Seminarium "Teoria cząstek elementarnych i kosmologia"

f(R) gravity represents the simplest purely geometrical generalization of the Einstein general theory of relativity without undesirable ghosts. The pioneer R+R^2 model of inflation (AS, 1980) contains only one adjustable parameter taken from observations, has a graceful exit from inflation and a natural mechanism for creation and heating of matter after its end, and produces a very good fit to existing observational data on the power spectrum of primordial scalar (adiabatic density) perturbations. Regarding its possible UV completion, it was recently shown that this model can be included as a particular solution into a weakly non-local UV-complete generalization of quantum gravity which is super-renormalizable or finite and does not contain ghosts. I consider the inverse problem of reconstruction of inflationary models in f(R) gravity using information on the power spectrum of scalar perturbations only, ambiguity in this procedure and how it can be fixed by some aesthetic assumptions on the absence of new physical scales during and after inflation. Also discussed is the problem on formation of inflation from generic classical curvature singularity preceding it, and which conditions are needed for this. Since this process is generic, too, for inflation to begin inside a patch including the observable part of the Universe, causal connection inside the whole patch is not necessary. However, it becomes obligatory for a graceful exit from inflation in order to have practically the same number of e-folds during inflation inside this patch.