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We investigate optimization strategies to measure primordial non-Gaussianity with future spectroscopic surveys. We forecast measurements coming from the 3D galaxy power spectrum and compute constraints on primordial non-Gaussianity parameters f_NL and n_NG. After studying the dependence on those parameters upon survey specifications such as redshift range, area, number density, we assume a reference mock survey and investigate the trade-off between number density and area surveyed. We then define the observational requirements to reach the detection of f_NL of order 1. Our results show that while power spectrum constraints on non-Gaussianity from future spectroscopic surveys can be competitive with current CMB limits, measurements from higher-order statistics will be needed to reach a sub unity precision in the measurements of the non-Gaussianity parameter f_NL.
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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.
Next-generation cosmological surveys will observe larger cosmic volumes than ever before, enabling us to access information on the primordial Universe, as well as on relativistic effects. We consider forthcoming 21cm intensity mapping surveys (SKAO) and optical galaxy surveys (DESI and Euclid), combining the information via multi-tracer cross-correlations that suppress cosmic variance on ultra-large scales. In order to fully incorporate wide-angle effects and redshift-bin cross-correlations, together with lensing magnification and other relativistic effects, we use the angular power spectra, $C_ell(z_i,z_j)$. Applying a Fisher analysis, we forecast the expected precision on $f_{rm NL}$ and the detectability of lensing and other relativistic effects. We find that the full combination of two pairs of 21cm and galaxy surveys, one pair at low redshift and one at high redshift, could deliver $sigma(f_{rm NL})sim 1.5$, detect the Doppler effect with a signal-to-noise ratio $sim$8 and measure the lensing convergence contribution at $sim$2% precision. In a companion paper, we show that the best-fit values of $f_{rm NL}$ and of standard cosmological parameters are significantly biased if the lensing contribution is neglected.
The Planck CMB experiment has delivered the best constraints so far on primordial non-Gaussianity, ruling out early-Universe models of inflation that generate large non-Gaussianity. Although small improvements in the CMB constraints are expected, the next frontier of precision will come from future large-scale surveys of the galaxy distribution. The advantage of such surveys is that they can measure many more modes than the CMB -- in particular, forthcoming radio surveys with the SKA will cover huge volumes. Radio continuum surveys deliver the largest volumes, but with the disadvantage of no redshift information. In order to mitigate this, we use two additional observables. First, the integrated Sachs-Wolfe effect -- the cross-correlation of the radio number counts with the CMB temperature anisotropies -- helps to reduce systematics on the large scales that are sensitive to non-Gaussianity. Second, optical data allows for cross-identification in order to gain some redshift information. We show that, while the single redshift bin case can provide a sigma(fNL) ~ 20, and is therefore not competitive with current and future constraints on non-Gaussianity, a tomographic analysis could improve the constraints by an order of magnitude, even with only two redshift bins. A huge improvement is provided by the addition of high-redshift sources, so having cross-ID for high-z galaxies and an even higher-z radio tail is key to enabling very precise measurements of fNL. Our results show that SKA continuum surveys could provide constraints competitive with CMB and forthcoming optical surveys, potentially allowing a measurement of sigma(fNL) ~ 1 to be made. Moreover, these measurements would act as a useful check of results obtained with other probes at other redshift ranges with other methods.
We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials $mathcal{P}_L$ and expansion coefficients $c_L$. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity competitive or improving upon current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of $f_{rm NL}^{rm loc} approx 1 (0.5)$ for the local shape, $f_{rm NL}$ of $mathcal{O}(10) (mathcal{O}(1))$ for the orthogonal, equilateral and folded shapes, and $c_{L=1} approx 80 (2)$, $c_{L=2} approx 400 (10)$ for angle-dependent non-Gaussianity. The more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach $sigma(c_{L=1})=10$, which can be considered as a typical (lower) value predicted by some (inflationary) models.
[Abridged] We consider how galaxy clustering data, from Mpc to Gpc scales, from upcoming large scale structure surveys, such as Euclid and DESI, can provide discriminating information about the bispectrum shape arising from a variety of inflationary scenarios. Through exploring in detail the weighting of shape properties in the calculation of the halo bias and halo mass function we show how they probe a broad range of configurations, beyond those in the squeezed limit, that can help distinguish between shapes with similar large scale bias behaviors. We assess the impact, on constraints for a diverse set of non-Gaussian shapes, of galaxy clustering information in the mildly non-linear regime, and surveys that span multiple redshifts and employ different galactic tracers of the dark matter distribution. Fisher forecasts are presented for a Euclid-like spectroscopic survey of H$alpha$-selected emission line galaxies (ELGs) using recent revisions of the expected H$alpha$ luminosity function, and a DESI-like survey, of luminous red galaxies (LRGs) and [O-II] doublet-selected ELGs, in combination with Planck-like CMB temperature and polarization data. While ELG samples provide better probes of shapes that are divergent in the squeezed limit, LRG constraints, centered below $z<1$, yield stronger constraints on shapes with scale-independent large-scale halo biases, such as the equilateral template. The ELG and LRG samples provide complementary degeneracy directions for distinguishing between different shapes. If the Gaussian galaxy bias is constrained to better than a percent level, such as can be determined from the galaxy bispectrum or weak lensing, then the LSS and CMB data could provide complementary constraints that will enable differentiation of bispectra with distinct theoretical origins but with similar large scale, squeezed-limit properties.
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