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
$k_0=0.0160^{+0.0041}_{-0.0035}$ [h/Mpc] (68% confidence) for an effective
redshift of 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=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 matter
density parameter $\Omega_Mh^2=0.136^{+0.026}_{-0.052}$ and on the redshift of
matter-radiation equality $z_{eq}=3274^{+631}_{-1260}$. All results are in
excellent agreement with the predictions of standard LCDM models. Our
constraints on the logarithmic slope of the power spectrum on scales larger
than the turnover is bounded in the lower limit with values only as low as -1
allowed, with the prediction of standard LCDM models easily accommodated by our
results. Lastly, we generate forecasts for the achievable precision of future
surveys at constraining $k_0$, $\Omega_Mh^2$, $z_{eq}$ and $N_{eff}$. We find
that BOSS should substantially improve upon the WiggleZ turnover constraint,
reaching a precision on $k_0$ of $\pm$9% (68% confidence), translating to
precisions on $\Omega_Mh^2$ and $z_{eq}$ of $\pm$10% (assuming a prior
$N_{eff}=3$) and on $N_{eff}$ of (+78/-56)% (assuming a prior
$\Omega_Mh^2=0.135$). This is sufficient precision to sharpen the constraints
on $N_{eff}$ from WMAP, particularly in its upper limit. For Euclid, we find
corresponding attainable precisions on $(k_0, \Omega_Mh^2, N_eff)$ of
(3,4,+17/-21)%. This represents a precision approaching our forecasts for the
Planck Surveyor.
