On cosmologies with “strong gravity in the past”

This short report is devoted to the study of cosmological solutions without initial singularity in scalar-tensor theories of gravity and the legitimacy of their classical treatment. Non-singular epoch -- genesis -- was constructed in a certain subclass of the Horndeski theory. Considered solution is stable at all times, and perturbations propagate subluminally. Moreover, it was show that in a specific range of Lagrangian parameters there is no strong coupling regime in the constructed model at early times, i.e. the classical field theory description is applicable. For this analysis of strong coupling problem we have used ``naive'' dimensional analysis. However, this analysis may sometimes badly fail in estimating the strong coupling scale. Indeed, examining the potential strong coupling problem at early times in a contracting cosmological model , which is conformally related to inflation, from naive dimensional analysis in the Jordan frame one would conclude that the quantum strong coupling energy scale can be lower than the classical energy scale, but from the Einstein frame prospective this should not be the case. We illustrate this point by calculation in the Jordan frame which shows cancellations of the dangerous contributions in the tree level amplitude. Therefore, it is necessary to use more accurate analysis of the strong coupling problem using unitarity bounds. To this end, useful unitarity relations and unitary bounds were found in a theory that contains scalar fields with different sound speeds.