A new search for features in the primordial power spectrum

TL;DR

This paper develops a high-resolution, non-parametric reconstruction of the primordial power spectrum $P^0(k)$ from the WMAP CMB angular power spectrum and tests its consistency with SDSS matter power data in $k\in[0.01,0.1]\,h\mathrm{Mpc}^{-1}$, while allowing the baryon fraction $f_b$ to vary. The method uses a smoothing-informed inversion with a window matrix $W$ to map $P^0(k)$ to $C_\ell$, calibrates the smoothing via $\epsilon$ so that $\chi^2$ matches data points, and propagates $P^0(k)$ through a CMBFAST transfer function to compare with SDSS through window effects and a bias $b$. Results show features in $P^0(k)$, especially near $k\sim0.05\,h\mathrm{Mpc}^{-1}$, that improve the joint fit to WMAP and SDSS for a model with a particular baryon content, reducing the need for a large $f_b$. The work demonstrates that relaxing a strict power-law form for $P^0(k)$ can enhance concordance among CMB, LSS, BBN, and $H_0$ measurements, with implications for fundamental physics and future data.

Abstract

We develop a new approach toward a high resolution non-parametric reconstruction of the primordial power spectrum using WMAP cosmic microwave background temperature anisotropies that we confront with SDSS large-scale structure data in the range k~0.01-0.1 h/Mpc. We utilise the standard LambdaCDM cosmological model but we allow the baryon fraction to vary. In particular, for the concordance baryon fraction, we compare indications of a possible feature at k~0.05 h/Mpc in WMAP data with suggestions of similar features in large scale structure surveys.

Figures (7)

• Figure 1: Reconstructed initial power spectrum in units of $2.95\times 10^{-9}$ from WMAP $C_\ell$'s with model 3 cosmological parameters. The irregular middle curve represent the mean and the surrounding curves are obtained by summing and subtracting the square root of the diagonal elements of the covariance matrix. The smooth line is a reference power law power spectrum given by $k^{n_{s}-1}$, where $n_{s}\approx 0.99$.
• Figure 2: The noisy thin curve connects the data from WMAP. The reconstructed power spectrum convolved back to multipole space is given by the thick smooth line, that shows clearly the effect of smoothing.
• Figure 3: Results from 5000 Monte Carlo realizations drawn form a power law power spectrum, given by $k^{n_{s}-1}$ where $n_{s}=0.99$, with model 3 cosmological parameters. The thin smooth line in the center is the exact initial power law and the dashed curve is the averaged reconstructed initial power spectrum. The two symmetric lines represent the standard deviation from the averaged reconstruction. No strong systematic bias appears in the reconstruction and possible candidates for features are given by the outliers respect to the one sigma band. The plot is in units of $2.95\times 10^{-9}$.
• Figure 4: The upper plot shows the WMAP best case (model 1). The reconstructed matter power spectrum convolved with the SDSS window functions and evolved at redshift zero is given by the black diamonds connected by a piecewise continuous line. The small error bars reflect the quality of WMAP data and are constructed with the square root of the diagonal elements of the full covariance matrix, which is used for the statistical analysis. The thin irregular curve is the mean reconstruction before convolution and the dash-joined triangles are the SDSS data with a maximising bias. The lower plot is the SDSS best case (model 2)
• Figure 5: The conventions are the same as for the previous figure. In the lower plot, model 5, with a low baryonic content, presents oscillations completely out of phase with some of the SDSS features. In the middle, model 3, our best case, mimics particularly well the SDSS feature at $k\sim0.05\,h\mathrm{Mpc^{-1}}$. Model 4 at the top represents a case with slightly higher baryonic fraction and is also a good fit.