Topological De Sitter Research Articles

DRGT theory of massive gravity from spontaneous symmetry breaking

In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory. We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the Einstein–Hilbert action plus the dRGT potential terms. In this vacuum, there are five (three from Goldstone modes) propagating degrees of freedom which form polarizations of a massive spin 2 particle, an extra healthy heavy scalar (Higgs) mode and no Boulware–Deser ghost mode. We further show that the action can be derived in a limit from a topological de Sitter invariant gauge theory in 4 dimensions.

Quantum effects in topological and Schwarzschild de Sitter brane: Aspects of torsion on $(D\!{\bar D})_4$-brane

We investigate an effective torsion curvature in a second-order formalism underlying a two-form world-volume dynamics in a D5-brane. In particular, we consider the two form in presence of a background (open string) metric in a U(1) gauge theory. Interestingly the formalism may be viewed via a noncoincident pair of [Formula: see text]-brane with a global Nereu–Schwarz (NS) two form on an anti-brane and a local two form on a brane. The energy–momentum tensor is computed in the six-dimensional (6D) conformal field theory (CFT). It is shown to source a metric fluctuation on a vacuum created pair of [Formula: see text]-brane at a cosmological horizon by the two-form quanta in the gauge theory. The emergent gravity scenario is shown to describe a low-energy (perturbative) string vacuum in 6D with a nonperturbative (NP) quantum correction by a lower (p < 5) dimensional Dp-brane or an anti-brane in the formalism. A closed string exchange between a pair of [Formula: see text]-brane, underlying a closed/open string duality, is argued to describe the Einstein vacuum in a low-energy limit. We obtain topological de Sitter (TdS) and Schwarzschild brane universe in six dimensions. The brane/anti-brane geometries are analyzed to explore some of their characteristic and thermal behaviors in presence of the quantum effects. They reveal an underlying nine-dimensional type IIA and IIB superstring theories on S1.

Entropy corrections to five-dimensional black holes and de Sitter spaces

It is shown that non-rotating black holes in three or four dimensions possess a canonical entropy. Recently study indicated that there were logarithmic corrections to Bekenstein–Hawking entropy in area with a uncertain coefficient which depends on specific models. In this paper, the thermal fluctuations on Bekenstein–Hawking entropy in five-dimensional topological AdS (TAds)-black holes and topological de Sitter (Tds) spaces will be considered based on a uniformly spaced area spectrum approach.

Phase transitions for the topological de Sitter spaces and Schwarzschild–de Sitter black hole

Abstract We study whether the Hawking–Page phase transition may occur in topological de Sitter spaces (TdS) and Schwarzschild–de Sitter black hole (SdS). We show that at the critical temperature T = T 1 , TdS with hyperbolic cosmological horizon can make the Hawking–Page transition from the zero mass de Sitter space to TdS. It is also shown that there is no Hawking–Page transition for TdS with Ricci-flat and spherical horizons, when the zero mass de Sitter space is taken as the thermal background. Also we find that the SdS undergoes a different phase transition at T = 0 which the Nariai black hole is formed. Finally we connect our results to the dS/CFT correspondence.

Logarithmic correction to the Brane equationin topological Reissner-Nordström de Sitter space

In this paper we study braneworld cosmology when the bulk space is a charged black hole in de Sitter space (topological Reissner-Nordstrom de Sitter Space) in a general number of dimensions; then we compute the leading order correction to the Friedmann equation that arises from logarithmic corrections to the entropy in the holographic-braneworld cosmological framework. Finally we consider the holographic entropy bounds in this scenario, and we show that the entropy bounds are also modified by a logarithmic term.

Relationship between five-dimensional black holes and de Sitter spaces

We study a close relationship between the topological anti-de Sitter (TAdS) black holes and topological de Sitter (TdS) spaces including the Schwarzschild–de Sitter (SdS) black hole in five dimensions. We show that all thermal properties of the TdS spaces can be found from those of the TAdS black holes by replacing k by −k. Also we find that all thermal information for the cosmological horizon of the SdS black hole is obtained from either the hyperbolic-AdS black hole or the Schwarzschild–TdS space by substituting m with −m. For this purpose we calculate thermal quantities of bulk (Euclidean) conformal field theory (ECFT) and moving domain wall by using the A(dS)/(E)CFT correspondences. Further, we compute logarithmic corrections to the Bekenstein–Hawking entropy, Cardy–Verlinde formula and Friedmann equation due to thermal fluctuations. It implies that in the thermal relation between the TdS spaces and TAdS black holes, the cosmological horizon plays the same role as the horizon of TAdS black holes. Finally we note that the dS/ECFT correspondence is valid for the TdS spaces in conjunction with the AdS/CFT correspondence for the TAdS black holes.

Logarithmic corrections to the Bekenstein–Hawking entropy for five-dimensional black holes and de Sitter spaces

We calculate corrections to the Bekenstein–Hawking entropy formula for the five-dimensional topological AdS (TAdS)-black holes and topological de Sitter (TdS) spaces due to thermal fluctuations. We can derive all thermal properties of the TdS spaces from those of the TAdS black holes by replacing k by −k. Also we obtain the same correction to the Cardy–Verlinde formula for TAdS and TdS cases including the cosmological horizon of the Schwarzschild–de Sitter (SdS) black hole. Finally we discuss the AdS/CFT and dS/CFT correspondences and their dynamic correspondences.

A holographic interpretation of asymptotically de Sitter spacetimes

One of the remarkable outcomes of the AdS/CFT correspondence has been the generalization of Cardy's entropy formula for arbitrary dimensionality, as well as a variety of anti-de Sitter scenarios. More recently, related work has been done in the realm of asymptotically de Sitter backgrounds. Such studies presume a well-defined dS/CFT duality, which has not yet attained the credibility of its AdS analogue. In this paper, we derive and interpret generalized forms of the Cardy entropy for a selection of asymptotically de Sitter spacetimes. These include the Schwarzschild–de Sitter black hole (as a review of Preprint hep-th/0112093), the Reissner–Nordstrom–de Sitter black hole and a special class of topological de Sitter solutions. Each of these cases is found to have interesting implications in the context of the proposed correspondence.

Check of the mass bound conjecture in de Sitter space

Recently an interesting conjecture was put forward which states that any asymptotically de Sitter space whose mass exceeds that of exact de Sitter space contains a cosmological singularity. In order to test this mass bound conjecture, we present two solutions. One is the topological de Sitter solution and the other is its dilatonic deformation. Although the latter is not an asymptotically de Sitter space, the two solutions have a cosmological horizon and a cosmological singularity. Using the surface counterterm method we compute the quasilocal stress-energy tensor of a gravitational field and the mass of the two solutions. It turns out that this conjecture holds within the two examples. Also we show that the thermodynamic quantities associated with the cosmological horizon of the two solutions obey the first law of thermodynamics. Furthermore, the nonconformal extension of dS/CFT correspondence is discussed.

Dynamic dS/CFT correspondence using the brane cosmology

We explore the dynamic dS/CFT correspondence using the moving domain wall(brane) approach in the brane cosmology. The bulk spacetimes are given by the Schwarzschild-de Sitter (SdS) black hole and the topological-de Sitter (TdS) solutions. We consider the embeddings of (Euclidean) moving domain walls into the (Euclidean) de Sitter spaces. The TdS solution is better to describe the static dS/CFT correspondence than the SdS black hole, while in the dynamic dS/CFT correspondence the SdS solution provides situation better than that of the TdS solution. However, we do not find a desirable cosmological scenario from the SdS black hole space.

Cardy–Verlinde formula and thermodynamics of black holes in de Sitter spaces

We continue the study of thermodynamics of black holes in de Sitter spaces. In a previous paper (hep-th/0111093), we have shown that the entropy of cosmological horizon in the Schwarzschild–de Sitter solutions and topological de Sitter solutions can be expressed in a form of the Cardy–Verlinde formula, if one adopts the prescription to compute the gravitational mass from data at early or late time infinity of de Sitter space. However, this definition of gravitational mass cannot give a similar expression like the Cardy–Verlinde formula for the entropy associated with the horizon of black holes in de Sitter spaces. In this paper, we first generalize the previous discussion to the cases of Reissner–Nordström–de Sitter solutions and Kerr–de Sitter solutions. Furthermore, we find that the entropy of black hole horizon can also be rewritten in terms of the Cardy–Verlinde formula for these black holes in de Sitter spaces, if we use the definition due to Abbott and Deser for conserved charges in asymptotically de Sitter spaces. We discuss the implication of our result. In addition, we give the first law of de Sitter black hole mechanics.

DS/CFT duality on the brane with a topological twist

We consider a brane universe in an asymptotically de Sitter background spacetime of arbitrary dimensionality. In particular, the bulk spacetime is described by a ‘topological de Sitter’ solution, which has recently been investigated by Cai et al (2001 Preprint hep-th/0110234). In the current study, we begin by showing that the brane evolution is described by Friedmann-like equations for radiative matter. Next, on the basis of the dS/CFT correspondence, we identify the thermodynamic properties of the brane universe. We then demonstrate that many (if not all) of the holographic aspects of analogous AdS-bulk scenarios persist. These include a (generalized) Cardy–Verlinde form for the CFT entropy and various coincidences when the brane crosses the cosmological horizon.

Cardy–Verlinde formula and asymptotically de Sitter spaces

In this paper we discuss the question of whether the entropy of cosmological horizon in some asymptotically de Sitter spaces can be described by the Cardy-Verlinde formula, which is supposed to be an entropy formula of conformal field theory in any dimension. For the Schwarzschild-de Sitter solution, although the gravitational mass is always negative (in the sense of the prescription in hep-th/0110108 to calculate the conserved charges of asymptotically de Sitter spaces), we find that indeed the entropy of cosmological horizon can be given by using naively the Cardy-Verlinde formula. The entropy of pure de Sitter spaces can also be expressed by the Cardy-Verlinde formula. For the topological de Sitter solutions, which have a cosmological horizon and a naked singularity, the Cardy-Verlinde formula also works well. Our result is in favour of the dS/CFT correspondence.