The simplest models of inflation predict small non-Gaussianities and a featureless power spectrum. However, there exist a large number of well-motivated theoretical scenarios in which large non-Gaussianties could be generated. In general, in these scenarios the primordial power spectrum will deviate from its standard power law shape. We study, in a model-independent manner, the constraints from future large-scale structure surveys on the local non-Gaussianity parameter $f_{\mathrm{NL}}$ when the standard power law assumption for the primordial power spectrum is relaxed. If the analyses are restricted to the large-scale-dependent bias induced in the linear matter power spectrum by non-Gaussianites, the errors on the $f_{\mathrm{NL}}$ parameter could be increased by 60% when exploiting data from the future DESI survey, if dealing with only one possible dark matter tracer. In the same context, a nontrivial bias $|\delta f_{\mathrm{NL}}|\sim 2.5$ could be induced if future data are fitted to the wrong primordial power spectrum. Combining all the possible DESI objects slightly ameliorates the problem, as the forecasted errors on $f_{\mathrm{NL}}$ would be degraded by 40% when relaxing the assumptions concerning the primordial power spectrum shape. Also, the shift on the non-Gaussianity parameter is reduced in this case, $|\delta f_{\mathrm{NL}}|\sim 1.6$. The addition of cosmic microwave background priors ensures robust future $f_{\mathrm{NL}}$ bounds, as the forecasted errors obtained including these measurements are almost independent on the primordial power spectrum features, and $|\delta f_{\mathrm{NL}}|\sim 0.2$, close to the standard single-field slow-roll paradigm prediction.

• Received 24 June 2015

DOI:https://doi.org/10.1103/PhysRevD.92.063510