Nonlinear Structure Formation, Backreaction and Weak Gravitational Fields

There is an ongoing debate in the literature concerning the effects of averaging out inhomogeneities (``backreaction'') in cosmology. In particular, some simple models of structure formation studied in the literature seem to indicate that the backreaction can play a significant role at late times, and it has also been suggested that the standard perturbed FLRW framework is no longer a good approximation during structure formation, when the density contrast becomes nonlinear. In this work we use Zalaletdinov's covariant averaging scheme (macroscopic gravity or MG) to show that as long as the metric of the Universe can be described by the perturbed FLRW form, the corrections due to averaging remain negligibly small. Further, using a fully relativistic and reasonably generic model of pressureless spherical collapse, we show that as long as matter velocities remain small (which is true in our model), the perturbed FLRW form of the metric can be explicitly recovered. Together, these results imply that the backreaction remains small even during nonlinear structure formation, and we confirm this within the toy model with a numerical calculation.Comment: 8 pages, eas format, talk given at July 2008 CRAL-IPNL conference on "Dark Energy and Dark Matter

A Geometric characterization of Arithmetic Varieties

A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid divisor. We define the notion of geometrically rigid divisors in surfaces and then show that every surface defined over a number field can be expressed as a cover of the projective plane with branch locus contained in a geometrically rigid divisor in the plane. The main result is the characterisation of arithmetically defined divisors in the plane as geometrically rigid divisors in the plane.Comment: 8 Pages, AMSLaTe

Seiberg-Witten Invariants-An Expository Account

In this note, we give an exposition of the construction of Seiberg-Witten invariants