The WiggleZ Dark Energy Survey: probing the epoch of radiation domination using large-scale structure

We place the most robust constraint to date on the scale of the turnover in the cosmological matter power spectrum using data from the WiggleZ Dark Energy Survey. We find this feature to lie at a scale of k_0 = 0.0160^(+ 0.0035)_(− 0.0041) (h Mpc^−1) (68 per cent confidence) for an effective redshift of z_(eff) = 0.62 and obtain from this the first ever turnover-derived distance and cosmology constraints: a measure of the cosmic distance–redshift relation in units of the horizon scale at the redshift of radiation–matter equality (r_H) of D_V(z_(eff) = 0.62)/r_H = 18.3^(+6.3)_(−3.3) and, assuming a prior on the number of extra relativistic degrees of freedom N_(eff) = 3, constraints on the cosmological matter density parameter Ω_M h^2 = 0.136^(+0.026)_(−0.052) and on the redshift of matter–radiation equality z_(eq) = 3274^(+631)_(−1260). We stress that these results are obtained within the theoretical framework of Gaussian primordial fluctuations and linear large-scale bias. With this caveat, all results are in excellent agreement with the predictions of standard ΛCDM models. Our constraints on the logarithmic slope of the power spectrum on scales larger than the turnover are bounded in the lower limit with values only as low as −1 allowed, with the prediction of P(k) ∝ k from standard ΛCDM models easily accommodated by our results. Finally, we generate forecasts to estimate the achievable precision of future surveys at constraining k_0, Ω_M h^2, z_(eq) and N_(eff). We find that the Baryon Oscillation Spectroscopic Survey should substantially improve upon the WiggleZ turnover constraint, reaching a precision on k_0 of ±9 per cent (68 per cent confidence), translating to precisions on Ω_M h^2 and z_(eq) of ±10 per cent (assuming a prior N_(eff) = 3) and on Neff of + 78− 56 per cent (assuming a prior Ω_M h^2 = 0.135). This represents sufficient precision to sharpen the constraints on N_(eff) from WMAP, particularly in its upper limit. For Euclid, we find corresponding attainable precisions on (k_0, Ω_M h^2, N_(eff)) of (3, 4,^(+ 17)_(− 21)) per cent. This represents a precision approaching our forecasts for the Planck Surveyor.