We study an inflationary scenario with a vector field coupled with an inflaton field and show that the inflationary Universe is endowed with anisotropy for a wide range of coupling functions. This anisotropic inflation is a tracking solution where the energy density of the vector field follows that of the inflaton field irrespective of initial conditions. We find a universal relation between the anisotropy and a slow-roll parameter of inflation. Our finding has observational implications and gives a counterexample to the cosmic no-hair conjecture.

We study (3+1)-dimensional holographic superconductors in Einstein-Gauss-Bonnet gravity both numerically and analytically. It is found that higher curvature corrections make condensation harder. We give an analytic proof of this result, and directly demonstrate an analytic approximation method that explains the qualitative features of superconductors as well as giving quantitatively good numerical results. We also calculate conductivity and ωg/Tc, for ωg and Tc the gap in the frequency dependent conductivity and the critical temperature respectively. It turns out that the 'universal' behaviour of conductivity, ωg/Tc ≃ 8, is not stable to the higher curvature corrections. In the appendix, for completeness, we show our analytic method can also explain (2+1)-dimensional superconductors.

We study the statistical nature of primordial fluctuations from an anisotropic inflation which is realized by a vector field coupled to an inflaton. We find a suitable gauge, which we call the canonical gauge, for anisotropic inflation by generalizing the flat slicing gauge in conventional isotropic inflation. Using the canonical gauge, we reveal the structure of the couplings between curvature perturbations, vector waves, and gravitational waves. We identify two sources of anisotropy, i.e. the anisotropy due to the anisotropic expansion of the universe and that due to the anisotropic couplings among variables. It turns out that the latter effect is dominant. Since the coupling between the curvature perturbations and vector waves is the strongest one, the statistical anisotropy in the curvature perturbations is larger than that in gravitational waves. We find the cross correlation between the curvature perturbations and gravitational waves which never occurs in conventional inflation. We also find the linear polarization of gravitational waves. Finally, we discuss cosmological implication of our results.Comment: 20 pages, 4 figures;(V2) a reference adde

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 ω(Ψ) = 3Ψ/2(1 − Ψ) on the positive tension brane and ω(Φ) = −3Φ/2(1 + Φ) on the negative tension brane, where Ψ and Φ 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 Ψ and Φ 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-scalartensor 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.

We consider Schwinger pair production in 1+1 dimensional de Sitter space, filled with a constant electric field E. This can be thought of as a model for describing false vacuum decay beyond the semiclassical approximation, where pairs of a quantum field ϕ of mass m and charge e play the role of vacuum bubbles. We find that the adiabatic ``in" vacuum associated with the flat chart develops a space-like expectation value for the current J, which manifestly breaks the de Sitter invariance of the background fields. We derive a simple expression for J(E), showing that both ``upward" and ``downward" tunneling contribute to the build-up of the current. For heavy fields, with m2 ≫ eE,H2, the current is exponentially suppressed, in agreement with the results of semiclassical instanton methods. Here, H is the inverse de Sitter radius. On the other hand, light fields with m ≪ H lead to a phenomenon of infrared hyperconductivity, where a very small electric field mH≲eE ≪ H2 leads to a very large current J ∼ H3/E. We also show that all Hadamard states for ϕ necessarily break de Sitter invariance. Finally, we comment on the role of initial conditions, and ``persistence of memory" effects.