### Viraj Sanghai

(Queen Mary University of London)

*Relativistic cosmological modelling for non-linear structures*

I will begin by giving a brief introduction on inhomogeneities in cosmology from a theoretical and observational perspective. Then I will talk about a specific approach we have developed to probe the effect of small-scale inhomogeneities on the large-scale expansion of the universe. In this approach, we take a bottom-up approach to relativistic cosmological modelling by splitting up our universe into cells. The matter content within each cell is described by the post-Newtonian formalism. At Newtonian order, we recover the standard Friedmann-like equations. At post-Newtonian orders, we obtain a correction to the large-scale expansion of the universe. As an example, we use this framework to investigate the cosmological evolution of a large number of regularly arranged point-like masses. At post-Newtonian orders, for a late time dust dominated universe, we get corrections to the dust term and we get an additional term that takes the same form as radiation. The radiation-like term is a result of the non-linearity of Einsteinâ€™s equations, and is due to the inhomogeneity present in our model. We then include a cosmological constant, radiation and spatial curvature in our model and study its influence on this radiation-like correction.