Reza Tavakol

The embedding of General Relativity in five dimensions

We argue that General Relativistic solutions can always be locally embedded in Ricci-flat 5-dimensional spaces. This is a direct consequence of a theorem of Campbell (given here for both a timelike and spacelike extra dimension, together with a special case of this theorem) which guarantees that anyn-dimensional Riemannian manifold can be locally embedded in an (n+1)-dimensional Ricci-flat Riemannian manifold. This is of great importance in establishing local generality for a proposal recently put forward and developed by Wesson and others, whereby vacuum (4+1)-dimensional field equations give rise to (3+1)-dimensional equations with sources. An important feature of Campbells procedure is that it automatically guarantees the compatibility of Gauss-Codazzi equations and therefore allows the construction of embeddings to be in principle always possible. We employ this procedure to construct such embeddings in a number of simple cases.

D-dimensional gravity from (D+1) dimensions

We generalize Wessons procedure, whereby vacuum (4 + 1)-dimensional field equations give rise to (3 + 1)-dimensional equations with sources, to arbitrary dimensions. We then employ this generalization to relate the usual (3 + 1)-dimensional vacuum field equations to (2 + 1)-dimensional field equations with sources and derive the analogues of the classes of solutions obtained by Ponce de Leon. This way of viewing lower dimensional gravity theories can be of importance in establishing a relationship between such theories and the usual four-dimensional general relativity, as well as giving a way of producing exact solutions in (2 + 1) dimensions that are naturally related to the vacuum (3 + 1)-dimensional solutions. An outcome of this correspondence, regarding the nature of lower dimensional gravity, is that the intuitions obtained in (3 + 1) dimensions may not be automatically transportable to lower dimensions. We also extend a number of physically motivated solutions studied by Wesson and Ponce de Leon to (D + 1) dimensions and employ the equivalence between the (D + 1) Kaluza - Klein theories with empty D-dimensional Brans - Dicke theories (with ) to throw some light on the solutions derived by these authors.

Evolution of fNL to the adiabatic limit

We study inflationary perturbations in multiple-field models, for which ζ typically evolves until all isocurvature modes decay — the adiabatic limit. We use numerical methods to explore the sensitivity of the local-shape bispectrum to the process by which this limit is achieved, finding an appreciable dependence on model-specific data such as the time at which slow-roll breaks down or the timescale of reheating. In models with a sum-separable potential where the isocurvature modes decay before the end of the slow-roll phase we give an analytic criterion for the asymptotic value of fNL to be large. Other examples can be constructed using a waterfall field to terminate inflation while fNL is transiently large, caused by descent from a ridge or convergence into a valley. We show that these two types of evolution are distinguished by the sign of the bispectrum, and give approximate expressions for the peak fNL.

On applications of Campbell's embedding theorem

A little known theorem due to Campbell is employed to establish the local embedding of a wide class of four-dimensional spacetimes in five-dimensional Ricci-flat spaces. An embedding for the class of n-dimensional Einstein spaces is also found. The local nature of Campbells theorem is highlighted by studying the embedding of some lower-dimensional spaces.

Density perturbations in f(R) gravity theories in metric and Palatini formalisms

We make a detailed study of matter density perturbations in both metric and Palatini formalisms. Considering general theories whose Lagrangian density is a general function,

Oscillatory universes in loop quantum cosmology and initial conditions for inflation

f(R)

Convective dynamos in spherical wedge geometry

, of the Ricci scalar

Chaotic inflation in modified gravitational theories

R

Inflationary Cosmology and Quantization Ambiguities in Semi-Classical Loop Quantum Gravity

, we derive the equation of matter density perturbations in each case, in a number of gauges, including comoving, longitudinal and uniform density gauges. We show that for viable

OSCILLATORY MIGRATING MAGNETIC FIELDS IN HELICAL TURBULENCE IN SPHERICAL DOMAINS

f(R)