Inflation in the closed FLRW model and the CMB
  Recent cosmic microwave background (CMB) observations put strong constraints
on the spatial curvature via estimation of the parameter $\Omega_k$ assuming an
almost scale invariant primordial power spectrum. We study the evolution of the
background geometry and gauge-invariant scalar perturbations in an inflationary
closed FLRW model and calculate the primordial power spectrum. We find that the
inflationary dynamics is modified due to the presence of spatial curvature,
leading to corrections to the nearly scale invariant power spectrum at the end
of inflation. When evolved to the surface of last scattering, the resulting
temperature anisotropy spectrum ($C_{\ell}^{TT}$) shows deficit of power at low
multipoles ($\ell<20$). By comparing our results with the recent Planck data we
discuss the role of spatial curvature in accounting for CMB anomalies and in
the estimation of the parameter $\Omega_k$. Since the curvature effects are
limited to low multipoles, the Planck estimation of cosmological parameters
remains robust under inclusion of positive spatial curvature.
