We prove that for a large class of generalized Randall-Sundrum type II models the characterization of the brane-gravity sector by the effective Einstein equation, Codazzi equation and the twice-contracted Gauss equation is equivalent to the bulk Einstein equation. We give the complete set of equations in the generic case of non-$Z_2$-symmetric bulk and arbitrary energy-momentum tensors both on the brane and in the bulk. Among these, the effective Einstein equation contains a varying cosmological “constant” and two new source terms. The first of these represents the deviation from $Z_2$ symmetry, while the second arises from the bulk energy-momentum tensor. We apply the formalism for the case of a perfect fluid on a Friedmann brane embedded in a generic bulk. The generalized Friedmann and Raychaudhuri equations are given in a form independent of both the embedding and the bulk matter. They contain two new functions obeying a first order differential system, both depending on the bulk matter and the embedding. Then we focus on Friedmann branes separating two nonidentical (inner or outer) regions of Reissner–Nordström–anti-de Sitter bulk space-times, generalizing previous non-$Z_2$-symmetric treatments. Finally the analysis is repeated for the Vaidya–anti-de Sitter bulk space-time, allowing for both ingoing and outgoing radiation in each region.

We study the inertial modes of slowly rotating, fully relativistic compact stars. The equations that govern perturbations of both barotropic and nonbarotropic models are discussed, but we present numerical results only for the barotropic case. For barotropic stars all inertial modes are a hybrid of axial and polar perturbations. We use a spectral method to solve for such modes of various polytropic models. Our main attention is on modes that can be driven unstable by the emission of gravitational waves. Hence, we calculate the gravitational-wave growth time scale for these unstable modes and compare the results to previous estimates obtained in Newtonian gravity (i.e. using post-Newtonian radiation formulas). We find that the inertial modes are slightly stabilized by relativistic effects, but that previous conclusions concerning, e.g., the unstable r modes remain essentially unaltered when the problem is studied in full general relativity.

We consider the space-time variation of gauge couplings in brane-world models induced by the coupling to a bulk scalar field. A variation is generated by the running of the gauge couplings with energy and a conformal anomaly while going from the Jordan to the Einstein frame. We indicate that the one-loop corrections cancel implying that one obtains a variation of the fine structure constant by either directly coupling the gauge fields to the bulk scalar field or having bulk scalar field dependent Yukawa couplings. Taking into account the cosmological dynamics of the bulk scalar field, we constrain the strength of the gauge coupling dependence on the bulk scalar field and relate it to modifications of gravity at low energy.

In this paper we review the separate universe approach for cosmological perturbations and point out that it is essentially the lowest order approximation to a gradient expansion. Using this approach, one can study the nonlinear evolution of inhomogeneous spacetimes and find the conditions under which the long wavelength curvature perturbation can vary with time. When there is one degree of freedom or a well-defined equation of state the nonlinear long wavelength curvature perturbation remains constant. With more degrees of freedom it can vary and this variation is determined by the nonadiabatic pressure perturbation, exactly as in linear theory. We identify combinations of spatial vectors characterizing the curvature perturbation which are invariant under a change of time hypersurfaces.

We study the definition of perturbations in the presence of a submanifold, such as, e.g., a brane. In the standard theory of cosmological perturbations, one compares quantities at the same coordinate points in the nonperturbed and the perturbed manifolds, identified via a (nonunique) mapping between the two manifolds. In the presence of a physical submanifold one needs to modify this definition in order to evaluate perturbations of quantities at the submanifold location. As an application, we compute the perturbed metric and the extrinsic curvature tensors at the brane position in a general gauge.

The differential equation governing the distance redshift for partially filled-beam optics in pressure-free Friedmann-Lemaître-Robertson-Walker (FLRW) cosmology is shown to be the Lamé equation. The distance redshift $D\left(z\right)\mathrm{}$ discussed is appropriate for observations in inhomogeneous cosmologies for which lensing by masses external to the observing beam is negligible and for which lensing by transparent matter within the beam can be approximated by a homogeneous mass density expanding with the FLRW background. Some solutions of the derived Lamé equation are given in terms of Weierstrass elliptic integrals. A new simplified and useful expression for filled-beam $D\left(z\right)\mathrm{}$ in standard flat FLRW is also given.

In contrast with the inflaton case, the curvature perturbations due to the curvaton field depend strongly on the evolution of the curvaton before its decay. We study in detail the dynamics of the curvaton evolution during and after inflation. We consider that the flatness of the curvaton potential may be affected by supergravity corrections, which introduce an effective mass proportional to the Hubble parameter. We also consider that the curvaton potential may be dominated by a quartic or by a non-renormalizable term. We find analytic solutions for the curvaton evolution for all these possibilities. In particular, we show that, in all the above cases, the curvaton density ratio with respect to the background density of the Universe decreases. Therefore, it is necessary that the curvaton decays only after its potential becomes dominated by the quadratic term, which results in (Hubble damped) sinusoidal oscillations. In the case when a non-renormalizable term dominates the potential, we find a possible non-oscillatory attractor solution that threatens to erase the curvature perturbation spectrum. Finally, we study the effects of thermal corrections to the curvaton potential and show that, if they ever dominate the effective mass, they lead to premature thermalization of the curvaton condensate. To avoid this danger, a stringent bound has to be imposed on the coupling of the curvaton to the thermal bath.

The Wilkinson Microwave Anisotropy Probe microwave background data may be giving us clues about new physics at the transition from a “stringy” epoch of the Universe to the standard Friedmann-Robertson-Walker description. Deviations on large angular scales of the data, as compared to theoretical expectations, as well as running of the spectral index of density perturbations, can be explained by new physics whose scale is set by the height of an inflationary potential. As examples of possible signatures for this new physics, we study the cosmic microwave background spectrum for two string inspired models: (1) modifications to the Friedmann equations and (2) velocity dependent potentials. The suppression of low $“l”$ modes in the microwave background data arises due to the new physics. In addition, the spectral index is red $\mathrm{}(n<\mathrm{}1\mathrm{})\mathrm{}$ on small scales and blue $\mathrm{}(n>\mathrm{}1\mathrm{})\mathrm{}$ on large scales, in agreement with data.

We investigate the CP-violating electron-quark interactions arising from the exchange of spin-1 and spin-0 leptoquarks coupled to the first fermion family and deduce the bounds on the CP-violating products of the effective leptoquark-fermion coupling constants from experimental limits on CP-violating electron-nucleon interactions.

In this paper we analyze discrete torsion in perturbative heterotic string theory. In previous work we have given a purely mathematical explanation of discrete torsion as the choice of orbifold group action on a B field, in the case that $dH=0;$ in this paper we perform the analogous calculations in heterotic strings where $\mathrm{dH}\ne 0.$

In this article we shall outline a derivation of the analogue of discrete torsion for the M-theory three-form potential. We find that some of the differences between orbifold group actions on the C field are classified by $H^3(\Gamma ,U(1\left)\mathrm{}\right).$ We also compute the phases that the low-energy effective action of a membrane on $T^3$ would see in the analogue of a twisted sector, and note that they are invariant under the obvious $SL(3,\mathbf{Z})$ action.

In this article we explain discrete torsion. Put simply, discrete torsion is the choice of orbifold group action on the B field. We derive the classification $H^2(\Gamma ,U(1\left)\mathrm{}\right),$ the twisted sector phases appearing in string loop partition functions, Douglas’s description of discrete torsion for D-branes in terms of a projective representation of the orbifold group, and outline how the results of Vafa and Witten fit into this framework. In addition, we observe that additional degrees of freedom (known as shift orbifolds) appear in describing orbifold group actions on B fields, in addition to those classified by $H^2(\Gamma ,U(1\left)\mathrm{}\right),$ and explain how these degrees of freedom appear in terms of twisted sector contributions to partition functions and in terms of orbifold actions on D-brane worldvolumes. This paper represents a technically simplified version of prior papers by the author on discrete torsion. We repeat here technically simplified versions of results from those papers, and have included some new material.

A black hole, surrounded by a reflecting shell, acts as an effective starlike object with respect to the outer region that leads to vacuum polarization outside, where the quantum fields are in the Boulware state. We find the quantum correction to the Hawking temperature, taking into account this circumstance. It is proportional to the integral of the trace of the total quantum stress-energy tensor over the whole space from the horizon to infinity. For the shell, sufficiently close to the horizon, the leading term comes from the boundary contribution of the Boulware state.

The chaotic inflationary model of the early Universe, proposed by Linde, is explored in the braneworld, considering matter described by a minimally coupled self-interacting scalar field. We obtain cosmological solutions which admit the evolution of a universe either from a singularity or without a singularity. It is found that a very weakly coupled self-interacting scalar field is necessary for a quartic type potential in the braneworld model compared to that which is necessary in general relativity. In a braneworld, sufficient inflation may be obtained even with an initial scalar field having a value less than the Planck scale. It is found that if the Universe is kinetic energy dominated to begin with, it transits to an inflationary stage subsequently.

In the first part of this paper, we study the back reaction of the large-$N$ light cone momentum on the maximally supersymmetric anti-$\mathrm{pp}$-wave background. This gives the type IIA geometry of large-$N$ D0-branes on curved space with fluxes. By taking an appropriate decoupling limit, we conjecture a new duality between string theory on that background and dual field theory on D0-branes, which we derive by calculating linear coupling terms. Agreement of decoupling quantities, $\mathrm{SO}\left(3\right)\mathrm{}\times \mathrm{SO}\left(6\right)\mathrm{}$ isometry, and the Higgs branch on both theories are shown. Also we find that, whenever the dual field theory is weakly coupled, the curvature of the geometry is large. In the second part of this paper, we derive the supermembrane action on a general $\mathrm{pp}$-wave background only through the properties of a null Killing vector and, through this, derive the matrix model.

We present the solution for effective couplings on a running de Sitter brane. A renormalization group formalism is developed for linearized gravity in a two de Sitter brane model. It is shown that the effective tension remains a constant, similar to the zero cosmological constant case. We also discuss the suppression of higher derivative terms.

An attempt is made to match the Kerr metric with Vaidya’s description of a black hole in a cosmological background. The attempt is unsuccessful and shows that the object at the center of Vaidya’s metric is certainly non-Kerr like.

We investigate the potential of observations of anisotropies in the cosmic microwave background (CMB) and large-scale structure in the Universe to detect possible modifications of standard inflationary models by physics beyond the Planck scale. A generic model of the primordial density fluctuations is investigated, and we derive constraints on its parameters from current data. We conclude that the currently available data do not put very stringent constraints on this model. Furthermore, we use simulated power spectra from the Sloan Digital Sky Survey (SDSS) and the Planck satellite to show that it is unlikely that a trans-Planckian signature of this type can be detected in CMB and large-scale structure data.

A modified gravity, which eliminates the need for dark energy and which seems to be stable, is considered. The terms with positive powers of curvature support the inflationary epoch while the terms with negative powers of curvature serve as effective dark energy, supporting current cosmic acceleration. The equivalent scalar-tensor gravity may be compatible with the simplest solar system experiments.

Cosmic shear measurements have now improved to the point where they deserve to be treated on par with cosmic microwave background (CMB) and galaxy clustering data for cosmological parameter analysis, using the full measured aperture mass variance curve rather than a mere phenomenological parametrization thereof. We perform a detailed 9-parameter analysis of recent lensing [the Red Sequence Cluster Survey (RCS)], CMB (up to Archeops) and galaxy clustering (2dF Collaboration) data, both separately and jointly. CMB and 2dF data are consistent with a simple flat adiabatic scale-invariant model with ${\Omega }_{\Lambda }=0.72\mathrm{}\pm 0.09,$ $h^2{\Omega }_{\mathrm{cdm}}=0.115\mathrm{}\pm 0.013,$ $h^2{\Omega }_{\mathrm{b}}=0.024\mathrm{}\pm 0.003,$ and a hint of reionization around $z\sim 8.$ Lensing helps further tighten these constraints, but reveals tension regarding the power spectrum normalization: including the RCS survey results raises ${\sigma }_8$ significantly and forces other parameters to uncomfortable values. Indeed, ${\sigma }_8$ is emerging as the currently most controversial cosmological parameter, and we discuss possible resolutions of this ${\sigma }_8$ problem. We also comment on the disturbing fact that many recent analyses (including this one) obtain error bars smaller than the Fisher matrix bound. We produce a CMB power spectrum combining all existing experiments, useful for a “WMAP versus world” comparison to test how realistic the error estimates have been in the cosmology community. Comparing with the WMAP results shows remarkably good agreement both on the power spectrum and on cosmological parameters, which means that precision cosmology has passed an important test.