Constraints on inflation from CMB and Lyman-alpha forest

TL;DR

This work tests single-field slow-roll inflation by jointly analyzing CMB data (COBE, Boomerang, MAXIMA) with Ly-alpha forest and PSCz galaxy power spectra to constrain the inflationary parameters $n$, $r$, and $dlnk$ at a pivot $k_0=0.05$ Mpc^{-1}. A likelihood approach combines $\chi^2$ contributions from CMB, PSCz, and Ly-alpha data in a flat cosmology, marginalizing over nuisance normalizations and $\tau$. The results favor $n$ around 0.9, $r$ below 0.3, and $dlnk$ near 0, implying small-field models are preferred and hybrid models are disfavored, with Ly-alpha data providing orthogonal constraint directions relative to CMB. Systematic uncertainties in the Ly-alpha inference could affect the small-scale power, motivating independent cross-checks of the Ly-alpha derived linear power spectrum.

Abstract

We constrain the spectrum of primordial curvature perturbations by using recent Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) data. Specifically, we consider CMB data from the COBE, Boomerang and Maxima experiments, the real space galaxy power spectrum from the IRAS PSCz survey, and the linear matter power spectrum inferred from Ly-alpha forest spectra. We study the case of single field slow roll inflationary models, and we extract bounds on the scalar spectral index, n, the tensor to scalar ratio, r, and the running of the scalar spectral index, dlnk, for various combinations of the observational data. We find that CMB data, when combined with data from Lyman-alpha forest, place strong constraints on the inflationary parameters. Specifically, we obtain n \approx 0.9, r < 0.3 and dlnk \approx 0, indicating that single field hybrid models are ruled out.

Figures (4)

• Figure 1: The various slow-roll models in $(n,r)$ and $(n,\partial_{{\rm ln} k})$ space. The dashed lines are the two attractors (here we have used $\kappa =5$ which is a typical value for a flat universe with a large cosmological constant). The figure $(n,\partial_{{\rm ln} k})$ is for $\xi^2=0$. The hatched regions move up and down by inclusion of the third derivative, $\xi^2 \neq 0$ (see Eq. \ref{['appendixEQ1']} in the appendix).
• Figure 2: The 1 and 2 $\sigma$ allowed regions for the two slow roll parameters $n$ and $\partial_{{\rm ln} k}$. The left panels assume a BBN prior on $\Omega_b h^2 = 0.019$, whereas the right panels are for $\Omega_b h^2 = 0.030$, the value which best fits the CMB data. The top row is for CMB data alone, the middle row is for Lyman-$\alpha$ data alone, and the bottom row is for the combined analysis.
• Figure 3: The 1 and 2 $\sigma$ allowed regions in the $(n,r)$ plane. The left panels assume a BBN prior on $\Omega_b h^2 = 0.019$, whereas the right panels are for $\Omega_b h^2 = 0.030$, the value which best fits the CMB data. The top panels are for CMB data alone, while the bottom panels are for the combined analysis. Hybrid models are to the right of the full line.
• Figure 4: The 1 and 2 $\sigma$ allowed regions in the $(n,r)$ plane. These results are obtained from the combined analysis, neglecting the last 3 data-points from croft. The left panels assume a BBN prior on $\Omega_b h^2 = 0.019$, whereas the right panels are for $\Omega_b h^2 = 0.030$, the value which best fits the CMB data. The top panels assume $\partial_{{\rm ln} k}=0$, whereas the lower panels have $\partial_{{\rm ln} k}$ as a free parameter. Hybrid models are to the right of the full line.