Probing primordial non-Gaussianity with the power spectrum and bispectrum of future 21 cm intensity maps
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 CDM 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 , 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 come from bounds on the amplitude of the bispectrum of CMB anisotropies [8], which for instance constrain so-called local-type PNG to be 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 (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, , with 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., and ). 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 where is directly related to the power spectrum of the primordial curvature perturbations (during the matter-dominated era, ), 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 , 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 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 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
References (162)
- et al.
Forecasts on the dark energy and primordial non-Gaussianity observations with the tianlai cylinder array
Astrophys. J.
(2015) - et al.
Large-scale galaxy bias
Phys. Rep.
(2018) - et al.
Large-scale structure of the universe and cosmological perturbation theory
Phys. Rep.
(2002) - et al.
Halo models of large scale structure
Phys. Rep.
(2002) - et al.
Planck 2018 results. VI. Cosmological parameters
Astron. Astrophys.
(2020) - et al.
Planck 2018 results. I. Overview and the cosmological legacy of Planck
Astron. Astrophys.
(2020) - et al.
The completed SDSS-IV extended baryon oscillation spectroscopic survey: measurement of the BAO and growth rate of structure of the emission line galaxy sample from the anisotropic power spectrum between redshift 0.6 and 1.1
(2020) - et al.
The completed SDSS-IV extended baryon oscillation spectroscopic survey: Large-scale structure catalogues and measurement of the isotropic bao between redshift 0.6 and 1.1 for the emission line galaxy sample
(2020) - et al.
Cosmological constraints from multiple probes in the dark energy survey
Phys. Rev. Lett.
(2019) - et al.
Kids-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis
(2020)
Dark energy survey year 1 results: Joint analysis of galaxy clustering, galaxy lensing, and CMB lensing two-point functions
Phys. Rev. D
Planck 2018 results. IX. Constraints on primordial non-Gaussianity
Astron. Astrophys.
The bispectrum of galaxies from high-redshift galaxy surveys: Primordial non-Gaussianity and non-linear galaxy bias
Phys. Rev. D
Non-Gaussian halo bias and future galaxy surveys
Astrophys. J. Lett.
Improved primordial non-Gaussianity constraints from measurements of galaxy clustering and the integrated sachs-wolfe effect
Phys. Rev. D
Search for primordial non-Gaussianity in the quasars of SDSS-III boss DR9
Mon. Not. R. Astron. Soc.
Redshift-weighted constraints on primordial non-Gaussianity from the clustering of the eBOSS DR14 quasars in fourier space
J. Cosmol. Astropart. Phys.
Measurement of the angular correlation function of radio galaxies from the NRAO VLA sky survey
Mon. Not. R. Astron. Soc.
The spatial clustering of radio sources in NVSS and FIRST: implications for galaxy clustering evolution
Astron. Astrophys.
The clustering characteristics of HI-selected galaxies from the 40% ALFALFA survey
Astrophys. J.
The clustering of ALFALFA galaxies: Dependence on h mass, relationship with optical samples, and clues of host halo properties
Astrophys. J.
Using HI to probe large scale structures at
J. Astrophys. Astron.
Neutral hydrogen surveys for high redshift galaxy clusters and proto-clusters
Mon. Not. R. Astron. Soc.
Fluctuations in 21-cm emission after reionization
Mon. Not. R. Astron. Soc.
Baryon acoustic oscillation intensity mapping of dark energy
Phys. Rev. Lett.
H i intensity mapping: a single dish approach
Mon. Not. R. Astron. Soc.
Cosmology on ultralarge scales with intensity mapping of the neutral hydrogen 21 cm emission: Limits on primordial non-Gaussianity
Phys. Rev. Lett.
Hunting down horizon-scale effects with multi-wavelength surveys
Astrophys. J. Lett.
Probing the primordial universe with MeerKAT and DES
Mon. Not. R. Astron. Soc.
Constraining primordial non-Gaussianity using two galaxy surveys and CMB lensing
Mon. Not. R. Astron. Soc.
Forecasts on primordial non-Gaussianity from 21 cm intensity mapping experiments
J. Cosmol. Astropart. Phys.
User’s guide to extracting cosmological information from line-intensity maps
Phys. Rev. D
Strategies to detect dark-matter decays with line-intensity mapping
Probing primordial non-Gaussianity with SKA galaxy redshift surveys: a fully relativistic analysis
Mon. Not. R. Astron. Soc.
Mon. Not. Roy. Astron. Soc.
Efficient computation of cosmic microwave background anisotropies in closed Friedmann-Robertson-Walker models
Astrophys. J.
Non-Gaussianity as a probe of the physics of the primordial universe and the astrophysics of the low redshift universe, astro2010: the astronomy and astrophysics decadal survey 2010
Nonlinear evolution of long-wavelength metric fluctuations in inflationary models
Phys. Rev. D
The three-point correlation function of the cosmic microwave background in inflationary models
Astrophys. J.
Large-scale structure, the cosmic microwave background and primordial non-Gaussianity
Mon. Not. R. Astron. Soc.
Acoustic signatures in the primary microwave background bispectrum
Phys. Rev. D
Limits on non-Gaussianities from WMAP data
J. Cosmol. Astropart. Phys.
Non-Gaussianities in single field inflation and their optimal limits from the WMAP 5-year data
J. Cosmol. Astropart. Phys.
Renormalized halo bias
J. Cosmol. Astropart. Phys.
Bias in the effective field theory of large scale structures
J. Cosmol. Astropart. Phys.
Biased tracers and time evolution
J. Cosmol. Astropart. Phys.
Stochastic nonlinear galaxy biasing
Astrophys. J.
Stochastic biasing and the galaxy-mass density relation in the weakly nonlinear regime
Astrophys. J.
Stochasticity of bias and nonlocality of galaxy formation: Linear scales
Astrophys. J.
Evidence for quadratic tidal tensor bias from the halo bispectrum
Phys. Rev. D
Imprints of primordial non-Gaussianities on large-scale structure: Scale-dependent bias and abundance of virialized objects
Phys. Rev. D
Cited by (26)
Multi-tracer power spectra and bispectra: formalism
2024, Journal of Cosmology and Astroparticle PhysicsHERA bound on x-ray luminosity when accounting for population III stars
2024, Physical Review DImproving constraints on primordial non-Gaussianity using neural network based reconstruction
2024, Journal of Cosmology and Astroparticle Physics