An Optimally Weighted Estimator of the Linear Power Spectrum
  Disentangling the Growth of Density Perturbations Across Galaxy Surveys
  Measuring the clustering of galaxies from surveys allows us to estimate the
power spectrum of matter density fluctuations, thus constraining cosmological
models. This requires careful modelling of observational effects to avoid
misinterpretation of data. In particular, signals coming from different
distances encode information from different epochs. This is known as
"light-cone effect" and is going to have a higher impact as upcoming galaxy
surveys probe larger redshift ranges. Generalising the method by Feldman et al.
(1994), I define a minimum-variance estimator of the linear power spectrum at a
fixed time, properly taking into account the light-cone effect. An analytic
expression for the estimator is provided, and that is consistent with the
findings of previous works in the literature. I test the method within the
context of the halo model, assuming Planck 2014 cosmological parameters. I show
that the estimator presented recovers the fiducial linear power spectrum at
present time within 5% accuracy up to $k \sim 0.80\;h\,\mathrm{Mpc}^{-1}$ and
within 10% up to $k \sim 0.94\;h\,\mathrm{Mpc}^{-1}$, well into the non-linear
regime of the growth of density perturbations. As such, the method could be
useful in the analysis of the data from future large-scale surveys, like
Euclid.
