Dark Radiation and Inflationary Freedom after Planck 2015

TL;DR

This paper assesses whether a flexible, non-parametric primordial power spectrum (PPS) form can bias constraints on dark radiation and neutrino properties using Planck 2015 data. By parameterizing the PPS with a PCHIP interpolation over 12 nodes and comparing to the standard power-law PPS, the authors quantify degeneracies with $N_{\rm eff}$, $\sum m_\nu$, sterile neutrinos, and thermal axions. They find that polarization data (TE, EE) substantially break these degeneracies, yielding results compatible with ΛCDM and a standard PPS, though mild hints of features at large scales persist. The study concludes that current data mildly favor a power-law PPS, but non-parametric PPS remains viable, highlighting the need for future measurements to decisively test inflationary scenarios and dark radiation properties.

Abstract

The simplest inflationary models predict a primordial power spectrum (PPS) of the curvature fluctuations that can be described by a power-law function that is nearly scale-invariant. It has been shown, however, that the low-multipole spectrum of the CMB anisotropies may hint the presence of some features in the shape of the scalar PPS, which could deviate from its canonical power-law form. We study the possible degeneracies of this non-standard PPS with the neutrino anisotropies, the neutrino masses, the effective number of relativistic species and a sterile neutrino or a thermal axion mass. The limits on these additional parameters are less constraining in a model with a non-standard PPS when only including the temperature auto-correlation spectrum measurements in the data analyses. The inclusion of the polarization spectra noticeably helps in reducing the degeneracies, leading to results that typically show no deviation from the $Λ$CDM model with a standard power-law PPS.

Figures (17)

• Figure 1: Comparison of the Planck 2015 data Adam:2015rua with the TT, TE and EE spectra obtained using the marginalized best-fit values from the analyses of Planck TT+lowP (black) and Planck TT,TE,EE+lowP (blue) in the $\Lambda\textrm{CDM}$ model with the power-law (PL) PPS, and from the analyses of Planck TT+lowP (red) and Planck TT,TE,EE+lowP (green) in the $\Lambda\textrm{CDM}$ model with the PCHIP PPS. The adopted values for each spectrum are reported in Tab. \ref{['tab:lcdm']}. We plot the $D_\ell=\ell(\ell+1)\,C_\ell/(2\pi)$ spectra and the relative (absolute for the case of the TE spectra) difference between each spectrum and the one obtained in the $\Lambda\textrm{CDM}$ (power-law PPS) model from the Planck TT+lowP data (black line).
• Figure 2: 68% and 95% CL constraints on $N_{\rm{eff}}$, obtained in the $\Lambda\textrm{CDM}$ + $N_{\rm{eff}}$ model. Different colors indicate Planck TT+lowP with PL PPS (black), Planck TT+lowP with PCHIP PPS (red), Planck TT,TE,EE+lowP with PL PPS (blue) and Planck TT,TE,EE+lowP with PCHIP PPS (green). For each color we plot 4 different datasets: from top to bottom, we have CMB only, CMB+MPkW, CMB+BAO and CMB+lensing. We also illustrate the results, in the context of the 8-nodes parameterization, for the Planck TT,TE,EE+lowP+MPkW dataset (last point in black).
• Figure 3: 68% and 95% CL constraints in the ($N_{\rm{eff}}$, $P_{s,j}$) planes, obtained in the $\Lambda\textrm{CDM}$ + $N_{\rm{eff}}$ model. We show the results for Planck TT+lowP (gray), Planck TT+lowP+MPkW (red), Planck TT,TE,EE+lowP (blue) and Planck TT,TE,EE+lowP+MPkW (green).
• Figure 4: As Fig. \ref{['fig:nnu_bars']} but for the $\Lambda\textrm{CDM}$ plus $\sum m_\nu$ case.
• Figure 5: As Fig. \ref{['fig:nnu_corr']} but for the $\Lambda\textrm{CDM}$ plus $\sum m_\nu$ case.