Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure (1001.4707v1)

Abstract: The most direct probe of non-Gaussian initial conditions has come from bispectrum measurements of temperature fluctuations in the Cosmic Microwave Background and of the matter and galaxy distribution at large scales. Such bispectrum estimators are expected to continue to provide the best constraints on the non-Gaussian parameters in future observations. We review and compare the theoretical and observational problems, current results and future prospects for the detection of a non-vanishing primordial component in the bispectrum of the Cosmic Microwave Background and large-scale structure, and the relation to specific predictions from different inflationary models.

Primordial Non-Gaussianity and Bispectrum Measurements in CMB and Large-Scale Structure

The paper "Primordial non-Gaussianity and Bispectrum Measurements in the Cosmic Microwave Background and Large-Scale Structure" by Michele Liguori, Emiliano Sefusatti, James R. Fergusson, and E.P.S. Shellard discusses the assessment of primordial non-Gaussianity through bispectrum measurements in the Cosmic Microwave Background (CMB) and Large-Scale Structure (LSS). This topic is pivotal for understanding the physics of the early universe, particularly the processes occurring during inflation.

The paper focuses on the non-Gaussian initial conditions that are closely tied to the predictions of various inflationary models. These are often represented as deviations from the Gaussian distribution in the form of bispectra—three-point correlation functions—of the initial curvature perturbations. These perturbations have a significant impact on the CMB temperature fluctuations and the distribution of matter at large scales, thus affecting both CMB and LSS measurements.

One of the primary aims of the research is to distinguish the contributions of different sources of non-Gaussianity: primordial non-Gaussianity characterized by the bispectrum of the curvature perturbations, non-linear gravity-induced non-Gaussianity, and nonlinear galaxy bias in LSS. The distinctive dependence of these sources on scale, bispectral shape, and redshift are crucial for disentangling their contributions.

Key Contributions:

1. Bispectrum in CMB Measurements:
   • The CMB bispectrum provides a direct probe of the primordial bispectrum. The measurements of temperature fluctuations in the CMB are central to constraining the non-Gaussian parameters such as $f_{\rm NL}$ for different shapes like local, equilateral, and orthogonal types of non-Gaussianity.
   • The paper elaborates on the formulation of optimal bispectrum estimators and their application to CMB datasets like that of the Wilkinson Microwave Anisotropy Probe (WMAP). It highlights the challenges of detecting bispectral signals amid cosmic variance and foreground contamination.
2. LSS Bispectrum and Bias:
   • The galaxy bispectrum offers another robust avenue for detecting primordial non-Gaussianity. The paper revisits the standard approach relying on Eulerian perturbation theory to model the bispectrum of matter and galaxies.
   • The authors address complications arising from the local galaxy bias model—primarily the challenges in isolating primordial signals from nonlinear bias and gravitational evolution effects.
   • An unexpected significant contribution to galaxy power spectrum measurements from non-Gaussian initial conditions has been identified, particularly for local models. This discovery has spurred new interest in using LSS data to complement CMB constraints.
3. Methodological Advances:
   • The research underscores the development of efficient computational methods for bispectrum analysis, such as separable mode expansions, making non-separable models tractable within data analysis frameworks.
   • Techniques include leveraging large-volume simulations and optimized N-point correlation function measurements to better understand the statistical properties of non-Gaussianity in LSS.

Implications and Future Outlook:

This body of work positions bispectrum measurements as a crucial method for probing the primordial processes responsible for cosmic structure formation. Current constraints from the WMAP set the groundwork, while upcoming experiments, such as the Planck mission and large-scale galaxy surveys like Euclid, promise more stringent tests. These advancements should enhance our understanding of the inflationary mechanisms at play during the early universe.

The discernment of primordial non-Gaussian signals amidst secondary anisotropies and data imperfections is an ongoing challenge. Nevertheless, the paper's findings indicate promising directions for future research, such as assessing the bispectrum's potential as an independent confirmation method of CMB-based discoveries and exploring the connections between bispectrum characteristics and other cosmological observations.

In summary, this research provides a comprehensive framework for using bispectrum measurements of the CMB and LSS to investigate the intriguing domain of primordial non-Gaussianity, significantly impacting our understanding of the early universe and inflationary paradigm.