One-loop Riemann correlators and dS invariance

          @misc{ pirsa_PIRSA:08100082,
            doi = {10.48660/08100082},
            url = {https://pirsa.org/08100082},
            author = {Roura, Albert},
            keywords = {Cosmology},
            language = {en},
            title = {One-loop Riemann correlators and dS invariance},
            publisher = {Perimeter Institute},
            year = {2010},
            month = {oct},
            note = {PIRSA:08100082 see, \url{https://pirsa.org}}
          }
          

Abstract

I will start with a brief qualitative discussion of the construction of a dS-invariant state for interacting theories using Euclidean methods and its real-time evolution within the closed-time-path formalism, as well as of the closely related in-in formalism. Next, I will focus on the two-point quantum correlation function for the Riemann tensor of the metric perturbations around dS including the one-loop correction from matter fields. A key object is the stress tensor two-point function, from which the one-loop Ricci correlator follows straightforwardly. We have obtained the exact result for minimally coupled fields with arbitrary mass in terms of maximally symmetric bitensors, which makes dS invariance manifest. Long range correlations are present for sufficiently small (but nonvanishing) masses, and the discontinuity of the massless limit can be understood in a simple way. Finally, I will comment on the implications for the tensorial power spectrum and on the calculation of the Weyl correlations.