Anisotropic Power-law Inflation

We study an inflationary scenario in supergravity model with a gauge kinetic function. We find exact anisotropic power-law inflationary solutions when both the potential function for an inflaton and the gauge kinetic function are exponential type. The dynamical system analysis tells us that the anisotropic power-law inflation is an attractor for a large parameter region.Comment: 14 pages, 1 figure. References added, minor corrections include

Anisotropic Inflation with Non-Abelian Gauge Kinetic Function

We study an anisotropic inflation model with a gauge kinetic function for a non-abelian gauge field. We find that, in contrast to abelian models, the anisotropy can be either a prolate or an oblate type, which could lead to a different prediction from abelian models for the statistical anisotropy in the power spectrum of cosmological fluctuations. During a reheating phase, we find chaotic behaviour of the non-abelian gauge field which is caused by the nonlinear self-coupling of the gauge field. We compute a Lyapunov exponent of the chaos which turns out to be uncorrelated with the anisotropy.Comment: 16 pages, 4 figure

Higher Curvature Corrections to Primordial Fluctuations in Slow-roll Inflation

We study higher curvature corrections to the scalar spectral index, the tensor spectral index, the tensor-to-scalar ratio, and the polarization of gravitational waves. We find that the higher curvature corrections can not be negligible in the dynamics of the scalar field, although they are energetically negligible. Indeed, it turns out that the tensor-to-scalar ratio could be enhanced and the tensor spectral index could be blue due to the Gauss-Bonnet term. We estimate the degree of circular polarization of gravitational waves generated during the slow-roll inflation. We argue that the circular polarization can be observable with the help both of the Gauss-Bonnet and parity violating terms. We also present several examples to reveal observational implications of higher curvature corrections for chaotic inflationary models.Comment: 12 pages, 4 figure

Radionic Non-uniform Black Strings

Non-uniform black strings in the two-brane system are investigated using the effective action approach. It is shown that the radion acts as a non-trivial hair of the black strings. From the brane point of view, the black string appears as the deformed dilatonic black hole which becomes dilatonic black hole in the single brane limit and reduces to the Reissner-Nordstr\"om black hole in the close limit of two-branes. The stability of solutions is demonstrated using the catastrophe theory. From the bulk point of view, the black strings are proved to be non-uniform. Nevertheless, the zeroth law of black hole thermodynamics still holds.Comment: 9 pages, 6 figure

Radion and Holographic Brane Gravity

The low energy effective theory for the Randall-Sundrum two brane system is investigated with an emphasis on the role of the non-linear radion in the brane world. The equations of motion in the bulk is solved using a low energy expansion method. This allows us, through the junction conditions, to deduce the effective equations of motion for the gravity on the brane. It is shown that the gravity on the brane world is described by a quasi-scalar-tensor theory with a specific coupling function omega(Psi) = 3 Psi / 2(1-Psi) on the positive tension brane and omega(Phi) = -3 Phi / 2(1+Phi) on the negative tension brane, where Psi and Phi are non-linear realizations of the radion on the positive and negative tension branes, respectively. In contrast to the usual scalar-tensor gravity, the quasi-scalar-tensor gravity couples with two kinds of matter, namely, the matters on both positive and negative tension branes, with different effective gravitational coupling constants. In particular, the radion disguised as the scalar fields Psi and Phi couples with the sum of the traces of the energy momentum tensor on both branes. In the course of the derivation, it has been revealed that the radion plays an essential role to convert the non-local Einstein gravity with the generalized dark radiation to the local quasi-scalar-tensor gravity. For completeness, we also derive the effective action for our theory by substituting the bulk solution into the original action. It is also shown that the quasi-scalar-tensor gravity works as holograms at the low energy in the sense that the bulk geometry can be reconstructed from the solution of the quasi-scalar-tensor gravity.Comment: Revtex4, 18 pages, revised version, conclusions unchanged, references adde

Probing polarization states of primordial gravitational waves with CMB anisotropies

We discuss the polarization signature of primordial gravitational waves imprinted in cosmic microwave background (CMB) anisotropies. The high-energy physics motivated by superstring theory or M-theory generically yield parity violating terms, which may produce a circularly polarized gravitational wave background (GWB) during inflation. In contrast to the standard prediction of inflation with un-polarized GWB, circularly polarized GWB generates non-vanishing TB and EB-mode power spectra of CMB anisotropies. We evaluate the TB and EB-mode power spectra taking into account the secondary effects and investigate the dependence of cosmological parameters. We then discuss current constraints on the circularly polarized GWB from large angular scales (l < 16) of the three year WMAP data. Prospects for future CMB experiments are also investigated based on a Monte Carlo analysis of parameter estimation, showing that the circular polarization degree, varepsilon, which is the asymmetry of the tensor power spectra between right- and left-handed modes normalized by the total amplitude, can be measured down to |varepsilon| 0.35(r/0.05)^{-0.6}.Comment: 28 pages, 9 figures, Accepted for publication in JCA

Quadrupole formula for Kaluza-Klein modes in the braneworld

The quadrupole formula in four-dimensional Einstein gravity is a useful tool to describe gravitational wave radiation. We derive the quadrupole formula for the Kaluza-Klein (KK) modes in the Randall-Sundrum braneworld model. The quadrupole formula provides transparent representation of the exterior weak gravitational field induced by localized sources. We find that a general isolated dynamical source gives rise to the 1/r^2 correction to the leading 1/r gravitational field. We apply the formula to an evaluation of the effective energy carried by the KK modes from the viewpoint of an observer on the brane. Contrary to the ordinary gravitational waves (zero mode), the flux of the induced KK modes by the non-spherical part of the quadrupole moment vanishes at infinity and only the spherical part contributes to the flux. Since the effect of the KK modes appears in the linear order of the metric perturbations, the effective energy flux observed on the brane is not always positive, but can become negative depending on the motion of the localized sources.Comment: 9 pages, no figures, REVTeX 4; version accepted for publication in CQ

Bulk gravitational field and dark radiation on the brane in dilatonic brane world

We discuss the connection between the dark radiation on the brane and the bulk gravitational field in a dilatonic brane world model proposed by Koyama and Takahashi where the exact solutions for the five dimensional cosmological perturbations can be obtained analytically. It is shown that the dark radiation perturbation is related to the non-normalizable Kaluza-Klein (KK) mode of the bulk perturbations. For the de Sitter brane in the anti-de Sitter bulk, the squared mass of this KK mode is $2 H^2$ where $H$ is the Hubble parameter on the brane. This mode is shown to be connected to the excitation of small black hole in the bulk in the long wavelength limit. The exact solution for an anisotropic stress on the brane induced by this KK mode is found, which plays an important role in the calculation of cosmic microwave background radiation anisotropies in the brane world.Comment: 11 page

Conservation equation on braneworlds in six dimensions

We study braneworlds in six-dimensional Einstein-Gauss-Bonnet gravity. The Gauss-Bonnet term is crucial for the equations to be well-posed in six dimensions when non-trivial matter on the brane is included (the also involved induced gravity term is not significant for their structure), and the matching conditions of the braneworld are known. We show that the energy-momentum of the brane is always conserved, independently of any regular bulk energy-momentum tensor, contrary to the situation of the five-dimensional case.Comment: References added, minor changes, 3 pages, RevTeX, to app. in Class. Quant. Gra