Probing primordial non-Gaussianity with the power spectrum and bispectrum of future 21 cm intensity maps

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Abstract

After reionisation, the 21 cm emission line of neutral hydrogen within galaxies provides a tracer of dark matter. Next-generation intensity mapping surveys, with the SKA and other radio telescopes, will cover large sky areas and a wide range of redshifts, facilitating their use as probes of primordial non-Gaussianity. Previous works have shown that the bispectrum can achieve tight constraints on primordial non-Gaussianity with future surveys that are purposely designed for intensity mapping in interferometer mode. Here we investigate the constraints attainable from surveys operating in single-dish mode, using the combined power spectrum and bispectrum signal. In the case of the power spectrum, single-dish surveys typically outperform interferometer surveys. We find that the reverse holds for the bispectrum: single-dish surveys are not competitive with surveys designed for interferometer mode.

Introduction

Observations of the cosmic microwave background (CMB) and studies of its anisotropies in temperature and polarisation [1], [2] have confirmed to a high degree of accuracy our current description of the (early) Universe in terms of the concordance ΛCDM cosmological model. On the other end of the spectrum, low-redshift measurements of the cosmic large-scale structure (LSS) point towards the same picture [3], [4], [5], [6], [7]. Nonetheless, several major questions remain unsolved, like the mechanism that drove the cosmological inflationary period in the primordial Universe, responsible for the formation of the seeds of both the CMB anisotropies and the LSS.

Inflation is the umbrella term for a family of theories describing how quantum fluctuations in the primordial Universe evolved to a macroscopic level, thus becoming the seeds of cosmic structures. One of the most common predictions of inflation – the so-called ‘smoking guns’ – is the presence of a certain (tiny) amount of non-Gaussianity in the distribution of primordial density perturbations. It is useful to parametrise such a primordial non-Gaussianity (PNG) in terms of fNL, namely the amplitude of the first term in a Taylor expansion around Gaussianity. Measurements of, or bounds on, this parameter have the potential to rule out entire classes of inflationary models, thus strengthening our understanding of the early phases of the Universe’s evolution.

Currently, the tightest constraints on fNL come from bounds on the amplitude of the bispectrum of CMB anisotropies [8], which for instance constrain so-called local-type PNG to be fNLloc=0.9±5.1 at 68% CL (more details on different types of PNG are given in the next section). However, most of the information on PNG has already been extracted from the CMB, and the next frontier is surveys of the LSS, which provide two complementary probes: the bispectrum (e.g. [9]) and the scale-dependent power spectrum of biased tracers (e.g. [10]). The latter has already been investigated with catalogues from state-of-the-art galaxy surveys, and has provided complementary constraints on fNL (e.g. [11], [12], [13]). In this paper, we focus instead on the combined power spectrum and bispectrum signal, with a new angle offered by forthcoming cosmological experiments at radio frequencies.

Cosmology in the radio band traditionally offered two main probes, both based on the study of galaxy clustering: continuum galaxies (e.g. [14], [15]) and neutral hydrogen (HI) 21 cm emission-line galaxies (e.g. [16], [17]). Each has its own advantages and disadvantages, but in this paper, we instead focus on a third probe proposed for cosmological studies: HI intensity mapping [18], [19], [20], [21], [22]. In the post-reionisation Universe, most HI resides in dense systems inside galaxies and thus provides us with a tracer of the cosmic LSS. The HI intensity mapping technique consists of making maps of the brightness temperature of the sky at different frequencies. Since no other emission lines appear at these radio frequencies, there is a unique relation between observed frequency and redshift, (1+z)ν=νHI=cλHI, with λHI=21cm the rest-frame wavelength of the HI hyperfine transition photon. Each pixel in the map contains many galaxies so that their combined emission yields a larger detectable signal. Finally, the temperature maps are analysed via summary statistics such as Fourier- or harmonic-space power spectra and bispectra.

The power spectrum of HI intensity mapping has already been suggested as a powerful probe to study PNG [23], [24], [25], [26], [27], and it has been shown that single-dish mode is the best experimental set up for this specific goal. On the other hand, [28] has explored the potential of bispectrum measurements from future HI intensity mapping experiments in interferometer mode, finding very competitive forecast results on PNG (e.g., σ(fNLloc)<1 and σ(fNLequil)<5). Here, we compare the capabilities of single-dish mode surveys with the interferometer mode results, while using the combined power spectrum and bispectrum signal.

A comprehensive and realistic treatment of the problem would be to simulate the data, including foregrounds and performing foreground subtraction. However, this is a major project which requires considerable further work (see e.g. [29], [30] for some recent analyses). Our aim is more limited, focusing on the comparison of the joint power spectrum and bispectrum PNG constraints using single-dish as opposed to interferometer surveys. For the power spectrum, PNG constraints for single-dish surveys are known to outperform those of interferometer surveys. However, this has not been assessed in the case of the joint power spectrum and bispectrum signal, and this is indeed the scope of our paper. In order to do this, we use the same simplified Fisher analysis as in the interferometer case [28].

This paper is organised as follows. In Section 2 we review the matter power spectrum and bispectrum model, as well as the PNG types considered here. In Section 3 we present the formalism for the HI bias, while in Section 4 the final model for the power spectrum and bispectrum of the HI fluctuations in redshift space is shown. In Section 5 the specifications of experiments under consideration are presented. In Section 6 we review the Fisher matrix formalism used to forecast the amplitude of PNG, while in Section 7 we discuss the observational limitations for each experimental mode assumed here. Finally, the results are presented in Section 8, followed by a discussion in Section 9.

Section snippets

Matter power spectrum and bispectrum

The power spectrum of the Bardeen gauge-invariant primordial gravitational potential is defined in Fourier space by Φ(k)Φ(k)=(2π)3δD(k+k)PΦ(k),where PΦ(k) is directly related to the power spectrum of the primordial curvature perturbations ζ (during the matter-dominated era, Φ(k)=3ζ(k)5), which are generated during inflation. They are expected to have a nearly perfect Gaussian distribution in the case of the standard single-field slow-roll inflationary scenario, which means that they can be

Bias of neutral hydrogen

Forecasting the amplitude of PNG from the power spectrum and bispectrum of future HI IM surveys (see Section 5 for details) requires a relation between the statistics of observed tracers and the underlying distribution of dark matter (see e.g. [32] for a review). The bias is a combination of two components: the bias relation between halos and dark matter and how the neutral hydrogen is distributed amongst the dark matter halos.

Here we consider halo bias up to second order, which is sufficient

HI intensity mapping power spectrum and bispectrum in redshift space

Observationally we determine the redshift, not the physical distance to a patch of the Universe and so we need to take into account the effect of redshift space distortions (RSD) [82], [83], [84], including the “fingers of god” (FOG) effect [85] in the non-perturbative regime. RSD can be modelled perturbatively [86], [87], by generalising the SPT kernels to include RSD and bias expansions. The FOG effect is treated phenomenologically, by introducing an exponential damping factor DFOG, which

HI intensity mapping surveys

Radio telescopes can be set up to measure the 3D power spectrum of HI intensity in two distinctive ways:

  • as interferometers correlating the signals from all dishes or dipole stations and immediately outputting the Fourier transform of the sky — interferometer (IF) mode;

  • as dishes providing separate maps of the sky, added to reduce noise, with the final map Fourier transformed — single-dish (SD) mode.

The noise power is dominated by instrumental noise, with a much smaller shot-noise contribution 

Forecasting method

We predict the precision of the PNG amplitude measurement from the surveys considered in Section 5 by utilising the Fisher information matrix formalism. In order to derive the covariance matrix, we approximate the surface around the maximum peak of the likelihood distribution with a multivariate Gaussian. This is not generally true for a cosmological parameter, although it is a reasonable approximation near the peak. To improve upon this, one would need to sample the likelihood at various

Observational window

The cosmological 21 cm signal is orders of magnitude fainter than the foreground emission from astrophysical sources [119], [129], [130], [131]. The separation between the two is based on the spectrally smooth nature of the foregrounds. This means that only the long-wavelength fluctuations along the line of sight are affected [119], [129], [132], [133], [134], [135], [136]; i.e., the small radial Fourier modes k(=kμ) are contaminated.

Reconstruction techniques have been developed, to estimate

Results

The Fisher matrix forecast results from the combined HI power spectrum and bispectrum signal are presented in this section. The cumulative 1σ forecast error for the amplitude of the three PNG shapes, in the case of the SKA precursor MeerKAT, is presented as a function of redshift in Fig. 2. The results for the two available MeerKAT bands are shown. The volumes probed by MeerKAT, as well as the scale limitations of the SD mode (see Section 7), restrict significantly the access to the large

Discussion

The goal of this paper was to study the combined HI IM power spectrum and bispectrum of current and planned experiments, in configurations not yet considered, in order to find the ideal set-up for such an analysis, in particular one targeting PNG. In the case of the MeerKAT, SKA-MID, HIRAX and PUMA experiments, we considered SD mode, while for SKA1-LOW and SKA2-LOW we considered IF mode. To determine the HI IM power spectrum and bispectrum we reviewed the matter model, the HI bias model, and

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

DK and RM are supported by the South African Radio Astronomy Observatory (SARAO) and the National Research Foundation (Grant No. 75415). JF was supported by the University of Padova under the STARS Grants programme CoGITO: Cosmology beyond Gaussianity, Inference, Theory and Observations and by the UK Science & Technology Facilities Council (STFC) Consolidated Grant ST/P000592/1. JF also thanks the University of the Western Cape for supporting a visit during which parts of this work were

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