Perturbative evaluation of the scalar two-point function in the cosmic microwave background power spectrum

Recent work in the literature has found a suppression or, instead, an enhancement of the cosmic microwave background power spectrum in quantum gravity, although the effect is too small to be observed in both cases. The present paper studies in detail the equations recently proposed for a Born-Oppenheimer– type analysis of the problem. By using a perturbative approach to the analysis of the nonlinear ordinary differential equation obeyed by the two-point function for scalar fluctuations, we find various explicit forms of such a two-point function, with the associated power spectrum. In particular, a new family of power spectra is obtained and studied. The theoretical prediction of power enhancement at large scales is hence confirmed.