Abstract: 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(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(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 vertical bar delta f(NL)vertical bar similar to 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(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, vertical bar delta f(NL)vertical bar similar to 1.6. The addition of cosmic microwave background priors ensures robust future f(NL) bounds, as the forecasted errors obtained including these measurements are almost independent on the primordial power spectrum features, and vertical bar delta f(NL)vertical bar similar to 0.2, close to the standard single-field slow-roll paradigm prediction.

Abstract: We propose here a novel method which singles out the a priori unavoidable dependence on the underlying cosmological model when extracting parameter constraints, providing robust limits which only depend on the considered dataset. Interestingly, when dealing with several possible cosmologies and interpreting the Bayesian preference in terms of the Gaussian statistical evidence, the preferred model is much less favored than when only two cases are compared. As a working example, we apply our approach to the cosmological neutrino mass bounds, which play a fundamental role not only in establishing the contribution of relic neutrinos to the dark matter of the Universe but also in the planning of future experimental searches of the neutrino character and of the neutrino mass ordering.

Abstract: We extend an alternative, phenomenological approach to inflation by means of an equation of state and a sound speed, both of them functions of the number of e-folds and four phenomenological parameters. This approach captures a number of possible inflationary models, including those with non-canonical kinetic terms or scale-dependent non-gaussianities. We perform Markov Chain Monte Carlo analyses using the latest cosmological publicly available measurements, which include Cosmic Microwave Background (CMB) data from the Planck satellite. Within this parameterization, we discard scale invariance with a significance of about 10 sigma, and the running of the spectral index is constrained as alpha(s) = -0.60(-0.10)(+0.08) x 10(-3) (68% CL errors). The limit on the tensor-to-scalar ratio is r < 0.005 at 95% CL from CMB data alone. We find no significant evidence for this alternative parameterization with present cosmological observations. The maximum amplitude of the equilateral non-gaussianity that we obtain, vertical bar f(NL)(equil)vertical bar < 1, is much smaller than the current Planck mission errors, strengthening the case for future high-redshift, all-sky surveys, which could reach the required accuracy on equilateral non-gaussianities.