Toy models in holographic cosmology

Abstract

The AdS/CFT correspondence relates holographically (meaning, a theory in a bulk geometry, with a theory on a boundary)a gravitational theory, usually of $AdS_{d+1}$ type, and sometimes coming from string theory, with a quantum field theory on the flat $d$-dimensional "boundary", one theory being weakly coupled, and the other strongly coupled. Initially, one used the gravitational side to calculate observables in the field theory side. However, in the last years, it has started to be applied to cosmology, of a strongly coupled type, by doing calculations in a 2+1 dimensional perturbative field theory. A phenomenological approach seems to be a strongly coupled alternative to inflation, giving results that can be matched to the CMBR and solve the Hot Big Bang problems as well as $\Lambda$ CDM plus inflation, though there are issues that need to be resolved. We will use very simple alternatives to the generic phenomenological 2+1 dimensional field theory ("toy models") to redo some of the calculations and see if they can be extended. (AU)