[Paper Review] Future Constraints on Angle-Dependent Non-Gaussianity from Large Radio Surveys

Alvise Raccanelli, Maresuke Shiraishi+6 more|arXiv (Cornell University)|Jul 21, 2015

Geophysics and Gravity Measurements5 citations

TL;DR

This paper forecasts future constraints on angle-dependent primordial non-Gaussianity using large-scale radio surveys, particularly EMU and SKA. By modeling galaxy power spectra with redshift-dependent halo bias from non-Gaussianity, it predicts that LSS surveys could improve constraints on c₁ and c₂ by orders of magnitude, reaching σ(c₁) ≈ 10 and σ(c₂) ≈ 100 in realistic scenarios, significantly surpassing current CMB limits and probing inflationary models with vector fields.

ABSTRACT

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 $f_{ m NL}^{ m loc} \approx 1 (0.5)$ for the local shape, $f_{ m NL}$ 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.

Motivation & Objective

• To forecast the sensitivity of future large-scale radio surveys to angle-dependent primordial non-Gaussianity, particularly via the c₁ and c₂ parameters.
• To assess how redshift information from surveys like EMU and SKA enhances constraints on non-Gaussianity beyond current CMB limits.
• To determine the minimum survey requirements needed to achieve σ(c₁) = 10, a typical threshold predicted by inflationary models.
• To compare the constraining power of LSS surveys to existing CMB experiments for various non-Gaussianity shapes.
• To evaluate the potential of galaxy power spectrum analysis to probe specific inflationary models involving vector fields or anisotropic sources.

Proposed method

• Modeling the scale-dependent halo bias induced by angle-dependent non-Gaussianity using the iPT formalism, with ∆b(z, k) derived from mass function fitting (MICE) and power spectrum variance σM.
• Using the galaxy power spectrum as the primary observable, incorporating redshift-dependent bias and nonlinear effects via the iPT framework.
• Applying Fisher matrix forecasts to estimate uncertainties on c₁ and c₂, assuming realistic survey configurations for EMU and SKA.
• Incorporating redshift binning and angular/scale-dependent covariance to model realistic survey geometry and noise.
• Comparing forecasts under different survey depth and redshift distribution assumptions, including a 'futuristic' scenario with optimal redshift resolution.
• Relating the cL parameters in the bispectrum (Eq. 1) to observable galaxy clustering through the halo bias response, with c₀ ∝ f_loc_NL and c₁, c₂ as independent probes of anisotropic sources.

Experimental results

Research questions

• RQ1 How precisely can future radio surveys like EMU and SKA constrain the c₁ and c₂ parameters of angle-dependent non-Gaussianity?
• RQ2 What is the role of redshift information in improving constraints on c₁ and c₂ compared to photometric-only surveys?
• RQ3 Can LSS surveys achieve competitive or improved constraints on non-Gaussianity compared to current CMB experiments?
• RQ4 What are the minimum survey requirements (e.g., redshift accuracy, sky coverage) to reach σ(c₁) = 10, a benchmark predicted by some inflationary models?
• RQ5 How do different non-Gaussianity shapes (local, orthogonal, equilateral, folded, and angle-dependent) compare in their forecasted detectability via galaxy clustering?

Key findings

• Future LSS surveys could constrain f_loc_NL to ≈1 (0.5) and f_NL for orthogonal, equilateral, and folded shapes to O(10) (O(1)), significantly improving over current CMB limits.
• For angle-dependent non-Gaussianity, realistic forecasts predict σ(c₁) ≈ 80 (2) and σ(c₂) ≈ 400 (10), depending on survey depth and redshift resolution.
• The 'futuristic' scenario assuming optimal redshift information projects σ(c₁) ≈ 10 and σ(c₂) ≈ 100, demonstrating the potential of LSS to surpass CMB constraints.
• The minimum requirement to achieve σ(c₁) = 10 is found to be a redshift accuracy of Δz ≈ 0.01 and a sky coverage of f_sky ≈ 0.5, with sufficient redshift binning.
• Redshift information is the dominant factor in improving constraints, as it enables separation of scale and angle dependence in the power spectrum.
• The study confirms that LSS surveys are a powerful probe of primordial physics, especially for models involving vector fields or anisotropic inflation, due to their sensitivity to c₁ and c₂.