Braneworld Cosmological Perturbation Theory at Low Energy

Homogeneous cosmology in the braneworld can be studied without solving bulk equations of motion explicitly. The reason is simply because the symmetry of the spacetime restricts possible corrections in the 4-dimensional effective equations of motion. It would be great if we could analyze cosmological perturbations without solving the bulk. For this purpose, we combine the geometrical approach and the low energy gradient expansion method to derive the 4-dimensional effective action. Given our effective action, the standard procedure to obtain the cosmological perturbation theory can be utilized and the temperature anisotropy of the cosmic background radiation can be computed without solving the bulk equations of motion explicitly.Comment: 10 pages, Based on a talk presented at ACRGR4, the 4th Australasian Conference on General Relativity and Gravitation, Monash University, Melbourne, January 2004. To appear in the proceedings, in General Relativity and Gravitatio

Braneworld Flux Inflation

We propose a geometrical model of brane inflation where inflation is driven by the flux generated by opposing brane charges and terminated by the collision of the branes, with charge annihilation. We assume the collision process is completely inelastic and the kinetic energy is transformed into the thermal energy after collision. Thereafter the two branes coalesce together and behave as a single brane universe with zero effective cosmological constant. In the Einstein frame, the 4-dimensional effective theory changes abruptly at the collision point. Therefore, our inflationary model is necessarily 5-dimensional in nature. As the collision process has no singularity in 5-dimensional gravity, we can follow the evolution of fluctuations during the whole history of the universe. It turns out that the radion field fluctuations have a steeply tilted, red spectrum, while the primordial gravitational waves have a flat spectrum. Instead, primordial density perturbations could be generated by a curvaton mechanism.Comment: 11 pages, 6 figures, references adde

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