Imprint of spatial curvature on inflation power spectrum

Abstract

If the Universe had a large curvature before inflation there is a deviation from the scale invariant perturbations of the inflaton at the beginning of inflation. This may have some effect on the cosmic microwave background anisotropy at large angular scales. We calculate the density perturbations for both open and closed universe cases using the Bunch-Davies vacuum condition on the initial state. We use our power spectrum to calculate the temperature anisotropy spectrum and compare the results with the Wilkinson microwave anisotropy map five year data. We find that our power spectrum gives a lower quadrupole anisotropy when $\ensuremath{\Omega}\ensuremath{-}1g0$, but matches the temperature anisotropy calculated from the standard Ratra-Peebles power spectrum at large $l$. The determination of spatial curvature from temperature anisotropy data is not much affected by the different power spectra which arise from the choice of different boundary conditions for the inflaton perturbation.