BNL-112147-2014-IR Testing Inflation with Large Scale Structure: Connecting Hopes with Reality Marcelo Alvarez April 2016 Department/Division/Office Brookhaven National Laboratory U.S. Department of Energy [High Energy Physics], [Astronomy and Astrophysics] Notice: This manuscript has been authored by employees of Brookhaven Science Associates, LLC under Contract No. DE- SC0012704 with the U.S. Department of Energy. The publisher by accepting the manuscript for publication acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. 3.0/3813e021.doc 1 (11/2015) 3.0/3813e021.doc 2 (11/2015) DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. 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The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. 3.0/3813e021.doc 3 (11/2015) BNL-1124147-2014-IR Testing Inflation with Large Scale Structure: Connecting Hopes with Reality Conveners: Olivier Dor´eand Daniel Green Marcelo Alvarez1, Tobias Baldauf2, J. Richard Bond1;3, Neal Dalal4, Roland de Putter5;6, Olivier Dor´e5;6, Daniel Green1;3, Chris Hirata7, Zhiqi Huang1, Dragan Huterer8, Donghui Jeong9, Matthew C. Johnson10;11, Elisabeth Krause12, Marilena Loverde13, Joel Meyers1, P. Daniel Meerburg1, Leonardo Senatore12, Sarah Shandera9, Eva Silverstein12, AnˇzeSlosar14, Kendrick Smith11, Matias Zaldarriaga1, Valentin Assassi15, Jonathan Braden1, Amir Hajian1, Takeshi Kobayashi1;11, George Stein1, Alexander van Engelen1 1Canadian Institute for Theoretical Astrophysics, University of Toronto, ON 2Institute of Advanced Studies, Princeton, NJ 3Canadian Institute for Advanced Research, Toronto, ON 4University of Illinois, Urbana-Champaign, IL 5Jet Propulsion Laboratory, Pasadena, CA 6California Institute of Technology, Pasadena, CA 7Ohio State University, Columbus, OH 8University of Michigan, Ann Arbor, MI 9Pennsylvania State, State College, PA 10York University, Toronto, ON 11Perimeter Institute, Waterloo, ON 12Stanford University, Stanford, CA 13University of Chicago, Chicago, IL 14Brookhaven National Laboratory, NY 15 Cambridge University, Cambridge, UK 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 domi- nant 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 pur- suing 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 loc eq quantified in terms of the local (equilateral) template amplitude fNL (fNL), natural target levels of loc;eq: sensitivity are ∆fNL ' 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 [Link]. Contents 1 Introduction 2 2 Theoretical motivation and targets for non-Gaussianity3 loc 2.1 Local Non-Gaussianity (fNL)5 2.1.1 Curvaton Scenario5 2.1.2 Modulated Reheating6 2.1.3 Discussion6 eq orth 2.2 Equilateral and Othorgonal Non-Gaussanity (fNL; fNL )7 2.3 Intermediate Shapes8 2.4 Theory targets summary8 2.5 Targets for the power spectrum9 loc 3 Observational status and prospects for fNL 10 3.1 Measurement status of primordial non-Gaussianity 10 3.2 Relevant planned surveys 12 loc 3.3 What would an ideal survey for constraining fNL with the power spectrum look like? 13 4 Beyond the Halo Power Spectrum 16 4.1 State of Bispectrum Observations 16 4.2 State of Bispectrum Forecasts 16 4.2.1 The Matter Bispectrum 17 4.2.2 The Halo Bispectrum 17 4.2.3 Redshift Space Distortions 18 4.2.4 Loop corrections to the halo bispectrum 19 4.2.5 Additional Effects 19 4.3 Mass function & other probes 19 4.4 Uncorrelated Primordial non-Gaussianity, Intermittency and LSS 20 5 Potential Systematic Effects 23 5.1 Theoretical Systematics 23 5.1.1 Non-linear systematics 23 5.1.2 General Relativistic effect 24 5.2 Observational Systematics 25 6 Conclusion 27 1 1 Introduction To date, the cosmic microwave background (CMB) has been the dominant source of information about the primordial curvature perturbations. The statistics of these fluctuations are, so far, our window into the period of inflation, where fluctuations are thought to have been generated. However, due to the limitations set by Silk damping and foregrounds, the CMB is unlikely to offer significant improvements in the statistics of the scalar1 fluctuations (e.g. those responsible for seeding large scale structure) beyond Planck. Large scale structure (LSS) is ultimately where drastic improvements can originate from. The purpose of this paper is to explain the theoretical motivations to pursuing such measurements and the challenges that lie ahead. Our understanding of inflation is currently best constrained by Planck through measurements of the power spectrum [2], bispectrum [3] and trispectrum. The power spectrum is well characterized −9 in terms of the amplitude, As = (2:23 ± 0:16) × 10 and the tilt ns = 0:9616 ± 0:0094. These values can give us insight into the underlying inflationary background. The bispectrum can be used to test a wide variety of models beyond the single-field slow-roll paradigm. Often these results are reported loc eq in terms of the local template [4,5], fNL = 2:7 ± 5:8, the equilateral template [6], fNL = −42 ± 75, orthogonal and the ortogonal template [7], fNL = −25 ± 39 . Similar constraints have been placed on several trispectrum templates [8,9]. While these results are impressive, we should ask if they have reached a theoretically desirable level of sensitivity. In other words, one should put these results into the context of what natural levels of non-Gaussianity might be expected under plausible theoretical expectations. In the specific context of the bispectrum, the local and equilateral templates probe qualita- tively different deformations of single-field slow-roll inflation and should be assessed independently. Local non-Gaussianity is a sensitive probe of multi-field models due to the single-field consistency relations [10, 11]. Equilateral non-Gaussianity is a probe of non-slow roll dynamics through self- interactions of the perturbations. Despite the clear differences between these probes, we will argue loc;eq: that a natural target level of sensitivity is ∆fNL < 1. Given the target level of sensitivity, there is still significant room for improvement beyond the limits set by the CMB. This presents a well-defined challenge for upcoming LSS surveys. The state of the art for testing non-Gaussianity in LSS is constraining the scale-dependent halo loc bias predicted for models with fNL [12]. These constraints can be derived from the halo power spec- trum which greatly simplifies the analysis. However, these measurements are prone to systematic effects which present a significant barrier for existing surveys to making this measurement competi- tive with the CMB. In addition, the halo bispectrum would be a necessary tool for testing non-local eq type non-Gaussianity like fNL. To date, there is no constraint on primordial non-Gaussianity from the halo bispectrum, despite suggestions that it contains substantially more signal to noise than the halo power spectrum [13]. Ultimately, the bispectrum will need to be used to make LSS as versatile a tool as the CMB has become. 1Significant improvements in sensitivity to tensor fluctuations are expected over the next decade through measure- ments of CMB polarization [1]. The scalar and tensor fluctuations probe different aspects of inflation and are therefore complimentary. 2 The goal of this paper is to summarize the status, motivations and challenges for testing loc inflation in large scale structure surveys. Our discussion will be somewhat weighted towards fNL because it has been demonstrated that large scale structure can give comparable constraints to the CMB. However, we will emphasize that there are a number of other interesting theoretical targets that deserve equal attention in future surveys that will ultimately be tested through probes other than scale dependent bias. This paper aims at sharing with the community the outcome of our workshop and thus should not be read as a review. Many relevant subjects were not discussed for lack of time and many relevant references are missing. The paper is organized as follows. In section2, we will review a number of theoretical targets loc;eq: that would be desirable to meet in future surveys. In particular, we will explain why ∆fNL < 1 are particularly interesting levels of sensitivity. In section3, we will discuss the status and prospects loc for measuring fNL ∼ 1 in future surveys. In section4, we will explain the status of the bispectrum as a tool for testing inflation. In section5, we will discuss systematics that may be relevant to making these measurements a reality. 2 Theoretical motivation and targets for non-Gaussianity The size and form of primordial non-Gaussianities in single-clock inflationary models (i.e.