Reconstructing the primordial power spectrum - a new algorithm

TL;DR

This work presents a Monte Carlo–based, model-independent algorithm to reconstruct the primordial power spectrum $P(k)$ from CMB and LSS data, compatible with existing MCMC pipelines. By binning in logarithmic $k$-space and interpolating in log space, the method tests for features without assuming a specific inflationary model, and a sliding-bin variant enhances sensitivity to narrow structures. Analyses of present data show no significant features, with a slight preference for negative curvature and a dip at large scales; mock Planck-like data demonstrate the method’s ability to recover a step or Gaussian feature without bias. The study also demonstrates that artificial glitches in $C_l$ can bias the recovered spectrum, highlighting the need for cautious interpretation of reconstructed $P(k)$ and potential running in the presence of data systematics.

Abstract

We propose an efficient and model independent method for reconstructing the primordial power spectrum from Cosmic Microwave Background (CMB) and large scale structure observations. The algorithm is based on a Monte Carlo principle and therefore very simple to incorporate into existing codes such as Markov Chain Monte Carlo. The algorithm has been used on present cosmological data to test for features in the primordial power spectrum. No significant evidence for features is found, although there is a slight preference for an overall bending of the spectrum, as well as a decrease in power at very large scales. We have also tested the algorithm on mock high precision CMB data, calculated from models with non-scale invariant primordial spectra. The algorithm efficiently extracts the underlying spectrum, as well as the other cosmological parameters in each case. Finally we have used the algorithm on a model where an artificial glitch in the CMB spectrum has been imposed, like the ones seen in the WMAP data. In this case it is found that, although the underlying cosmological parameters can be extracted, the recovered power spectrum can show significant spurious features, such as bending, even if the true spectrum is scale invariant.

Figures (12)

• Figure 1: Reconstructed best fit power spectra to the WMAP data from the fixed bin algorithm. The full line is for $N=2$, the dashed for $N=4$, and the dotted for $N=8$.
• Figure 2: Reconstructed best fit power spectra to all present data from the fixed bin algorithm. The full line is for $N=2$, the dashed for $N=4$, and the dotted for $N=8$.
• Figure 3: The temperature (TT) power spectra for the best fit models to the WMAP only data. The solid line is for $N=2$, the dashed for $N=4$, and the dotted for $N=8$. The black lines are the binned WMAP data.
• Figure 4: The temperature (TT) and temperature-polarization (TE) power spectra for the best fit models to the WMAP only data. The solid line is for $N=2$, the dashed for $N=4$, and the dotted for $N=8$. Only the low-$l$ parts of the spectra are shown. The black lines are the WMAP data.
• Figure 5: Reconstructed best fit power spectra to the WMAP data from the sliding bin algorithm. The full line is for $N=2$, the dashed for $N=4$, and the dotted for $N=8$.