Holographic temperature bound in the slow-roll inflation

We investigate the relationship between the holographic temperature bound and the slow-roll inflation. For this purpose we introduce the holographic temperature bound for a radiation matter :$T \ge T_{\rm H}$. Here $T_{\rm H}$ is the Hubble temperature which arises from the cosmological holographic description of for a radiation-dominated universe. For the quasi-de Sitter phase of slow-roll inflation, we find that the holographic temperature bound of $T_{\rm GH} \ge T_{\rm H}$ is guaranteed with the Gibbons-Hawking temperature $T_{\rm GH}$. When $T_{\rm GH}= T_{\rm H}$, inflation ends.Comment: 9 pages, 1figur

A gauge boson from the Kaluza-Klein approach of the Randall-Sundrum brane world

We clarify a mechanism to obtain a massless gauge boson from the Kaluza-Klein approach of the Randall-Sundrum(RS) brane world. This corresponds exactly to the same mechanism of achieving a localization of the gauge boson by adding both the bulk and brane mass terms. Accordingly this work puts another example for a localization-mechanism of the gauge boson on the brane.Comment: 7 pages, typo corrected and comments adde

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.Comment: 13 pages, revised version including the new interpretation for energy terms in the Friedmann equation of the Euclidean space approach to appear in PL

Standard cosmology from the brane cosmology with a localized matter

We discuss the brane cosmology in the 5D anti de Sitter Reissner-Nordstrom (AdSRN$_5$) spacetime. A brane with the tension $\sigma$ is defined as the edge of an AdSRN$_5$ space with mass $M$ and charge $Q$. In this case we get the CFT-radiation term $(\rho_{CFT})$ from $M$ and the charged dust $(-\rho^2_{cd})$ from $Q^2$ in the Friedmann-like equation. However, this equation is not justified because it contains $\rho_{cd}^2$-term with the negative sign. This is unconventional in view of the standard cosmology. In order to resolve this problem, we introduce a localized dust matter which satisfies $P_{dm}=0$. If \rho_{dm}=\fr{\sqrt 3}{2}\rho_{cd}, the unwanted $-\rho_{cd}^2$ is cancelled against $\rho_{dm}^2$ and thus one recovers a standard Friedmann-Robertson-Walker universe with CFT-radiation and dust matter. For the stiff matter consideration, we can set $\rho_{csti}\sim Q^2$ with the negative sign. Here we introduce a massless scalar which plays the role of a stiff matter with $P_{sca}=\rho_{sca}$ to cancel $-\rho_{csti}$. In this case, however, we find a mixed version of the standard and brane cosmologies.Comment: 8 pages, Latex, version to appear in MPL

Holographic entropy bounds in the inflationary universe

We introduce the relation between the holographic entropy bounds and the inflationary universe. First the holographic entropy bounds for radiation-dominated universe, radiation-dominated universe with a positive cosmological constant are introduced. For an exact de Sitter phase, we use the maximal entropy bound. We classify the inflation based on the quasi-de Sitter spacetime into three steps: slow-roll period of inflation, epoch of reheating, and radiation-dominated era. Then we study how to apply three entropy bounds to the three steps of the inflation. Finally we discuss our results.Comment: 16 pages, two eps figure

Chiral boson, W∞W_\infty-coherent state and edge states in the quantum Hall effect

We perform consistently the Gupta-Bleuler quantization combined with Dirac procedure for a chiral boson with the parameter ($\alpha$) on the circle, the boundary of the circular droplet. For $\alpha =1$, we obtain the holomorphic constraints. Using the representation of Bargmann-Fock space and the Schr\"odinger equation, we construct the holomorphic wave functions. In order to interpret these functions, we introduce the $W_\infty$-coherent state to account for the infinite-dimensional translation symmetry for the Fourier (edge) modes. The $\alpha=1$ wave functions explain the neutral edge states for $\nu =1$ quantum Hall fluid very well. In the case of $\alpha = -1$, we obtain the new wave functions which may describe the higher modes (radial excitations) of edge states. Finally, the charged edge states are described by the $|\alpha| \not=1$ wave functions.Comment: 19 pages, RevTeX, the invited paper for Nuclear Science and Technique

On the stability of two-dimensional extremal black holes

We discuss the stability of the extremal ground states of a two-dimensional (2D) charged black hole which carries both electric ($Q_E$) and magnetic ($Q_M$) charges. The method is first to find the physical field and then to derive the equation of the Schr\"odinger type. It is found that the presenting potential to an on-coming tachyon (as a spectator) takes a barrier-well type. This provides the bound state solution, which implies an exponentially growing mode with respect to time. The 2D extremal ground states all are classically unstable. We conclude that the 2D extremal charged black holes are not considered as the candidates for the stable endpoint of the Hawking evaporation.Comment: 12 pages 2 figures, RevTeX, to obtain figures contact author ([email protected]

Entropy Problem in the AdS3_3/CFT correspondence

We resolve the entropy problem in the AdS$_3$/CFT correspondence by introducing both the normalizable and non-normalizable bulk modes. On the boundary, the normalizable Liouville states gives us $c=1$ conformal field theory(CFT), whereas the non-normalizable Liouville states provide $c = {3 \ell \over 2 G}$ CFT. Such (boundary) non-normalizable modes come from non-normalizable bulk modes which serve as classical, non-fluctuating bulk background and encode the choice of local operator insertion on the boundary. Since the non-normalizable bulk modes can transfer information from bulk to boundary, it suggests that counting of non-normalizable states on the boundary at infinity leads to the entropy($S={2 \pi r_+ \over 4 G}$) of (2+1)-dimensional gravity with $\Lambda= -1/\ell^2$.Comment: 7 pages, reference added, and roles of tachyon and dilaton discusse

Comment on "Metric Fluctuations in Brane Worlds"

Recently, Ivanov and Volovich (hep-th/9912242) claimed that the perturbation of $h_{\mu\nu}$ with nonvanishing transverse components $h_{5\mu}$ is not localized on the brane because $h_{\mu\nu}$ depends on the fifth coordinate $z$ linearly. Consequently, it may indicate that the effective theory is unstable. However, we point out that such linear dependence on $z$ can be {\it gauged away}. Hence the solution does not belong to the physical one. Therefore, even if one includes $h_{5\mu}$, Randall and Sundrum's argument for the localized gravity on the brane remains correct.Comment: 4 pages, revte

Schwarzschild black hole in the dilatonic domain wall

In the dilatonic domain wall model, we study the Schwarzschild black hole as a solution to the Kaluza-Klein (KK) zero mode effective action which is equivalent to the Brans-Dicke (BD) model with a potential. This can describe the large Randall-Sundrum (RS) black hole whose horizon is to be the intersection of the black cigar with the brane. The black cigar located far from the AdS$_5$-horizon is known to be stable, but any explicit calculation for stability of the RS black hole at $z=0$ is not yet performed. Here its stability is investigated against the $z$-independent perturbations composed of odd, even parities of graviton ($h_{\mu\nu}$) and BD scalar($h_{44} = 2\phi$). It seems that the RS black hole is classically unstable because it has a potential instability at wavelength with $\lambda > 1/(2k)$. However, this is not allowed inside an AdS$_5$-box of the size with $1/(2k)$. Thus the RS black hole becomes stable. The RS black hole can be considered as a stable remnant at $z=0$ of the black cigar.Comment: 10 pages, title changed, a crucial comment on the brane world black hole added, and to appear in Phys. Rev.