Inflationary tensor fluctuations, as viewed by Ashtekar variables and their imaginary friends

Abstract

We investigate tensor modes in inflationary scenarios from the point of view of Ashtekar variables and their generalizations labelled by Immirzi parameter \gamma, which we'll assume imaginary. By defining the classical perturbed Hamiltonian, we reproduce, on-shell, the usual expression found in cosmological perturbation theory. However the quantum Hamiltonian displays significant differences, namely in the vacuum energy and fluctuations of the various modes. Graviton states are represented by combinations of metric and connection variables. It turns out that half of these modes have negative energy but after defining the inner product we conclude that they are non-physical and should be selected out. We are left with the usual graviton modes but with a chiral asymmetry in the the vacuum energy and fluctuations. The latter depends on \gamma and on the ordering prescription (namely in the Hamiltonian constraint). Such an effect would leave a distinctive imprint in the polarization of the cosmic microwave background, thus finally engaging quantum gravity in meaningful experimental test.