Measuring primordial non-Gaussianity with weak-lensing surveys
  We study the ability of future weak lensing (WL) surveys to constrain
primordial non-Gaussianity of the local type. We use a large ensemble of
simulated WL maps with survey specifications relevant to Euclid and LSST. The
simulations assume Cold Dark Matter cosmologies that vary certain parameters
around fiducial values: the non-Gaussianity parameter f_NL, the matter density
parameter Omega_m, the amplitude of the matter power spectrum sigma_8, the
spectral index of the primordial power spectrum n_s, and the dark-energy
equation-of-state parameter w_0. We assess the sensitivity of the cosmic shear
correlation functions, the third-order aperture mass statistics, and the
abundance of shear peaks to these parameters. We find that each of the
considered probes provides unmarginalized constraints of Delta f_NL ~ 20 on
f_NL. Marginalized constraints from any individual WL probe are much weaker due
to strong correlations between parameters. However, the parameter errors can be
substantially reduced by combining information from different WL probes.
Combining all WL probes yields the following marginal (68% confidence level)
uncertainties: Delta f_NL ~ 50, Delta Omega_m ~ 0.002, Delta sigma_8 ~ 0.004,
Delta n_s ~ 0.007, and Delta w_0 ~ 0.03. We examine the bias induced by
neglecting f_NL on the constraints on the other parameters. We find sigma_8 and
w_0 to be the most affected. Moreover, neglecting non-Gaussianity leads to a
severe underestimation of the uncertainties in the other cosmological
parameters.
