Knot reconstruction of the scalar primordial power spectrum with Planck, ACT, and SPT CMB data

Abstract

We investigate a non-parametric Bayesian method for reconstructing the primordial power spectrum (PPS) of scalar perturbations using temperature and polarisation data from the {\em Planck}, ACT, and SPT CMB experiments. This reconstruction method is based on linear splines for the PPS between nodes in $k$-space whose amplitudes and positions are allowed to vary. All three data sets consistently show no significant deviations from a power-law form in the range $0.005\lesssim k\mathrm{Mpc}\lesssim 0.16$ independent of the number of knots adopted to perform the reconstruction. The addition of high-resolution CMB measurements from ACT and SPT slightly improves the range of scales of the scalar PPS which are well constrained around a power law up to $k\simeq 0.25{\mathrm{Mpc}}^{-1}$ and $k\simeq 0.2{\mathrm{Mpc}}^{-1}$, respectively. At large scales, a potential oscillatory feature in the primordial power spectrum appears when we consider six or more nodes. We test the robustness of the methodology and our results by varying the detailed number of knots from $N=2$ to $N=10$. We have used the reconstructed scalar PPS to derive several quantities related to inflationary dynamics, such as the effective scalar spectral index, which describes the dependence of the PPS on the scales and parameters associated with the effective field theory of inflation, to provide information on possible departures from the standard single-field canonical case. Finally, we investigate whether the excess of smoothing in the region of the acoustic peaks of the CMB anisotropy temperature power spectrum in the \textit{Planck} PR3 data is degenerate with our reconstructions of the PPS, but find no significant correlation between them.

20 pages, 12 figures

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