Gibbons-Hawking Temperature Research Articles

Thermodynamics and Decay of de Sitter Vacuum

We discuss the consequences of the unique symmetry of de Sitter spacetime. This symmetry leads to the specific thermodynamic properties of the de Sitter vacuum, which produces a thermal bath for matter. de Sitter spacetime is invariant under the modified translations, r→r−eHta, where H is the Hubble parameter. For H→0, this symmetry corresponds to the conventional invariance of Minkowski spacetime under translations r→r−a. Due to this symmetry, all the comoving observers at any point of the de Sitter space perceive the de Sitter environment as the thermal bath with temperature T=H/π, which is twice as large as the Gibbons–Hawking temperature of the cosmological horizon. This temperature does not violate de Sitter symmetry and, thus, does not require the preferred reference frame, as distinct from the thermal state of matter, which violates de Sitter symmetry. This leads to the heat exchange between gravity and matter and to the instability of the de Sitter state towards the creation of matter, its further heating, and finally the decay of the de Sitter state. The temperature T=H/π determines different processes in the de Sitter environment that are not possible in the Minkowski vacuum, such as the process of ionization of an atom in the de Sitter environment. This temperature also determines the local entropy of the de Sitter vacuum state, and this allows us to calculate the total entropy of the volume inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which is attributed to the cosmological horizon, Shor=4πKA, where K=1/(16πG). This supports the holographic properties of the cosmological event horizon. We extend the consideration of the local thermodynamics of the de Sitter state using the f(R) gravity. In this thermodynamics, the Ricci scalar curvature R and the effective gravitational coupling K are thermodynamically conjugate variables. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon remains the same but with the gravitational coupling K=df/dR. Such a connection takes place only in the 3+1 spacetime, where there is a special symmetry due to which the variables K and R have the same dimensionality. We also consider the lessons from de Sitter symmetry for the thermodynamics of black and white holes.

BCS in the sky: signatures of inflationary fermion condensation

We consider a Bardeen-Cooper-Schrieffer (BCS)-like model in the inflationary background. We show that with an axial chemical potential, the attractive quartic fermion self-interaction can lead to a BCS-like condensation. In the rigid-de Sitter (dS) limit of inflation where backreaction from the inflaton and graviton is neglected, we perform the first computation of the non-perturbative effective potential that includes the full spacetime curvature effects in the presence of the chemical potential, subject to the mean-field approximation whose validity has been checked via the Ginzburg criterion. The corresponding BCS phase transition is always first-order, when the varying Hubble is interpreted as an effective Gibbons-Hawking temperature of dS spacetime. In the condensed phase, the theory can be understood from UV and IR sides as fermionic and bosonic, respectively. This leads to distinctive signatures in the primordial non-Gaussianity of curvature perturbations. Namely, the oscillatory cosmological collider signal is smoothly turned off at a finite momentum ratio, since different momentum ratios effectively probe different energy scales. In addition, such BCS phase transitions can also source stochastic gravitational waves, which are feasible for future experiments.

De Sitter Local Thermodynamics in f(R) Gravity

We consider the local thermodynamics of the de Sitter state in the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(\\mathcal{R})$$\\end{document} gravity. The local temperature, which is the same for all points of the de Sitter space, is \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}, where H is the Hubble parameter. It is twice larger than the Gibbons–Hawking temperature of the cosmological horizon, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{T}_{{{\ ext{GH}}}}} = H{\ ext{/}}2\\pi $$\\end{document}. The local temperature is not related to the cosmological horizon. It determines the rate of the activation processes, which are possible in the de Sitter environment. The typical example is the process of the ionization of the atom in the de Sitter environment, which rate is determined by temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}. The local temperature determines the local entropy of the de Sitter vacuum state, and this allows to calculate the total entropy inside the cosmological horizon. The result reproduces the Gibbons–Hawking area law, which corresponds to the Wald entropy, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{S}_{{{\ ext{hor}}}}} = 4\\pi KA$$\\end{document}. Here, K is the effective gravitational coupling, \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K = df{\ ext{/}}d\\mathcal{R}$$\\end{document}. In the local thermodynamic approach, K is the thermodynamic variable, which is conjugate to the Ricci scalar curvature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{R}$$\\end{document}. The holographic connection between the bulk entropy of the Hubble volume and the surface entropy of the cosmological horizon supports the suggestion that the de Sitter quantum vacuum is characterized by the local thermodynamics with the local temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document}. The local temperature \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$T = H{\ ext{/}}\\pi $$\\end{document} of the de Sitter vacuum suggests that the de Sitter vacuum is locally unstable towards the creation of matter and its further heating. The decay of the de Sitter vacuum due to such processes determines the quantum breaking time of the space-times with positive cosmological constant.

Analog of the Sommerfeld Law in Quantum Vacuum

The activation temperature T in the de Sitter environment is twice the Gibbons–Hawking temperature, related to the cosmological horizon. We consider the activation temperature as the local temperature of the de Sitter vacuum, and construct the local thermodynamics of the de Sitter state. This thermodynamics includes also the gravitational coupling K and the scalar Riemann curvature mathcal{R} as the thermodynamically conjugate variables. These variables modify the thermodynamics of the Gibbs–Duhem relation in the de Sitter state. The free energy density is proportional to - {{T}^{2}}, which is similar to that in the nonrelativistic Fermi liquids and in relativistic matter with equation of state w = 1. The local entropy is proportional to the local temperature, while the total entropy inside the cosmological horizon is A{text{/}}4G, where A is the area of the horizon. This entropy is usually interpreted as the entropy of the cosmological horizon. We also consider the possible application of the de Sitter thermodynamics to the Schwarzschild–de Sitter black hole and to black and white holes with the de Sitter cores.

Understanding thermal nature of de Sitter spacetime via inter-detector interaction

We investigate the interaction potential of two static detectors (atoms) at the same radial but different azimuthal coordinates in the de Sitter invariant vacuum. We show that for two detectors very far away from the cosmological horizon, the interaction potential is different from that of two static ones in a thermal bath in Minkowski spacetime at a temperature equal to the Gibbons-Hawking temperature, suggesting that de Sitter spacetime in regard to its thermal nature basically differs from a thermal bath in Minkowski spacetime. For two detectors very close to the cosmological horizon, the interaction potential behaves as ∼[TUρ4ln⁡(4TUρ)]−1 with TU and ρ the Unruh temperature associated with the proper acceleration and the proper separation of the detectors, which deviates dramatically from ∼(TUρ4)−1, the behavior of the interaction potential of two synchronously uniformly accelerated detectors in Minkowski spacetime, indicating that thermal nature of de Sitter spacetime also differs essentially from the Unruh thermal bath.

On the Global Temperature of the Schwarzschild–de Sitter Spacetime

It is shown that the Schwarzschild–de Sitter spacetime has the universal temperature. This temperature describes the thermal processes of decay of the composite particles and the other processes, which are energetically forbidden in the Minkowski spacetime, but are allowed in the de Sitter and in Schwarzschild–de Sitter backgrounds. In particular, this temperature describes the probability of ionization of the atom in the Schwarzschild–de Sitter, which is observed by the stationary observer at the point where the shift function (velocity) in the Arnowitt–Deser–Misner formalism changes sign. This activation temperature does not depend on the black hole mass and is fully determined by the Hubble parameter, {{T}_{{{text{SdS}}}}} = sqrt 3 H{text{/}}pi . This temperature is twice the Bousso–Hawking temperature {{T}_{{{text{BH}}}}}, which characterizes the limit of degenerate Lorentzian Schwarzschild–de Sitter universe, when the cosmological and black hole horizons are close to each other, {{T}_{{{text{SdS}}}}} = 2{{T}_{{{text{BH}}}}}. The similar doubling of the temperature of Hawking radiation is known in the pure de Sitter spacetime, where the corresponding local temperature describing the ionization of atoms is twice the Gibbons–Hawking temperature, {{T}_{{{text{dS}}}}} = 2{{T}_{{{text{GH}}}}} = H{text{/}}pi . We suggest that the activation temperature {{T}_{{{text{dS}}}}} can be considered as the thermodynamic temperature of the de Sitter state, which determines the local entropy in this state, s = 3H{text{/}}4G.

Unified formalism for the law of emergence from the first law of thermodynamics

We derive a unified expansion law for our Universe from the first law of thermodynamics on the apparent horizon, where entropic evolution depicts the emergence of cosmic space. The derivation advances a general form for degrees of freedom on the surface and bulk, which provides a natural generalization for the expansion law proposed by Padmanabhan. The general expression for the surface degrees of freedom differs from the natural expectation, ${N}_{\mathrm{sur}}=4S$ in the emergent gravity paradigm for general theories of gravity. The derivation also provides justification for the selection of Gibbons-Hawking temperature in the original expansion law and for the use of areal volume in the nonflat Friedmann-Robertson-Walker universe. Since the unified expansion law exclusively depends on the form of entropy, the method is applicable to obtain the expansion law in any gravity theory without any additional ad hoc assumptions. From the general expansion law, we have obtained the expansion law corresponding to different theories of gravity like ($n+1$) Einstein, Gauss-Bonnet, Lovelock, and Ho\ifmmode \check{r}\else \v{r}\fi{}ava-Lifshitz. We also obtained the expansion law for nonextensive entropy like Tsallis entropy from the unified expansion law.

Automorphic scalar fields in two-dimensional de Sitter space

We study non-interacting automorphic quantum scalar fields with positive mass in two-dimensional de Sitter space. We find that there are no Hadamard states which are de Sitter invariant except in the periodic case, extending the result of Epstein and Moschella for the anti-periodic case. We construct the two-point Wightman functions for the non-Hadamard de Sitter-invariant states by exploiting the fact that they are functions of the geodesic distance between the two points satisfying an ordinary differential equation. We then examine a certain Hadamard state, which is not de Sitter invariant, and show that it is approximately a thermal state with the Gibbons–Hawking temperature when restricted to a static region of the spacetime.

Radiative gravastar with Gibbons-Hawking temperature

We study the quantum particle creation in a toy model of spherically symmetric gravitational collapse whose final product is not a black hole but a gravastar. Precedent studies revealed that even in the case of the gravitational collapse to form a horizonless ultra-compact object, thermal radiation named transient Hawking radiation is generated at the late stage of the gravitational collapse, and a sudden stop of collapsing motion to form a horizonless ultra-compact object causes one or two bursts of quantum particle creation. The very different behavior of the model studied in this paper from the precedent ones is quantum radiation with a thermal spectrum from the gravastar between two bursts. The temperature of the radiation is not the same as the Hawking one determined by the gravitational mass of the system but the Gibbons-Hawking one of the de Sitter core inside the gravastar.

On thermal radiation of de Sitter space in the semiclassical Jackiw–Teitelboim model

In general, the Gibbons–Hawking temperature based on the Euclidean functional approach shows that de Sitter space in the Bunch–Davies vacuum is globally thermal. In the exactly soluble semiclassical Jackiw–Teitelboim model, we investigate thermal property of de Sitter space by taking into account the quantum back reaction of the geometry. The proper temperature of de Sitter space in the Bunch–Davies vacuum is found to vanish. In case of a certain quantum state breaking the de Sitter symmetry, de Sitter space can be made thermally exited; however, in this case the dilaton singularity cannot be avoided. Consequently, in the Jackiw–Teitelboim model the proper temperature of de Sitter space in the Bunch–Davies vacuum turns out to be zero and the Bunch–Davies vacuum is found to be the only physical vacuum without any naked singularities.

Expanding edges of quantum Hall systems in a cosmology language: Hawking radiation from de Sitter horizon in edge modes

Expanding edge experiments are promising to open new physics windows of quantum Hall systems. In a static edge, the edge excitation, which is described by free fields decoupled with the bulk dynamics, is gapless, and the dynamics preserve conformal symmetry. When the edge expands, such properties need not be preserved. We formulate a quantum field theory in 1+1 dimensional curved spacetimes to analyze the edge dynamics. We propose methods to address the following questions using edge waveforms from the expanding region: Does the conformal symmetry survive? Is the nonlinear interaction of the edge excitations induced by edge expansion? Do the edge excitations interact with the bulk excitations? We additionally show that the expanding edges can be regarded as expanding universe simulators of two-dimensional dilaton-gravity models, including the Jackiw-Teitelboim gravity model. As an application, we point out that our theoretical setup might simulate emission of analog Hawking radiation with the Gibbons-Hawking temperature from the future de Sitter horizon formed in the expanding edge region.

Can Gibbons–Hawking radiation and inflation arise due to spacetime quanta?

In this study, we provide an alternatively reformulated interpretation of Gibbons-Hawking radiation as well as inflation. By using a spacetime quantization procedure, proposed recently by L.C. C\'eleri et al., in anti-de Sitter space we show that Gibbons-Hawking radiation is an intrinsic property of the concerned space, that arises due to the existence of a scalar field whose quanta "carry" a length $l$ (i.e. the radius of the hyperboloid curvature). Furthermore, within the context of Tsallis q-framework, we propose an inflationary model that depends on the non-extensive parameter $q$. The main source of such an inflation is the same scalar field mentioned before. Being constrained by the observational data, the q-parameter along with the rest of the model's parameters has been used to estimate the time at which inflation ends as well as the reheating temperature. The latter is found to be related to Gibbons-Hawking temperature. Thus, the present model offers an alternative perspective regarding the nature of the cosmic background radiation (CMB).

Bell inequalities violation within non-Bunch–Davies states

In this Letter, we study the quantum nature of non-Bunch–Davies states in de Sitter space by evaluating CHSH inequality on a localized two-atom system. We show that quantum nonlocality can be generated through the Markovian evolution of two-atom, witnessed by a violation of CHSH inequality on its final equilibrium state. We find that the upper bound of inequality violation is determined by different choices of de Sitter-invariant vacua sectors. In particular, with growing Gibbons–Hawking temperature, the CHSH bound degrades monotonously for Bunch–Davies vacuum sector. Due to the intrinsic correlation of non-Bunch–Davies vacua, we find that the related violation of inequality can however drastically increase after certain turning point, and may persist for arbitrarily large environment decoherence. This implies that the CHSH inequality is useful to classify the initial quantum state of the Universe. Finally, we clarify that the witnessed intrinsic correlation of non-Bunch–Davies vacua can be utilized for quantum information applications, e.g., surpassing the Heisenberg uncertainty bound of quantum measurement in de Sitter space.

QCD axion window and low-scale inflation

We show that the upper bound of the classical QCD axion window can be significantly relaxed for low-scale inflation. If the Gibbons-Hawking temperature during inflation is lower than the QCD scale, the initial QCD axion misalignment angle follows the Bunch-Davies distribution. The distribution is peaked at the strong CP conserving minimum if there is no other light degree of freedom contributing to the strong CP phase. As a result, the axion overproduction problem is significantly relaxed even for an axion decay constant larger than $10^{12}$GeV. We also provide concrete hilltop inflation models where the Hubble parameter during inflation is comparable to or much smaller than the QCD scale, with successful reheating taking place via perturbative decays or dissipation processes.

Gibbons-Hawking radiation of gravitons in the Poincaré and static patches of de Sitter spacetime

We discuss the quantization of linearized gravity in the background de Sitter spacetime using a gauge-invariant formalism to write the perturbed gravitational field in the static patch. This field is quantized after fixing the gauge completely. The response rate of this field to monochromatic multipole sources is then computed in the thermal equilibrium state with the well known Gibbons-Hawking temperature. We compare this response rate with the one obtained in the Bunch-Davies-like vacuum state defined in the Poincar\'e patch. These response rates are found to be the same as expected. This agreement serves as a verification of the infrared finite graviton two-point function in the static patch of de Sitter spacetime found previously.

Quintessence Reissner Nordström Anti de Sitter Black Holes and Joule Thomson Effect

In this work we investigate corrections of the quintessence regime of the dark energy on the Joule-Thomson (JT) effect of the Reissner Nordstr\"om anti de Sitter (RNAdS) black hole. The quintessence dark energy has equation of state as $p_q=\omega\rho_q$ in which $-1<\omega<-\frac{1}{3}.$ Our calculations are restricted to ansatz: $\omega=-1$ (the cosmological constant regime) and $\omega=-\frac{2}{3}$ (quintessence dark energy). To study the JT expansion of the AdS gas under the constant black hole mass, we calculate inversion temperature $T_i$ of the quintessence RNAdS black hole where its cooling phase is changed to heating phase at a particular (inverse) pressure $P_i.$ Position of the inverse point $\{T_i,P_i\}$ is determined by crossing the inverse curves with the corresponding Gibbons-Hawking temperature on the T-P plan. We determine position of the inverse point verse different numerical values of the mass $M$ and the charge $Q$ of the quintessence AdS RN black hole. The cooling-heating phase transition (JT effect) is happened for $M>Q$ in which the causal singularity is still covered by the horizon. Our calculations show sensitivity of the inverse point $\{T_i,P_i\}$ position on the T-P plan to existence of the quintessence dark energy just for large numerical values of the AdS RN black holes charge $Q$. In other words the quintessence dark energy dose not affects on position of the inverse point when the AdS RN black hole takes on small charges.

Quantum Gravity Effects in Cosmology

Within the geometrodynamic approach to quantum cosmology, we studied the quantum gravity effects in cosmology. The Gibbons-Hawking temperature is corrected by quantum gravity due to spacetime fluctuations and the power spectrum as well as any probe field will experience the effective temperature, a quantum gravity effect.

Gibbons–Hawking temperature corrected by quantum cosmology

We explore a quantum cosmology description of the de Sitter (dS) radiation and its back-reaction to a dS space, inherent in the wave function of the Wheeler–DeWitt equation for pure gravity with a cosmological constant. We first investigate the quantum Friedmann–Lemaitre–Robertson–Walker cosmological model and then consider the possible effects of inhomogeneities of the universe on the dS radiation. In both the cases we obtain the modified Friedmann equation, including the back-reaction from spacetime fluctuations, and the quantum-corrected Gibbons–Hawking (GH) temperature. It is shown that the quantum correction increases the GH temperature with the increment characterized by the ratio of the dS scale to the Planck scale.

Thermodynamical aspects of running vacuum models

The thermal history of a large class of running vacuum models in which the effective cosmological term is described by a truncated power series of the Hubble rate, whose dominant term is $\Lambda (H) \propto H^{n+2}$, is discussed in detail. Specifically, by assuming that the ultra-relativistic particles produced by the vacuum decay emerge into space-time in such a way that its energy density $\rho_r \propto T^{4}$, the temperature evolution law and the increasing entropy function are analytically calculated. For the whole class of vacuum models explored here we findthat the primeval value of the comoving radiation entropy density (associated to effectively massless particles) starts from zero and evolves extremely fast until reaching a maximum near the end of the vacuum decay phase, where it saturates. The late time conservation of the radiation entropy during the adiabatic FRW phase also guarantees that the whole class of running vacuum models predicts thesame correct value of the present day entropy, $S_{0} \sim 10^{87-88}$ (in natural units), independently of the initial conditions. In addition, by assuming Gibbons-Hawking temperature as an initial condition, we find that the ratio between the late time and primordial vacuum energy densities is in agreement with naive estimates from quantum field theory, namely, $\rho_{\Lambda 0}/\rho_{\Lambda I} \sim10^{-123}$. Such results are independent on the power $n$ and suggests that the observed Universe may evolve smoothly between two extreme, unstable, nonsingular de Sitter phases.

Inflation in the light of BICEP2 and PLANCK

The BICEP2 /Keck + PLANCK joint analysis of the B-model polarization and polarization by foreground dust sets an upper bound on the tensor-to-scalar ratio of r0.05 < 0.12 at 95% CL. The popular Starorbinsky model Higgs-inflation or the conformally equivalent Higgs-inflation model allow low r values (∼ 10−3). We survey the generalizations of the Starobinsky–Higgs models which would allow larger values (r ∼ 0.1). The Starobinsky–Higgs inflation models require an exponential potential which can be naturally derived from SUGRA models. We show that a variation of the no-scale SUGRA model can give rise to the generalized Starobinsky models which give large r. We also examine non-standard boundary conditions which would allow a large deviation of the tensor spectral index from the slow roll values and propose that the presence of a thermal component in the tensor spectrum arises from Gibbons–Hawking temperature of the de-Sitter space.