Cosmological constraints from the CMB and Ly-alpha forest revisited

TL;DR

This work reassesses cosmological constraints from the Ly-α forest and the CMB by using hundreds of simulations on a 6-dimensional grid to map the flux power spectrum $P_F(k)$ to the linear power spectrum $P_L(k)$, explicitly marginalizing over nuisance parameters such as the mean transmitted flux $\bar{F}$. It shows that uncertainties in $\bar{F}$ and non-linear, model-dependent mappings between $P_F(k)$ and $P_L(k)$ expand the allowed parameter space, weakening evidence for running of the spectral index $dn/d\ln k$. The joint CMB+Ly-α analysis finds a best-fit with $n\approx 0.98\pm0.03$ and $dn/d\ln k\approx 0$, with no tensors required, implying that current data do not necessitate departing from a scale-invariant model. The study emphasizes robust treatment of Ly-α systematics and the need for comprehensive simulations to avoid overstating constraints on the primordial power spectrum shape.

Abstract

The WMAP team has recently highlighted the usefulness of combining the Ly-alpha forest constraints with those from the cosmic microwave background (CMB). This combination is particularly powerful as a probe of the primordial shape of the power spectrum. Converting between the Ly-alpha forest observations and the linear mass power spectrum requires a careful treatment of nuisance parameters and modeling with cosmological simulations. We point out several issues which lead to an expansion of the errors, the two most important being the range of cosmological parameters explored in simulations and the treatment of the mean transmitted flux constraints. We employ a likelihood calculator for the current Ly-alpha data set based on an extensive 6-dimensional grid of simulations. We show that the current uncertainties in the mean transmission and the flux power spectrum define a degeneracy line in the amplitude-slope plane. The CMB degeneracy due to the primordial power spectrum shape follows a similar relation in this plane. This weakens the statistical significance of the primordial power spectrum shape constraints based on combined CMB+Ly-alpha forest analysis. Using the current data the simplest n=1 scale invariant model with dn/dln k=0 and no tensors has a Delta chi^2=4 compared to the best fitting model in which these 3 parameters are free. Current data therefore do not require relaxing these parameters to improve the fit.

Figures (2)

• Figure 1: Constraints on effective slope $n_{eff}$ and amplitude $\Delta^2$ at $k_p=0.03$ s/km. (a) The large, solid square with error bars is the original C02 result for a power law fit, while the large empty square is our similar fit to the C02 $P_L(k)$ points. Small empty symbols are our fits to the C02 and GH $P_L(k)$ results using a CDM shape of the transfer function (which differs from a pure power law fit, which does not include the fact that the effective slope is rapidly changing even in the narrow range probed here) -- triangle and square: fits to C02 and GH, respectively, using their error bars; pentagon and hexagon: similar with expanded errors on the last 3 points (slope errors are from the fit, amplitude calibration errors are all similar to the original C02 point). Small solid symbols and 68% contours are constraints from our direct fits to the C02 $P_F(k)$ points -- square and solid contour: our full procedure using C02 $\bar{F}$ constraints; triangle and dashed contour: similar with degraded simulation resolution; hexagon and dotted contour: degraded resolution and no correction using fully hydrodynamic simulations. (b) The empty square and its associated errors show our estimate of the Ly-$\alpha$ constraint used by WMAP (we apply an 11% amplitude increase over the GH points). Solid symbols and contours are our fits to the C02 $P_F(k)$ points for different assumptions about $\bar{F}$ -- hexagon and long dashed contour: $\bar{F}=0.705\pm 0.012$; triangle and short dashed contour: $\bar{F}=0.705\pm 0.027$; pentagon and dotted contour: $\bar{F}=0.742\pm 0.012$; square and solid contour: $\bar{F}=0.742\pm 0.027$. The latter is our final result, for which we also show the 95% contour.
• Figure 2: Our Ly-$\alpha$ constraints (solid square and solid contours), CMB (WMAP+ACBAR+CBI) constraints (dashed contours) and the Ly-$\alpha$ constraint used by WMAP (empty square with errors). The CMB contours follow $dn/d\ln k$, with more negative values leading to low amplitude and low slope: very roughly, $n_{\rm eff}\sim -2.45$ corresponds to $dn/d\ln k=0$, $n_{\rm eff}\sim -2.7$ to $dn/d\ln k=-0.03$ (final WMAP value) and $n_{\rm eff}\sim -2.85$ to $dn/d\ln k=-0.05$ (WMAPext value). We warn that due to a small number of Markov Chain elements (around 25000) the contours shown here may be an underestimate of the true 68% and 95% contours for the CMB. While the Ly-$\alpha$ constraint as used by WMAP pulls towards negative $dn/d\ln k$, our Ly-$\alpha$ constraints have a strong degeneracy, with the best fit preferring less negative $dn/d\ln k$. Filled triangles show the models obtained from the CMB-only chain with $dn/d\ln k>0$.