamics of the static patch should be understood. We argue the confusion arises because of a mistaken interpretation of the matter Killing energy as the total internal energy, and resolve the puzzle by introducing a system boundary at which a proper thermodynamic ensemble can be specified. When this boundary shrinks to zero size the total internal energy of the ensemble (the Brown-York energy) vanishes, as does its variation. Part of this vanishing variation is thermalized, captured by the horizon entropy variation, and part is the matter contribution, which may or may not be thermalized. If the matter is in global equilibrium at the de Sitter temperature, the first law becomes the statement that the generalized entropy is stationary.

Small Schwarzschild de Sitter black holes, quantum extremal surfaces and islands

We study 4-dimensional Schwarzschild de Sitter black holes in the regime where the black hole mass is small compared with the de Sitter scale. Then the de Sitter temperature is very low compared with that of the black hole and we study the black hole, approximating the ambient de Sitter space as a frozen classical background. We consider distant observers in the static diamond, far from the black hole but within the cosmological horizon. Using 2-dimensional tools, we find that the entanglement entropy of radiation exhibits linear growth in time, indicative of the information paradox for the black hole. Self-consistently including an appropriate island emerging at late times near the black hole horizon leads to a reasonable Page curve. There are close parallels with flat space Schwarzschild black holes in the regime we consider.

Entanglement entropy of [formula omitted] de Sitter vacuum

de Sitter vacuum of nonconformal gauge theories is non-equilibrium, manifested by a nonvanishing rate of the comoving entropy production at asymptotically late times. This entropy production rate is related to the entanglement entropy of the de Sitter vacuum of the theory. We use holographic correspondence to compute vacuum entanglement entropy density sent of mass deformed N=4 supersymmetric Yang-Mills theory — the N=2⁎ gauge theory — for various values of the masses and the coupling constant to the background space-time curvature. For a particular choice of the curvature coupling, the Euclidean model can be solved exactly using the supersymmetric localization. We show that N=2⁎ de Sitter entanglement entropy is not the thermodynamic entropy of the localization free energy at de Sitter temperature. Neither it is related to the thermal entropy of de Sitter vacuum of pair-produced particles.

MOND as a regime of quantum gravity

We propose that there is a regime of quantum gravity phenomena, for the case that the cosmological constant is small and positive, which concerns phenomena at temperatures below the deSitter temperature, or length scales larger than the horizon. We observe that the standard form of the equivalence principle does not apply in this regime; we consider instead that a weakened form of the equivalence principle might hold in which the ratio of gravitational to inertial mass is a function of environmental and global parameters. We consider possible principles to determine that function. These lead to behaviour that, in the limit of hbar to zero and the speed of light is taken to infinity, reproduces the modifications of Newtonian dynamics first proposed by Milgrom. Thus MOND is elucidated as coding the physics of a novel regime of quantum gravity phenomena. We propose also an effective description of this regime in terms of a bi-metric theory, valid in the approximation where the metric is static. This predicts a new effect, which modifies gravity for radial motions.

Thermal interpretation of infrared dynamics in de Sitter

The infrared dynamics of a light, minimally coupled scalar field in de Sitter spacetime with Ricci curvature R = 12H2, averaged over horizon sized regions of physical volume VH = (4π/3)(1/H)3, can be interpreted as Brownian motion in a medium with de Sitter temperature TDS = ℏH/2π. We demonstrate this by directly deriving the effective action of scalar field fluctuations with wavelengths larger than the de Sitter curvature radius and generalizing Starobinsky's seminal results on stochastic inflation. The effective action describes stochastic dynamics and the fluctuating force drives the field to an equilibrium characterized by a thermal Gibbs distribution at temperature TDS which corresponds to a de Sitter invariant state. Hence, approach towards this state can be interpreted as thermalization. We show that the stochastic kinetic energy of the coarse-grained description corresponds to the norm of ∂μϕ and takes a well defined value per horizon volume ½⟨(∇ϕ)2⟩ = − ½TDS/VH. This approach allows for the non-perturbative computation of the de Sitter invariant stress energy tensor ⟨Tμν⟩ for an arbitrary scalar potential.

Horizon complementarity in elliptic de Sitter space

We study a quantum field in elliptic de Sitter space dS_4/Z_2 - the spacetime obtained from identifying antipodal points in dS_4. We find that the operator algebra and Hilbert space cannot be defined for the entire space, but only for observable causal patches. This makes the system into an explicit realization of the horizon complementarity principle. In the absence of a global quantum theory, we propose a recipe for translating operators and states between observers. This translation involves information loss, in accordance with the fact that two observers see different patches of the spacetime. As a check, we recover the thermal state at the de Sitter temperature as a state that appears the same to all observers. This thermal state arises from the same functional that, in ordinary dS_4, describes the Bunch-Davies vacuum.

Our Universe from the cosmological constant

The issue of the origin of the Universe and of its contents is addressed in the framework of bouncing cosmologies, as described for example by loop quantum gravity. If the current acceleration is due to a true cosmological constant, this constant is naturally conserved through the bounce and the Universe should also be in a (contracting) de Sitter phase in the remote past. We investigate here the possibility that the de Sitter temperature in the contracting branch fills the Universe with radiation that causes the bounce and the subsequent inflation and reheating. We also consider the possibility that this gives rise to a cyclic model of the Universe and suggest some possible tests.

Decoherence delays false vacuum decay

We show that gravitational interactions between massless thermal modes and a nucleating Coleman–de Luccia bubble may lead to efficient decoherence and strongly suppress metastable vacuum decay for bubbles that are small compared to the Hubble radius. The vacuum decay rate including gravity and thermal photon interactions has the exponential scaling , where ΓCDL is the Coleman–de Luccia decay rate neglecting photon interactions. For the lowest metastable initial state an efficient quantum Zeno effect occurs due to thermal radiation of temperatures as low as the de Sitter temperature. This strong decoherence effect is a consequence of gravitational interactions with light external mode. We argue that efficient decoherence does not occur for the case of Hawking–Moss decay. This observation is consistent with requirements set by Poincaré recurrence in de Sitter space.

The Thermodynamic Evolution of the Cosmological Event Horizon

By manipulating the integral expression for the proper radius R e of the cosmological event horizon (CEH) in a Friedmann-Robertson-Walker (FRW) universe we obtain an analytical expression for the change δR e in response to a uniform fluctuation δρ in the average cosmic background density ρ. We stipulate that the fluctuation arises within a vanishing interval of proper time, during which the CEH is approximately stationary, and evolves subsequently such that δρ/ρ is constant. The respective variations 2πR e δR e and δE e in the horizon entropy S e and enclosed energy E e should be therefore related through the cosmological Clausius relation. In that manner we find that the temperature T e of the CEH at an arbitrary time in a flat FRW universe is E e /S e , which recovers asymptotically the usual static de Sitter temperature. Furthermore it is proven that during radiation-dominance and in late times the CEH conforms to the fully dynamical First Law T e dS e =PdV e −dE e , where V e is the enclosed volume and P is the average cosmic pressure.

Acceleration-induced deconfinement transitions in de Sitter spacetime

In this note, we consider confining gauge theories in $D=2,3,4$ defined by $S^2$ or $T^2$ compactification of higher-dimensional conformal field theories with gravity duals. We investigate the behavior of these theories on de Sitter spacetime as a function of the Hubble parameter. We find that in each case, the de Sitter vacuum state of the field theory (defined by Euclidian continuation from a sphere) undergoes a deconfinement transition as the Hubble parameter is increased past a critical value. In each case, the corresponding critical de Sitter temperature is smaller than the corresponding Minkowski-space deconfinement temperature by a factor nearly equal to the dimension of the de Sitter spacetime. The behavior is qualitatively and quantitatively similar to that for confining theories defined by $S^1$ compactification of CFTs, studied recently in arXiv:1007.3996.

Thermodynamics of phantom energy in the presence of a Reissner-Nordström black hole

In this paper, we study the validity of the generalized second law (GSL) in phantom dominated universe in the presence of a Reissner-Nordström (RN) black hole. Our study is independent of the origin of the phantom like behavior of the considered universe. We also discuss the GSL in the neighborhood of transition from quintessence to phantom regime. We show that for a constant equation of state parameter, the GSL may be satisfied provided that the temperature is proportional to de Sitter temperature. It is shown that in models with (only) a transition from quintessence to phantom regime the generalized second law does not hold in the transition epoch. Next we show that if the phantom energy has a chemical potential, then the GSL will hold if the mass of black hole is above from a critical value.

Holographic models of de Sitter QFTs

We describe the dynamics of strongly coupled field theories in de Sitter spacetime using the holographic gauge/gravity duality. The main motivation for this is to explore the possibility of dynamical phase transitions during cosmological evolution. Specifically, we study two classes of theories: (i) conformal field theories on de Sitter in the static patch which are maintained in equilibrium at temperatures that may differ from the de Sitter temperature and (ii) confining gauge theories on de Sitter spacetime. In the former case we show that such states make sense from the holographic viewpoint in that they have regular bulk gravity solutions. In the latter situation we add to the evidence for a confinement/deconfinement transition for a large N planar gauge theory as the cosmological acceleration is increased past a critical value. For the field theories we study, the critical acceleration corresponds to a de Sitter temperature which is less than the Minkowski space deconfinement transition temperature by a factor of the spacetime dimension.

SEMICLASSICAL (QUANTUM FIELD THEORY) AND QUANTUM (STRING) DE SITTER REGIMES: NEW RESULTS

We compute the quantum string entropy S s (m, H) from the microscopic string density of states ρ s (m, H) of mass m in de Sitter space–time. We find for high m (high Hm → c/α') a new phase transition at the critical string temperature T s = (1/2πk B )L cl c2/α', higher than the flat space (Hagedorn) temperature t s (L cl = c/H, the Hubble constant H acts at the transition, producing a smaller string constant α' and thus, a higher tension). T s is the precise quantum dual of the semiclassical (QFT Hawking–Gibbons) de Sitter temperature T sem = ħ c/(2πk B L cl ). By precisely identifying the semiclassical and quantum (string) de Sitter regimes, we find a new formula for the full de Sitter entropy S sem (H), as a function of the usual Bekenstein–Hawking entropy [Formula: see text]. For L cl ≫ ℓ Planck , i.e. for low [Formula: see text] is the leading term, but for high H near c/ℓ Planck , a new phase transition operates and the whole entropy S sem (H) is drastically different from the Bekenstein–Hawking entropy [Formula: see text]. We compute the string quantum emission cross-section σ string by a black hole in de Sitter (or asymptotically de Sitter) space–time (bhdS). For T sem bhdS ℓ T s (early evaporation stage), it shows the QFT Hawking emission with temperature T sem bhdS (semiclassical regime). For T sem bhdS → T s , σ string exhibits a phase transition into a string de Sitter state of size [Formula: see text], [Formula: see text], and string de Sitter temperature T s . Instead of featuring a single pole singularity in the temperature (Carlitz transition), it features a square root branch point (de Vega–Sanchez transition). New bounds on the black hole radius r g emerge in the bhdS string regime: it can become r g = L s /2, or it can reach a more quantum value, r g = 0.365 ℓ s .

Schwarzschild black hole and generalized second law in phantom-dominated universe

In this Letter which is an extension of the work [G. Izquierdo, D. Pavon, Phys. Lett. B 639 (2006) 1], we study the conditions required for validity of the generalized second law in phantom-dominated universe in the presence of Schwarzschild black hole. Our study is independent of the origin of the phantom like behavior of the considered universe. We also discuss the generalized second law in the neighborhood of transition (from quintessence to phantom regime) time. We show that even for a constant equation of state parameter, the generalized second law may be satisfied provided that the temperature is not taken as de Sitter temperature. It is shown that in models with (only) a transition from quintessence to phantom regime the generalized second law does not hold in the transition epoch.

Coincident brane nucleation and the neutralization ofΛ

Nucleation of branes by a four-form field has recently been considered in string motivated scenarios for the neutralization of the cosmological constant. An interesting question in this context is whether the nucleation of stacks of coincident branes is possible, and if so, at what rate does it proceed. Feng et al. have suggested that, at high ambient de Sitter temperature, the rate may be strongly enhanced, due to large degeneracy factors associated with the number of light species living on the worldsheet. This might facilitate the quick relaxation from a large effective cosmological constant down to the observed value. Here, we analyse this possibility in some detail. In four dimensions, and after the moduli are stabilized, branes interact via repulsive long range forces. Because of that, the Coleman-de Luccia (CdL) instanton for coincident brane nucleation may not exist, unless there is some short range interaction which keeps the branes together. If the CdL instanton exists, we find that the degeneracy factor depends only mildly on the ambient de Sitter temperature, and does not switch off even in the case of tunneling from flat space. This would result in catastrophic decay of the present vacuum. If, on the contrary, the CdL instanton does not exist, coindident brane nucleation may still proceed through a "static" instanton, representing pair creation of critical bubbles -- a process somewhat analogous to thermal activation in flat space. In that case, the branes may stick together due to thermal symmetry restoration, and the pair creation rate depends exponentially on the ambient de Sitter temperature, switching off sharply as the temperature approaches zero. Such static instanton may be well suited for the "saltatory" relaxation scenario proposed by Feng et al.

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.

QFT, string temperature, and the string phase of de Sitter space-time

The density of mass levels $\ensuremath{\rho}(m)$ and the critical temperature for strings in de Sitter space-time are found. QFT and string theory in de Sitter space are compared. A ``dual'' transform is introduced which relates classical to quantum string lengths, and more generally, QFT and string domains. Interestingly, the string temperature in de Sitter space turns out to be the dual transform of the QFT Hawking-Gibbons temperature. The back reaction problem for strings in de Sitter space is addressed self-consistently in the framework of the ``string analogue'' model (or thermodynamical approach), which is well suited to combine QFT and string study. We find de Sitter space-time is a self-consistent solution of the semiclassical Einstein equations in this framework. Two branches for the scalar curvature $R(\ifmmode\pm\else\textpm\fi{})$ show up: a classical, low curvature solution $(\ensuremath{-}),$ and a quantum high curvature solution $(+),$ entirely sustained by the strings. There is a maximal value for the curvature ${R}_{\mathrm{max}}$ due to the string back reaction. Interestingly, our dual relation manifests itself in the back reaction solutions: the $(\ensuremath{-})$ branch is a classical phase for the geometry with the intrinsic temperature given by the QFT Hawking-Gibbons temperature. The $(+)$ is a stringy phase for the geometry with a temperature given by the intrinsic string de Sitter temperature. $2+1$ dimensions are considered, but conclusions hold generically in D dimensions.

Fermions in quantum cosmology.

This paper considers the extension of the ideas of quantum cosmology and, in particular, the proposal of Hartle and Hawking for the boundary conditions of the Universe, to models which incorporate fermions in a realistic manner. We consider inhomogeneous fermionic perturbations about a homogeneous, isotropic minisuperspace background model, by expanding the fermion fields in spinor harmonics on the spatial sections, taken to be three-spheres. The Dirac action is thus found to take the form of an infinite sum of terms, each describing a time-dependent Fermi oscillator. On quantization, we find that the Wheeler-DeWitt equation for the wave function of the Universe may be decomposed into a set of time-dependent Schroumldinger equations, one for each fermion mode, and a background minisuperspace Wheeler-DeWitt equation, which includes a term in its potential describing the back reaction of the fermionic perturbations on the homogeneous modes. Our quantization procedure employs the holomorphic representation for the fermion modes, which permits them to be treated in a manner very similar to the case of bosonic perturbations considered by Halliwell and Hawking. We set initial conditions for the Schr\odinger equations by applying the proposal of Hartle and Hawking that the quantum state of the Universe is defined by a path integral over compact four-metrics and regular matter fields. We find this to imply that the fermion modes start out in their ground state. Particles are created in the subsequent (inflationary) evolution, and their number, defined with respect to instantaneous Hamiltonian diagonalization, is calculated and is found to be finite. We calculate the back-reaction term and find, after regularization, that its effect is negligible. We construct a model of a fermionic particle detector and, in the case of an exact de Sitter background, examine its response to the state picked out by the Hartle-Hawking proposal. We show that it experiences a thermal spectrum at the de Sitter temperature, with a distribution of the Fermi-Dirac form, although the distribution does not have the correct density-of-states factor to be precisely Planckian.