Three years ago, we introduced a new way to quantize the static Schwarzschild black hole(SSBH), there the SSBH was first treated as a single periodic Euclidean system and then the Bohr-Sommerfeld quantum condition of action was used to obtain a quantum theory of Schwarzschild black hole.[1] Now in this short report, we try to extend the above method to quantize the static de Sitter(SDS) space-time and establish a quantum theory of both SDS space and dark energy.
We introduce novel Einstein spaces which are the {\it stationary analogs of de Sitter and ani-de Sitter} spacetimes. Having $Λ$ as their only parameter, the inherent anisotropy in these solutions appears as a dilemma if we treat the cosmological term as a constant background curvature. Since the cosmological term is an inseparable element of the current cosmological models, further development of these models as well as resolution of the problems related to this term, including any quantum aspect will crucially depend on the true nature of this term. These solutions, which to the best of our k…
We consider an exponential model within the so-called f(T) theory of gravity, where $T$ denotes the torsion scalar. We focus our work on a cosmological feature of such a model, checking whether it may describe the de Sitter stage of the current universe through the analysis of the redshift z. Our results shows that the model reproduces the de Sitter stage only for low-redshifts, where the perturbation function goes toward zero as the low values of the redshift are reached, whereas the effective parameter of equation of state goes to -1, which is the expected behavior for any model able to repr…
Based on Reissner-Nordstrom-anti-de Sitter(RN-AdS) black hole surrounded by perfect fluid dark matter, we study the thermodynamics and phase transition by extending the phase space defined by the charge square $Q^{2}$ and the conjugate quantity $ψ$, where $ψ$ is a function of horizon radius. The first law of thermodynamics and the equation of state are derived in the form $Q^{2}=Q^{2}(T,ψ)$. By investigating the critical behaviour of perfect fluid dark matter around Reissner-Nordstrom-anti-de Sitter black hole, we find that these thermodynamics system are similar to Van der Waals system, and c…
Starting from a discussion of the black hole information loss paradox, we argue that Primordial Black Hole Remnants (PBHRs) of Planck mass, should they exist, are a plausible candidate for dark energy. We call this proposal the PBHR model. We also find an instability of de Sitter space towards a space with power-law accelerating expansion, the time dependence of the cosmological constant and the resulting form of the metric, and propose that this is the dominant instability of de Sitter space. We conjecture that a similar instability does not afflict a space sourced by PBHRs. We find that the …
We obtain the Kerr-anti-de-sitter (Kerr-AdS) and Kerr-de-sitter (Kerr-dS) black hole (BH) solutions to the Einstein field equation in the perfect fluid dark matter background using the Newman-Janis method and Mathematica package. We discuss in detail the black hole properties and obtain the following main results: (i) From the horizon equation $g_{rr}=0$, we derive the relation between the perfect fluid dark matter parameter $α$ and the cosmological constant $Λ$ when the cosmological horizon $r_Λ$ exists. For $Λ=0$, we find that $α$ is in the range $0<α<2M$ for $α>0$ and $-7.18M<α<0$ for $α<0$…
In this paper we investigate circular orbits for test particles around Schwarzschild-de Sitter (dS) black hole surrounded by perfect fluid dark matter. We determine the region of circular orbits bounded by innermost and outermost stable circular orbits. We show that the impact of the perfect fluid dark matter shrinks the region where circular orbits can exist as the values of both innermost and outermost stable circular orbits decrease. We find that for specific lower and upper values of dark matter parameter there exist double matching values for inner and outermost stable circular orbits. It…
In this paper we shall study the phase space of a coupled dark energy-dark matter fluids system, in which the dark energy has a generalized logarithmic corrected equation of state. Particularly, the equation of state for the dark energy will contain a logarithmic function of the dark energy density $ρ_d$ and will also have quadratic and Chaplygin gas-like terms, expressed in terms of $ρ_d$. We shall use the dynamical system approach in order to study the cosmological dynamics, and by appropriately choosing the dynamical system variables, we shall construct an autonomous dynamical system. The s…
I develop a physical picture of dark energy (DE) based on fundamental principles and constants of quantum mechanics (QM) and general relativity (GR) theories. It derives from a conjecture of non-zero masses for nearly standard-model photons, based on QM localization at a cosmological scale. Dark energy is associated with de Sitter space and that has a fundamentally invariant event horizon. I conceive of DE as a Bose-Einstein condensate (BEC) of cosmologically massive photons and I estimate fundamentally the binding energy per particle originating from an effectively attractive QM potential in …
During this work, using subtraction renormalization mechanism, zero point quantum fluctuations for bosonic scalar fields in a de-Sitter like background are investigated. By virtue of the observed value for spectral index, $n_s(k)$, for massive scalar field the best value for the first slow roll parameter, $ε$, is achieved. In addition the energy density of vacuum quantum fluctuations for massless scalar field is obtained. The effects of these fluctuations on other components of the Universe are studied. By solving the conservation equation, for some different examples, the energy density for d…
In the same way as the realization of some of the famous gedanken experiments imagined by the founding fathers of quantum mechanics has recently led to the current renewal of the interpretation of quantum physics, it seems that the most recent progresses of observational astrophysics can be interpreted as the realization of some cosmological gedanken experiments such as the removal from the universe of the whole visible matter or the cosmic time travel leading to a new cosmological standard model. This standard model involves two dark components of the universe, dark energy and dark matter. Wh…
AdS - de Sitter transition in interacting dark energy models
Observatório Nacional（国家天文台）；Instituto de Física, Universidade Federal da Bahia（巴伊亚联邦大学物理研究所）；PPGCosmo, Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学宇宙学研究生项目）
In the teleparallel framework of cosmology, a quintessence with non-minimal couplings to the scalar torsion and a boundary term is considered. A conformal coupling to matter density is also taken into account. It is shown that the model can describe the onset of cosmic acceleration after an epoch of matter dominated era, where dark energy is negligible, via $Z_2$ symmetry breaking. While the conformal coupling holds the Universe in a state with zero dark energy density in the early epoch, the non-minimal couplings lead the Universe to a stable state with de Sitter expansion at the late time.
The replacement of the Poincaré-invariant Einstein special relativity by a de Sitter-invariant special relativity produces concomitant changes in all relativistic theories, including general relativity. A crucial change in the latter is that both the background de Sitter curvature and the gravitational dynamical curvature turns out to be included in a single curvature tensor. This means that the cosmological term no longer explicitly appears in Einstein equation, and is consequently not restricted to be constant. In this paper, the Newtonian limit of such theory is obtained, and the ensuing Ne…
We address the question of regular primordial black holes with de Sitter interior, their remnants and gravitational vacuum solitons G-lumps as heavy dark matter candidates providing signatures for inhomogeneity of early universe, which is severely constrained by the condition that the contribution of these objects in the modern density does not exceed the total density of dark matter. Primordial black holes and their remnants seem to be most elusive among dark matter candidates. However, we reveal a nontrivial property of compact objects with de Sitter interior to induce proton decay or decay …
In this paper, we generalize the simplified Dark Matter models with graviton mediator to the curved space-time, in particular to the de Sitter space. We obtain the generating functional of the Green's functions in the Euclidean de Sitter space for the covariant free gravitons. We determine the generating functional of the interacting theory between Dark Matter particles and the covariant gravitons. Also, we calculate explicitly the 2-point and 3-point interacting Green's functions for the symmetric traceless divergence-less covariant graviton. The results derived here are general in the sense …
The {\bf k-}essence emergent Reissner-Nordstrom-de Sitter spacetime has exactly mapped on to the Robinson-Trautman (RT) type spacetime with cosmological constant $Ł$ for certain configuration of {\bf k-}essence scalar field. Theoretically, we evaluated that the thermodynamical quantities for the RT type emergent black hole is different from the usual one in the presence of kinetic energy of the {\bf k-}essence scalar field i.e., the dark energy density. We restrict ourselves into the fact that the dark energy density (K) is to be unity, then the effective temperature and pressure both are nega…
The anti-de Sitter (AdS) black hole plays an important role in the holographic principle. In this study, the upper bound in energy corresponding to the mass of the Schwarzschild black hole is modified to be that of the AdS black hole. Via the correspondence between the ultraviolet (UV) and infrared (IR) cutoffs, the constant term in the energy density of the holographic dark energy (HDE) can be obtained from the negative cosmological constant from the black hole. Interestingly, the proposed dark energy model could drive the late-time expansion of the Universe without the causality violation. T…
Our aim is studying the thermodynamics of cosmological models including initial and final de-Sitter eras. For this propose, bearing Cai-Kim temperature in mind, we investigate the thermodynamic properties of a dark energy candidate with variable energy density, and show that the state parameter of this dark energy candidate should obey the $ω_D\neq-1$ constraint, whiles there is no interaction between the fluids filled the universe, and the universe is not in the de-Sitter eras. Additionally, based on thermal fluctuation theory, we study the possibility of inducing fluctuations to the entropy …
A nonminimally coupled hybrid dark energy model is introduced. The dark energy evolution is triggered by mass varying neutrinos. Quintessence evolution begins from an initial point, with an insignificant dark energy density, and arrives at a final de Sitter attractor. While initially, for a Higgs-like potential, the non-minimal coupling keeps the system in a state with negligible dark energy density, finally the second quintessence conducts the evolution to a stable fixed point. These evolutions occur through successive $Z_2$ symmetry breakings.
Since the Schwarzschild-de Sitter spacetime is static inside the cosmological event horizon, if the dark energy state parameter is sufficiently close to $-1$, apparently one could still expect an effectively static geometry, in the attraction dominated region inside the maximum turn around radius, $R_{\rm TA, max}$, of a cosmic structure. We take the first order metric derived recently assuming a static and ideal dark energy fluid with equation of state $P(r)=αρ(r)$ as a source in Ref. [1], which reproduced the expression for $R_{\rm TA, max}$ found earlier in the cosmological McVittie spaceti…
This is the second in a series of papers investigating the formulation of the simplified Dark Matter models with graviton mediators in cosmological backgrounds. We address here the crucial problem of the fundamental observable of interest, namely the graviton spectrum in a FRW cosmological background with an arbitrary Dark Matter background component. We calculate the correction to the free graviton two-point function up to the second order in the coupling constant between the Dark Matter and the graviton in the simplified Dark Matter model with graviton mediators approach in the de Sitter spa…
Many different forms of the de Sitter metric in different coordinate systems are used in the general relativity literature. Two of them are the most common, the static form and the cosmological (exponentially expanding) form. The staticity and non-stationarity of these two different forms are traced back to the noncomoving and comoving nature of the corresponding coordinate systems. In this paper using the quasi-Maxwell form of the Einstein field equations and a definition of static spacetimes based upon them, we look at these two different forms of the same solution from a new perspective whi…
We determine the scalar field evolution of a braneworld localized black hole with both dark matter and dark energy components, obtained within a dynamical and continuous embedding formalism by use of Nash's theorem. We further extract the associated quasinormal modes for both de Sitter-Schwarzschild-Dark matter and anti-de Sitter-Schwarzschild-Dark matter solutions, for the different causal structures (one, two or three horizon spacetimes) given by the space of parameters. By comparison with standard General Relativity solutions, we infer possible observable astrophysical differences, and rema…
Although equivalent to general relativity, teleparallel gravity is conceptually speaking a completely different theory. In this theory, the gravitational field is described by torsion, not by curvature. By working in this context, a new model is proposed in which the four-derivative of a canonical scalar field representing dark energy is nonminimally coupled to the "vector torsion". This type of coupling is motivated by the fact that a scalar field couples to torsion through its four-derivative, which is consistent with local spacetime kinematics regulated by the de Sitter group $SO(1,4)$. It …
A formalism for the appearance of dark energy in the matter dominated era, leading to a persistent de Sitter expansion at the late time is proposed. Our framework is a hybrid quintessence model with a non-minimal coupling to the Ricci scalar. Coupling to the curvature triggers the dark energy evolution, while the coupling of scalar fields drives this evolution to a de Sitter stable fixed point. These occur via successive $Z_2$ symmetry breakings.
We construct a piecewise model that gives a physical viable realization of finite-time future singularity for a spatially flat Friedmann-Robertson-Walker universe within the interacting dark matter--dark energy framework, with the latter one in the form of a variable vacuum energy. The scale factor solutions provided by the model are accommodated in several branches defined in four regions delimited by the scale factor and the effective energy density. A branch starts from a big bang singularity and describes an expanding matter-dominated universe until the sudden future singularity occurs. Th…
The well-known brane world model of cosmology is an alternative to the standard model of cosmology, called ΛCDM (Lambda Cold Dark Matter) model. However, the quadratical energy density of the brane universe requires an undesirable fine tuning. The paper develops a new Anti-de Sitter (AdS) brane world model without the quadratical energy density by using a second Einstein equation, which arises canonically during a holographic renormalisation. On the AdS boundary it is demonstrated that this brane model equals an effective de Sitter ΛCDM model, whereas the brane model near the AdS boundary agre…
The effective field theory of dark energy and modified gravity is supposed to well describe, at low energies, the behaviour of the gravity modifications due to one extra scalar degree of freedom. The usual curvature perturbation is very useful when studying the conditions for the avoidance of ghost instabilities as well as the positivity of the squared speeds of propagation for both the scalar and tensor modes, or the Stückelberg field performs perfectly when investigating the evolution of linear perturbations. We show that the viable parameters space identified by requiring no-ghost instabili…
In this paper, vacuum expectation value (VEV) of the energy-momentum tensor for a conformally coupled scalar field in de Sitter space-time is investigated through the Krein-Gupta-Bleuler construction. This construction has already been successfully applied to the de Sitter minimally coupled massless scalar field and massless spin-2 field to obtain a causal and fully covariant quantum field on the de Sitter background. We also consider the effects of boundary conditions. In this respect, Casimir energy-momentum tensor induced by Dirichlet boundary condition on a curved brane is evaluated.
