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Testing Inflation with Large Scale Structure: Connecting Hopes with Reality

Marcelo Alvarez, Tobias Baldauf, J. Richard Bond, Neal Dalal, Roland de Putter, Olivier Doré, Daniel Green, Chris Hirata, Zhiqi Huang, Dragan Huterer, Donghui Jeong, Matthew C. Johnson, Elisabeth Krause, Marilena Loverde, Joel Meyers, P. Daniel Meerburg, Leonardo Senatore, Sarah Shandera, Eva Silverstein, Anže Slosar, Kendrick Smith, Matias Zaldarriaga, Valentin Assassi, Jonathan Braden, Amir Hajian, Takeshi Kobayashi, George Stein, Alexander van Engelen

TL;DR

This paper argues that large-scale structure offers a promising path to tighten constraints on inflation beyond the CMB, with a central target of achieving $\Delta f_{\rm NL}^{\rm loc,eq} \approx 1$ via 2-, 3-, and 4-point statistics. It details theoretical motivations across local, equilateral, and intermediate shapes, linking them to multi-field and single-field inflation through the EFT of inflation and associated scales $\Lambda$, $H$, and $\dot H$. The authors assess the observational status, review planned surveys, and outline an ideal survey design (e.g., near-full-sky imaging with multi-tracer capabilities) to reach $\sigma(f_{\rm NL}^{\rm loc}) \approx 1$, while also addressing the state of bispectrum measurements, halo modeling, and systematic challenges. They emphasize that controlling theoretical and observational systematics is essential to realize these gains, and highlight the potential of the bispectrum and mass-function probes to complement power-spectrum analyses in distinguishing inflationary scenarios. Overall, the work provides a targeted, workshop-derived framework for exploiting LSS to test inflation with high precision and broad theoretical reach.

Abstract

The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude $f_{\rm NL}^{\rm loc}$ ($f_{\rm NL}^{\rm eq}$), natural target levels of sensitivity are $Δf_{\rm NL}^{\rm loc, eq.} \simeq 1$. We highlight that such levels are within reach of future surveys by measuring 2-, 3- and 4-point statistics of the galaxy spatial distribution. This paper summarizes a workshop held at CITA (University of Toronto) on October 23-24, 2014.

Testing Inflation with Large Scale Structure: Connecting Hopes with Reality

TL;DR

This paper argues that large-scale structure offers a promising path to tighten constraints on inflation beyond the CMB, with a central target of achieving via 2-, 3-, and 4-point statistics. It details theoretical motivations across local, equilateral, and intermediate shapes, linking them to multi-field and single-field inflation through the EFT of inflation and associated scales , , and . The authors assess the observational status, review planned surveys, and outline an ideal survey design (e.g., near-full-sky imaging with multi-tracer capabilities) to reach , while also addressing the state of bispectrum measurements, halo modeling, and systematic challenges. They emphasize that controlling theoretical and observational systematics is essential to realize these gains, and highlight the potential of the bispectrum and mass-function probes to complement power-spectrum analyses in distinguishing inflationary scenarios. Overall, the work provides a targeted, workshop-derived framework for exploiting LSS to test inflation with high precision and broad theoretical reach.

Abstract

The statistics of primordial curvature fluctuations are our window into the period of inflation, where these fluctuations were generated. To date, the cosmic microwave background has been the dominant source of information about these perturbations. Large scale structure is however from where drastic improvements should originate. In this paper, we explain the theoretical motivations for pursuing such measurements and the challenges that lie ahead. In particular, we discuss and identify theoretical targets regarding the measurement of primordial non-Gaussianity. We argue that when quantified in terms of the local (equilateral) template amplitude (), natural target levels of sensitivity are . We highlight that such levels are within reach of future surveys by measuring 2-, 3- and 4-point statistics of the galaxy spatial distribution. This paper summarizes a workshop held at CITA (University of Toronto) on October 23-24, 2014.

Paper Structure

This paper contains 30 sections, 27 equations, 1 figure, 2 tables.

Table of Contents

  1. Introduction
  2. Theoretical motivation and targets for non-Gaussianity
  3. Local Non-Gaussianity ($f_{\rm NL}^{\rm loc}$)
  4. Curvaton Scenario
  5. Modulated Reheating
  6. Discussion
  7. Equilateral and Othorgonal Non-Gaussanity ($f_{\rm NL}^{\rm eq}, f_{\rm NL}^{\rm orth}$)
  8. Intermediate Shapes
  9. Theory targets summary
  10. Targets for the power spectrum
  11. Observational status and prospects for $f_{\rm NL}^{\rm loc}$
  12. Measurement status of primordial non-Gaussianity
  13. Relevant planned surveys
  14. What would an ideal survey for constraining $f_{\rm NL}^{\rm loc}$ with the power spectrum look like?
  15. Beyond the Halo Power Spectrum
  16. ...and 15 more sections

Figures (1)

  • Figure 1: Left: Fisher information on $f_{\rm NL}$ (proportional to $1/\sigma^2(f_{\rm NL})$) relative to that of a survey with perfect (spectroscopic) redshifts, as a function of redshift scatter. Solid curves assume use of the multi-tracer technique and dashed assume a single tracer. We show results for moderate and high number density surveys, represented by stellar mass cuts $M_* > 10^{11} M_\odot$ and $M_* > 10^{10} M_\odot$, respectively. Right: Single-(dashed) and multi-(solid) tracer uncertainties on $f_{\rm NL}$ for a toy model of a multi-band imaging survey, as a function of an $i$-band magnitude cut (and corresponding number density on the lower horizontal axis). We assume a sky coverage $f_{\rm sky}= 0.75$. Stellar mass is used as a proxy for host halo mass (and therefore bias) and we show results for two different values of the stellar mass scatter relative to the mean stellar mass - halo mass relation. For both figures, we refer to the text and fnlsurvey for details.