Speaker
Description
Outlined are the two simplest classes of phenomenological models of slow-roll inflation in the early Universe based either on scalar fields in General Relativity or on modified $f(R)$ gravity, their relation and basic assumptions necessary for their realization. At the present state-of-the-art, the simplest inflationary models from these classes producing the best fit to all existing astronomical data requires one, maximum two dimensionless parameters taken from observations only. It is shown that inflation in $f(R)$ gravity represents an intermediate dynamical attractor for slow-rolling scalar fields strongly coupled to gravity. The main discoveries expected for these models in future are discussed, too. Among them the most fundamental are primordial quantum gravitational waves generated during inflation. It is argued that the measured value of the slope $n_s-1$ of the primordial scalar power spectrum, under the additional assumption of the absence of new fundamental scales both during and after inflation, implies small, but not too small tensor-to-scalar ratio $r \sim 3(1-n_s)^2 \sim 0.0004$ or even more, similar to that in the original $R+R^2$ inflationary model (1980). Another possible discovery is related to small local features in the CMB temperature anisotropy power spectrum in the multipole range $l=(20-40)$ beyond which new physics during inflation may be hidden. Also considered is the onset of inflation from generic anisotropic curvature singularity preceding it in GR and $f(R)$ gravity, and which conditions are needed for it. 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.