Future Event Horizon Research Articles

K-essential covariant holography

The holographic principle is applied to a flat Friedmann–Robertson–Walker space-time dominated by dark energy when this is due to the presence of a k-essence scalar field, both for dark energy and phantom scenarios. In this framework, a geometrical covariant approach permits the construction of holographic hypersurfaces. The resulting covariant preferred screens, both for phantom and non-phantom regions, are then compared with those obtained by using the holographic dark energy model with the future event horizon as the infrared cut-off. In the phantom case, one of the two obtained holographic screens is placed on the big rip hypersurface, both for the covariant holographic formalism and the holographic phantom model. It is also analysed whether this covariant formalism allows a mathematically consistent formulation of fundamental theories based on the existence of a S-matrix at infinite distances.

Dark energy model with generalized cosmological horizon

We discuss the evolution of the newly proposed dark-energy model with a generalized event horizon (a generalized form of the holographic dark-energy model with a future event horizon) in the flat and nonflat universes. We consider the interacting scenario of this model with cold dark matter. We use the well-known logarithmic approach to evaluate the equation of state parameter and explore its present values. It is found that this parameter shows phantom crossing in some cases of the generalized event horizon parameters. The ω-ω′ plane is also developed for three different cases of the generalized event horizon parameters. The corresponding phase plane provides thawing and freezing regions. Finally, the validity of a generalized second law of thermodynamics is explored which holds in certain ranges of constant parameters.

Covariant holography of a tachyonic accelerating universe

We apply the holographic principle to a flat dark energy dominated Friedmann-Robertson-Walker spacetime filled with a tachyon scalar field with constant equation of state $w=p/\rho$, both for $w>-1$ and $w<-1$. By using a geometrical covariant procedure, which allows the construction of holographic hypersurfaces, we have obtained for each case the position of the preferred screen and have then compared these with those obtained by using the holographic dark energy model with the future event horizon as the infrared cutoff. In the phantom scenario, one of the two obtained holographic screens is placed on the big rip hypersurface, both for the covariant holographic formalism and the holographic phantom model. It is also analyzed whether the existence of these preferred screens allows a mathematically consistent formulation of fundamental theories based on the existence of a S matrix at infinite distances.

(m, n)-TYPE HOLOGRAPHIC DARK ENERGY MODELS

We construct (m, n)-type holographic dark energy models at a phenomenological level, which can be viewed as a generalization of agegraphic models with the conformal-like age as the holographic characteristic size. For some values of (m, n) the holographic dark energy can automatically evolve across ω = -1 into a phantom phase even without introducing an interaction between the dark energy and background matter. Our construction is also applicable to the holographic dark energy with generalized future event horizon as the characteristic size. Finally, we address the issue on the stability of our model and show that they are generally stable under the scalar perturbation.

Cosmological constraints on the new holographic dark energy model with action principle

Recently, a New HDE model with action principle was proposed (Li and Miao, arXiv:1210.0966). This model completely solves the causality and circular problems in the original HDE model, and is similar to the original model except a new term that can be interpreted as dark radiation. In this paper, we make further investigations on this model from the aspect of cosmological observations. Numerically, we confirm that the equations of motion force the $L(z=-1)=0$, making the cut-off $aL$ exactly the future event horizon. We also perform detailed analysis on the dynamical properties of the model, divided into the $c<6$ and $c\geq6$ cases ($c$ is a dimensionless parameter which should be decided by the data). From a combination of the present Union2.1+BAO+CMB+$H_0$ data, we find the model yields $\chi^2_{\rm min}=548.798$ (in a non-flat Universe), comparable to the results of the original HDE model (549.461) and the concordant $\Lambda$CDM model (550.354). At 95.4% CL, we get $1.41<c<3.09$ and correspondingly $-2.25<w(z=-1)<-1.39$, implying the Big Rip fate of the Universe at a high confidence level. Besides, for the constraints on dark radiation, we also get a rough estimation $N_{\rm \rm eff}=3.54^{+0.32+0.67}_{\rm -0.45-0.76}$, with the central value slightly larger than the standard value 3.046.

Nonlinear instability of scalar fields on extremal black holes

We prove a new type of finite time blow-up for a class of semilinear wave equations on extremal black holes. The initial data can be taken to be arbitrarily close to the trivial data. The first singularity occurs along the (degenerate) future event horizon. No analogue of this instability occurs for subextremal black holes or the Minkowski spacetime.

Causality problem in a holographic-dark-energy model

In the model of holographic dark energy, there is a notorious problem of circular reasoning between the introduction of future event horizon and the accelerating expansion of the universe. We examine the problem after dividing it into two parts, the causality problem of the equation of motion and the circular logic on the use of the future event horizon. We specify and isolate the root of the two problems as a boundary condition from the causal equation of motion, which can be determined from the initial data of the universe. We show that the causality will be kept if we define it based on our recognizability and the circular-logic problem can be reduced to imposing an initial condition. We additionally find that the model constant of the holographic dark energy is close to unity from the present data of the universe.

Instability of higher dimensional extreme black holes

We study linearized gravitational perturbations of extreme black hole solutions of the vacuum Einstein equation in any number of dimensions. We find that the equations governing such perturbations can be decoupled at the future event horizon. Using these equations, we show that the transverse derivatives of certain gauge invariant quantities blow up at late time along the horizon if the black hole solution satisfies certain conditions. We find that these conditions are indeed satisfied by many extreme Myers–Perry solutions, including all such solutions in five dimensions.

Formation of black holes in topologically massive gravity

We present an exact solution in three-dimensional topologically massive gravity with a negative cosmological constant, which dynamically interpolates between a past horizon and a chiral anti--de Sitter $pp$ wave. Similarly, upon time reversal, one obtains an anti--de Sitter $pp$ wave with a future event horizon.

Generalized second law of thermodynamics in f(T) gravity with entropy corrections

We study the generalized second law (GSL) of thermodynamics in $f(T)$ cosmology. We consider the universe as a closed bounded system filled with $n$ component fluids in the thermal equilibrium with the cosmological boundary. We use two different cosmic horizons: the future event horizon and the apparent horizon. We show the conditions under which the GSL will be valid in specific scenarios of the quintessence and the phantom energy dominated eras. Further we associate two different entropies with the cosmological horizons: with a logarithmic correction term and a power-law correction term. We also find the conditions for the GSL to be satisfied or violated by imposing constraints on model parameters.

Power-law entropy-corrected Ricci dark energy and dynamics of scalar fields

Motivated by the holographic principle, it has previously been suggested that the dark energy (DE) density can be inversely proportional to the area A of the event horizon of the Universe. However, this kind of model would have a casuality problem. In this work, we study the power-law entropy-corrected holographic DE (PLECHDE) model in the non-flat Friedmann–Robertson–Walker universe, with the future event horizon replaced by the average radius of the Ricci scalar curvature. We derive the equation of state parameter ωΛ, the deceleration parameter q and the evolution of energy density parameter ΩD′ in the presence of interaction between DE and dark matter. We consider the correspondence between our Ricci-PLECHDE model and the modified Chaplygin gas and the tachyon, K-essence, dilaton and quintessence scalar fields. The potential and dynamics of the scalar field models have been reconstructed according to the evolutionary behaviour of the interacting entropy-corrected holographic DE model.

Decay of axisymmetric solutions of the wave equation on extreme Kerr backgrounds

We study the Cauchy problem for the wave equation □gψ=0 on extreme Kerr backgrounds. Specifically, we consider regular axisymmetric initial data prescribed on a Cauchy hypersurface Σ0 which connects the future event horizon with spacelike or null infinity, and we solve the linear wave equation on the domain of dependence of Σ0. We show that the spacetime integral of an energy-type density is bounded by the initial conserved flux corresponding to the stationary Killing field T, and we derive boundedness of the non-degenerate energy flux corresponding to a globally timelike vector field N. Finally, we prove uniform pointwise boundedness and power-law decay for ψ up to and including the event horizon H+.

Constraints on the holographic dark energy model via type Ia supernovae, baryon acoustic oscillation, and WMAP7

In this paper, the holographic dark energy (HDE) model, where the future event horizon is taken as an IR cut-off, is confronted by using currently available cosmic observational data sets which include type Ia supernovae, baryon acoustic oscillation and cosmic microwave background radiation from full information of WMAP-7yr. Via the Markov Chain Monte Carlo method, we obtain the values of model parameter $c= 0.696_{- 0.0737- 0.132- 0.190}^{+ 0.0736+ 0.159+ 0.264}$ with $1,2,3\sigma$ regions. Therefore one can conclude that at lest $3\sigma$ level the future Universe will be dominated by phantom like dark energy. It is not consistent with positive energy condition, however this condition must be satisfied to derive the holographic bound. It implies that the current cosmic observational data points disfavor the HDE model.

Interacting Ricci dark energy with logarithmic correction

Motivated by the holographic principle, it has been suggested that the dark energy density may be inversely proportional to the area $A$ of the event horizon of the universe. However, such a model would have a causality problem. In this work, we consider the entropy-corrected version of the holographic dark energy model in the non-flat FRW universe and we propose to replace the future event horizon area with the inverse of the Ricci scalar curvature. We obtain the equation of state (EoS) parameter $\omega_{\Lambda}$, the deceleration parameter $q$ and $\Omega_D'$ in the presence of interaction between Dark Energy (DE) and Dark Matter (DM). Moreover, we reconstruct the potential and the dynamics of the tachyon, K-essence, dilaton and quintessence scalar field models according to the evolutionary behavior of the interacting entropy-corrected holographic dark energy model.

A bound on the scale of spacetime noncommutativity from the reheating phase after inflation

In an approach to noncommutative gauge theories, where the full noncommutative behavior is delimited by the presence of the UV and IR cutoffs, we consider the possibility of describing a system at a temperature T in a box of size L. Employing a specific form of UV/IR relationship inherent in such an approach of restrictive noncommutativity, we derive, for a given temperature T, an upper bound on the parameter of spacetime noncommutativity ΛNC∼|θ|−1/2. Considering such epochs in the very early universe which are expected to reflect spacetime noncommutativity to a quite degree, like the reheating stage after inflation, or believable pre-inflation radiation-dominated epochs, the best limits on ΛNC are obtained. We also demonstrate how the nature and size of the thermal system (for instance, the Hubble distance versus the future event horizon) can affect our bounds.

Future deceleration due to cosmic backreaction in presence of the event horizon

ABSTRACT The present acceleration of the Universe leads to the formation of a cosmological future event horizon. We explore the effects of the event horizon on cosmological backreaction due to inhomogeneities in the universe. Beginning from the onset of the present accelerating era, we show that backreaction in presence of the event horizon causes acceleration to slow down in the subsequent evolution. Transition to another decelerating era could ensue eventually at a future epoch, ensuring avoidance of a big rip.

Interacting modified holographic dark energy in Kaluza-Klein universe

The interaction of modified holographic dark energy and dark matter with varying $G$ in flat Kaluza Klein universe is considered. Further, we take infrared cutoff scale $L$ as future event horizon. In this scenario, equations of state parameter as well as evolution are explored. We also check the validity of the generalized second law of thermodynamics. It is interesting to mention here that our results show consistency with the present observations.

Fractional Action Cosmology: Emergent, Logamediate, Intermediate, Power Law Scenarios of the Universe and Generalized Second Law of Thermodynamics

In the framework of Fractional Action Cosmology (FAC), we study the generalized second law of thermodynamics for the Friedmann Universe enclosed by a boundary. We use the four well-known cosmic horizons as boundaries namely, apparent horizon, future event horizon, Hubble horizon and particle horizon. We construct the generalized second law (GSL) using and without using the first law of thermodynamics. To check the validity of GSL, we express the law in the form of four different scale factors namely emergent, logamediate, intermediate and power law. For Hubble, apparent and particle horizons, the GSL holds for emergent and logamediate expansions of the universe when we apply with and without using first law. For intermediate scenario, the GSL is valid for Hubble, apparent, particle horizons when we apply with and without first law. Also for intermediate scenario, the GSL is valid for event horizon when we apply first law but it breaks down without using first law. But for power law expansion, the GSL may be valid for some cases and breaks down otherwise.

Constraints on Λ(t)CDM models as holographic and agegraphic dark energy with the observational Hubble parameter data

The newly released observational H(z) data (OHD) is used to constrain Λ(t)CDM models as holographic and agegraphic dark energy. By the use of the length scale and time scale as the IR cut-off including Hubble horizon (HH), future event horizon (FEH), age of the universe (AU), and conformal time (CT), we achieve four different Λ(t)CDM models which can describe the present cosmological acceleration respectively. In order to get a comparison between such Λ(t)CDM models and standard ΛCDM model, we use the information criteria (IC), Om(z) diagnostic, and statefinder diagnostic to measure the deviations. Furthermore, by simulating a larger Hubble parameter data sample in the redshift range of 0.1 < z < 2.0, we get the improved constraints and more sufficient comparison. We show that OHD is not only able to play almost the same role in constraining cosmological parameters as SNe Ia does but also provides the effective measurement of the deviation of the DE models from standard ΛCDM model. In the holographic and agegraphic scenarios, the results indicate that the FEH is more preferable than HH scenario. However, both two time scenarios show better approximations to ΛCDM model than the length scenarios.

Quintessential holography

By using the Bousso geometrical covariant procedure we consider in this paper the holographic principle as applied to asymptotic Friedmann-Robertson-Walker space-times whose vacuum dark energy is due to the presence of a quintessential dark and phantom-energy scalar field with constant equation of state $p=\ensuremath{\omega}\ensuremath{\rho}$, both for $w&gt;\ensuremath{-}1$ and $w&lt;\ensuremath{-}1$. We have obtained the positions of the optimal screen for each case, deriving for them moreover expressions for the future event horizon and hence holographic dark-energy models of the Li and Huang and Li types, which are compared with the most consistent results derived from the covariant Bousso procedure. It is also seen that one of the two obtained holographic screens is placed on the big rip hypersurface in the phantom-energy case, both for the covariant holographic formalism and holographic phantom models. Consistency of fundamental theories is analyzed in the light of the largest physical regions allowed by the existence of a holographic screen in the future.