We study the constraining power on primordial non-Gaussianity of future surveys of the large-scale structure of the Universe for both near-term surveys (such as the Dark Energy Survey - DES) as well as longer term projects such as Euclid and WFIRST. Specifically we perform a Fisher matrix analysis forecast for such surveys, using DES-like and Euclid-like configurations as examples, and take account of any expected photometric and spectroscopic data. We focus on two-point statistics and we consider three observables: the 3D galaxy power spectrum in redshift space, the angular galaxy power spectrum, and the projected weak-lensing shear power spectrum. We study the effects of adding a few extra parameters to the basic LCDM set. We include the two standard parameters to model the current value for the dark energy equation of state and its time derivative, w_0, w_a, and we account for the possibility of primordial non-Gaussianity of the local, equilateral and orthogonal types, of parameter fNL and, optionally, of spectral index n_fNL. We present forecasted constraints on these parameters using the different observational probes. We show that accounting for models that include primordial non-Gaussianity does not degrade the constraint on the standard LCDM set nor on the dark-energy equation of state. By combining the weak lensing data and the information on projected galaxy clustering, consistently including all two-point functions and their covariance, we find forecasted marginalised errors sigma (fNL) ~ 3, sigma (n_fNL) ~ 0.12 from a Euclid-like survey for the local shape of primordial non-Gaussianity, while the orthogonal and equilateral constraints are weakened for the galaxy clustering case, due to the weaker scale-dependence of the bias. In the lensing case, the constraints remain instead similar in all configurations.
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