Primordial nucleosynthesis in higher dimensional cosmology

We investigate nucleosynthesis and element formation in the early universe in the framework of higher dimensional cosmology. For this purpose we utilize a previous solution of the present author, which may be termed as the generalized Friedmann-Robertson-Walker model. We find that temperature decays less rapidly in higher dimensional cosmology, which we believe may have nontrivial consequences \emph{vis-a-vis} primordial physics

Spherical collapse of a heat conducting fluid in higher dimensions without horizon

We consider a scenario where the interior spacetime,described by a heat conducting fluid sphere is matched to a Vaidya metric in higher dimensions.Interestingly we get a class of solutions, where following heat radiation the boundary surface collapses without the appearance of an event horizon at any stage and this happens with reasonable properties of matter field.The non-occurrence of a horizon is due to the fact that the rate of mass loss exactly counterbalanced by the fall of boundary radius.Evidently this poses a counter example to the so-called cosmic censorship hypothesis.Two explicit examples of this class of solutions are also given and it is observed that the rate of collapse is delayed with the introduction of extra dimensions.The work extends to higher dimensions our previous investigation in 4D.Comment: 6 page

Applications of Stein's method for concentration inequalities

Stein's method for concentration inequalities was introduced to prove concentration of measure in problems involving complex dependencies such as random permutations and Gibbs measures. In this paper, we provide some extensions of the theory and three applications: (1) We obtain a concentration inequality for the magnetization in the Curie--Weiss model at critical temperature (where it obeys a nonstandard normalization and super-Gaussian concentration). (2) We derive exact large deviation asymptotics for the number of triangles in the Erd\H{o}s--R\'{e}nyi random graph $G(n,p)$ when $p\ge0.31$. Similar results are derived also for general subgraph counts. (3) We obtain some interesting concentration inequalities for the Ising model on lattices that hold at all temperatures.Comment: Published in at http://dx.doi.org/10.1214/10-AOP542 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org