PUMA

Context

In the next decade, three flagship US-led dark energy projects will be nearing completion: (i) DESI, a highly multiplexed optical spectrograph capable of measuring spectra of 5000 objects simultaneously on the 4m Mayal telescope; (ii) LSST, a 3 Gpixel camera on a new 8m-class telescope in Chile, enabling an extreme wide-field imaging survey to 27th magnitude in six filters; and (iii) WFIRST, a NASA space mission with a significant dark energy component, measuring both spectra and images of galaxies over very small but very deep fields. These experiments will characterize dark energy at lower redshift with an exquisite precision. However, a clear successor to this generation of experiments has not yet emerged.

This white paper proposes a revolutionary post-DESI, post-LSST (dark energy) program based on intensity mapping of the redshifted 21 cm emission line from neutral hydrogen from essentially our cosmological neighborhood at z ∼ 3 out to redshift just after reionization z ∼ 6. The proposed intensity mapping survey has the unique capability to quadruple the volume of the Universe surveyed by the optical programs, providing a percent-level measurement of the expansion history and growth to z ∼ 6 and thereby opening a window for new physics beyond the concordance ΛCDM model, as well as significantly improving precision on standard cosmological parameters. In baddition, characterization of dark energy and new physics will be powerfully enhanced by multiple cross-correlations with optical surveys and cosmic microwave background measurements.

The rich dataset produced by such an intensity mapping instrument will be simultaneously useful in exploring the time-domain physics of fast radio transients and pulsars, potentially in live “multi-messenger” coincidence with other observatories.

This program is based around six basic measurements of which two relate to fundamental advances in dark energy and modified gravity, two probe the inflationary period and the last two touch the more traditional radio astronomy themes: detection and characterization of FRBs and pulsars. It turns out that these six goals can be fulfilled by the same specialized instrument as outlined in the Table 1. These goals described are our fundamental science drivers that set the design of the instrument, but as any synoptic project, it will open doors to numerous other analysis, which we briefly mention in Secton 3.2.

Comparison with existing projects

It is important to note that this project has been optimized for the particular scientific goals outlined in Table 1 from its inception. The design of an instrument to map large swathes of the sky at very modest resolution, but high sensitivity, is always going to be fundamentally different from that of radio telescopes specializing in imaging of individual radio sources. Therefore, this experiment is not competition to ngVLA [4] or SKA [5] telescopes. Instead, PUMA is an evolution of a different lineage of experiments, including CHIME [6], HIRAX [7], Tian-Lai [8] and BINGO [9], which we call Stage I experiments. Compared to high-resolution imaging arrays, our telescope is fundamentally different in three aspects:

The array elements are non-tracking and with considerably simpler mechanical design, but are larger in number
The array elements are closely-packed together, providing information on the angular scales that matters for the science at hand
The system provides extremely large instantaneous bandwidth and relies on FFT beam-forming to process the data

In Figure 1 we show comparison of some relevant experiments in terms of intensity mapping figure of merit, which is the total number of baselines probing linear scales multiplied by single element collecting area. ngVLA is not plotted becuase it does not reach into relevant frequency area. Despite cheaper than SKA-MID, PUMA is a winning design in this figure of merit, because it has been optimized for this science from the very beginning. As a concrete example, at the redshifts of interest, the SKA-MID will either under-resolve the baryonic acoustic oscillations (BAO) operating in single-dish mode or over-resolving them if using the array as an interferometer [10].

Figure 1: Figure of merit for intensity mapping experiments is the total number of baselines in the linear regime multiplied by collecting area of each element (see e.g. Equation D4 of [3]). We plot this Figure of merit as a function of redshift for a selection of experiments including Stage I experiment (HIRAX and CHIME), proposed Stage II experiment and a future general radio telescope (SKA-MID). Dashed line show the value assuming all baselines in the experiment are in linear regime. For CHIME we take D = (cylinder area=(feeds per cylinder))^1/2 ∼ 2.8m. For SKA-MID we assume 197×15m dishes observing at 30° off zenith and assign a 3× boost to account for better noise and optical performance.

Of the Stage I experiments, the currently most advanced is the Canadian experiment CHIME consisting of 1024 elements and operating at 400-800MHz. It received first light in 2018 and has already published ground-breaking results on FRBs [11], [12]. HIRAX is a similar experiment in the same frequency band with the same number of elements, but relying on dishes rather than parabolic reflectors and is currently under construction in South Africa.

The success and lessons learned from these Stage I experiments will be instrumental in ensuring that PUMA delivers its science goals. We note that compared to these experiments, which are already operational, PUMA in its petite configuration is only modestly more ambitious (∼ 5× the number of dishes ∼ 2× the bandwidth). However, we plan a strong understanding and technique development of system calibration and performance in advance of deploying the array.

Many of the enabling technologies in particular commodity DSP hardware operating at GHz frequencies developed for telecommunications industry, ultra-wideband transducers and off-the-shelf networking of sufficient capacity make the coming decade a sweet-spot for development of thisn project (see Section 4).

From Science Drivers to Instrument Design

Basic Science Drivers

The PUMA requirements are based on achieving 6 main science drivers:

Characterize expansion history in the pre-acceleration era. By the time PUMA becomes operational, multiple experiments will have measured the expansion history to near the sample-variance limit to redshift z ∼ 1.5 and with some precision to z ∼ 3. PUMA will enable BAO measurements to nearly sample-variance limit all the way to z = 6 and thus complete the long-term programmatic goal of characterizing the expansion history across the cosmic ages [13].
Characterize structure growth in the pre-acceleration era. Measuring the growth of structure over the same redshift-range as the expansion history allows one to do a fundamental test of general relativity [13]. If general relativity is correct, then growth of structure is uniquely determined from expansion history. Disagreement between the two measurements is a smoking gun of modified gravity and one of the most promising probes of detecting it. PUMA will measure growth by relying on the weakly non-linear regime where degeneracy between bias and growth can be broken by the shape of the power spectrum [14].
Constrain or detect the primordial non-Gaussianity. Primordial non-Gaussianity is one of the very few handles that we have on the physics of inflation [15]. Deviations from Gaussianity at a detectable level would be a strong evidence for non-minimal inflation implying either multiple-field or breakage of slow roll. It would be a monumental discovery in physics probing physics up to potentially grand unification scale.
Constrain or detect features in the primordial power spectrum. Features in the primordial power spectrum are another, often overlooked, handle on the physics of inflation [16]. They are generically produced in a wide class of models of inflation and its alternatives. They would give hints about fine structure in the inflationary potential that will have profound impact on our understanding of inflation if found.
Fast Radio Burst Tomography of the Unseen Universe. Fast radio bursts (FRBs) offer a unique probe of the far off Universe should one have a survey with large numbers of precisely localized sources [17]. Faraday rotation provides a precision probe of intergalactic magnetic fields, and time-delay microlensing allows for a cosmic census of compact objects (including constraining black holes as the dark matter). Dispersion can be used to measure the free electron power spectrum, breaking a degeneracy for interpretations of kSZ measurements.
Monitor all pulsars discovered by SKA. SKA-MID and SKA-LOW arrays will detected of the order of 20-30 thousand pulsars and essentially complete the census of all galactic pulsars. PUMA will complement this capability by being capable of daily monitoring of all of these pulsars for at least some time, even in the petite array configuration.

From Science to Instrument. These science drivers motivate the design of the instrument as explained in the Table 1. In short, for every intensity mapping goal, there is a natural resolution necessary to achieve a given science goals. This determines the longest baseline and thus the linear extend of the array. The required sensitivity determines the product N × D, where N is the number of elements in the array and D is the linear dimension of each element⁷. Finally we argue that dishes should be as small as possible in order to allow closely-spaced baselines probing large scale modes that are crucial for science goals. At the same time, in order to minimize systematics, we set D to be at least a few wavelengths across at the highest redshift of interest in order to have some primary beam localization on the sky. For practicality, we set D = 6m corresponding to ∼ 4 wavelengths across at the highest redhift. After determining necessary parameters for goals A – D, we can check and potentially expand the scope to include final science goals E and F.

⁷ At fixed linear array size, the survey noise power spectrum scales with N × D ∝ A_tot/D, (with total collecting area scaling as A_tot ∝ ND²).

The science goals thus naturally determine the basic parameters of the experiment, which we list in Table 2. We notice that array parameters required for goals A and F are considerably more relaxed constraints compared to other science goals. However, both require a compact array filled at approximately 50%. This leads us to a two stage concept in which we start with a smaller array, called petite, which can achieve science goals A and F and make inroads into all the other science goals and a full array which can achieve all science goals. This two stage concept is also attractive from the point of view of commissioning and validating the full array.

The simplified argument presented here is supported by more sophisticated forecasting, which can be found in [3]. We conservatively take into account baseline distribution and various noise contributions, including imperfect coupling to the sky, ground contamination, etc. The properties of neutral hydrogen distribution at redshifts above z = 2 are poorly understood and are the biggest uncertainty in our forecasts.

Additional Science

The six basic science goals are considered sufficiently mature to allow us to guarantee their performance assuming the key performance parameters of the instrument are achieved. However, the total science reach of this experiment is considerably wide. Here we give a brief overview of some of the other exiting science capabilities of PUMA:

Broadband power spectrum information. In addition to BAO and redshift-space distortion extraction, the exquisite precision with which we measure the linear power spectrum will allow strong constraints to be put on numerous basic parameters, when combined with CMB and other LSS data. Among the parameter constraints forecasted in [3], we would like to emphasize two: i) in combination with CMB-S4, the error on light relics parameter N_eff halves to σ[ΔN_eff] = 0:013; ii) it strongly breaks the m_ν - w degeneracy allowing dark energy parameter of state w to be constrainted with sub percent precision even in cosmologies with free neutrino mass.
Weak lensing & Linear Field Reconstruction. The apparent non-Gaussianity of the observed fields will be mostly generated by two mechanisms: weak lensing along the line of sight and non-linear evolution of modes. These effects can be used to back-out both the weak lensing potential (analogous to how CMB measures weak lensing) and the primordial linear field. Both possibilities are extremely interesting. Extraction of primordial linear field will allow cross-correlation with lensing tracers, such as CMB lensing and galaxy lensing, but also calibration of photometric redhisft in photometric experiments. Weak-lensing reconstruction will again provide more lensing planes allowing even more cross-correlations, many of them internal to PUMA and enabled by the extremely large redshift range we are covering.
Using PUMA to extract new information from the secondary CMB. Using Sunyaev Zel'dovich (SZ) tomography PUMA will measure a tomographic reconstruction of the remote CMB dipole and quadrupole fields [18–22] by appropriate cross-correlations with CMB observations. It can be used to reconstruct long-wavelength radial modes (e.g. those most affected by foregrounds in 21cm intensity mapping) from the statistics of small-scale transverse modes. While SZ tomography can be performed with large photometric redshift surveys such as LSST, doing this with 21 cm intensity mapping offers mapping of more volume at higher signal-to-noise, increasing the reach of the experimnent to fundamental physics [23–25].
Multi-messenger probes. PUMA will have considerable instantaneous field of view (around 1000-2000 square degrees), which will likely cover some of the gravitational wave events by pure coincidence. An immediate trigger from the array of gravitational detectors expected to come online in the coming decade will allow a ring-buffer dump, which would allow reconstruction of any coincident low-frequency counter-part. For transients with knows locations, their fluxes could be measured by dedicating them a number of real-time beamforming beam. PUMA’s pulsar monitoring program will also be able to associate pulsar timing glitches to bursts of gravitational waves due to crustal rearrangements, as laid out in [26].
Direct probe of expansion history. Probing the expansion history of the universe directly, i.e. measuring the redshifts of galaxies in the universe increasing in time would open new avenues for studying the dark energy and gravitational potentials [27]. In optical, this is possible, but fraught with calibration issues, while in radio the clocks are sufficiently stable over a decade can be bought off the shelf. PUMA could make this measurements by either relying on cold absorbers [28] or measure the statistics on overall field. There are significant technical hurdles, but this is a potentially exciting science that deserves further investigation.
Time-domain survey for pulsars and magnetars. [29] summarize the next decade’s opportunities to use time-domain radio astronomy to understand strong-field gravity, ultra-dense mater, high-energy astrophysics. This includes testing scenarios such as that laid out in [?]. They argue for surveys visits the same patch of the sky on a regular cadence, with roughly 1 hour dwell time, and using telescopes with wide field of view, large collecting area, wide band, and operating in the 100MHz to GHz range.

Science Objective	Scientific Measurement Requirement	Measurement objective	Instrument requirements
A. Characterize expansion history in the pre-acceleration era Decadal Science Whitepaper: [13]	Measure Baryonic Acoustic Oscillations to volume limited accuracy	Measure 21 cm intensity – over 2 < z < 6 – to k ∼ 0.4hMpc^-1 – with SNR per mode ∼ 1 at k ∼ 0.2hMpc^-1	Bandwidth must include 200-475MHz Maximum baseline L_max ≳ 600 m ND > 25km at L_max = 600m^*
B. Characterize structure growth in the pre-acceleration era Decadal Science Whitepaper: [13]	Measure growth through 21 cm power spectrum on weakly non-linear scales to volume limited accuracy	Measure 21 cm intensity: – over 2 < z < 6 – to k ∼ 1:0hMpc^-1 – with SNR per mode ∼ 1 at k ∼ 0.6hMpc^-1	Bandwidth must include 200-475MHz Maximum baseline L_max ≳ 1500 m ND > 200km at L_max = 1500m^*
C.Constrain or detect primordial inflationary non-Gaussianity Decadal Science Whitepaper: [15]	Measure 21 cm bispectrum to achieve non-Gaussianity parameter sensitivity: – orthogonal: σ [f_NL^ortho] < 10 – equiliateral: σ [f_NL^equil] < 10	Measure ≳ 10⁹ linear modes with SNR per mode ∼ 1	Same as above plus: bandwidth 200 — 1100MHz (z ∼ 0.3 — 6) assuming f_sky ∼ 0.5
D. Constrain or detect features in primordial power spectrum Decadal Science Whitepaper: [16]	Constrain features in the matter power spectrum over available scales to – sensitivity σ[A_lin] < 10^-3	Same as above.	Same as above.
E. Fast Radio Burst Tomography Decadal Science Whitepapers: [17][26][29][30]	Volume limited measurement of electron power spectrum, stellar mass census	– 100 million FRBs – covering two frequency octaves – 3” localization precision	N^3/2Δν^3/4 ≳ 10⁹ MHz† Provide real-time FRB back-end Provide baseband buffer with triggered readout
F.Monitor pulsars Decadal Science Whitepapers: [29][31-35]	Monitor all pulsars discovered by SKA	Detect all pulsars in current Field of View brighter than 10μJy	10 σ point source sensitivity >10μJy / transit Provide real-time pulsar back-end

Table 1: Science Traceability Matrix for main science drivers. All derived instrument parameters assume certain fixed system properties such as amplifier temperature, sky background and various efficiency factors as outlined in [3]. The total integration time is assumed to be five years^*. At fixed linear dimension of the array, the noise power scales as ND, where N is the number of elements and D is their linear dimension. † This calculation makes a number of necessary assumptions about FRB distribution.

Antenna Array	Hexagonal close-packed transit array
	Petite	Full	Petite array: Achieve science goals A. & F. and ∼ 30% of B.-E.
array diameter	600m	1500m
fill factor	50%	50%	Full array: Achieve all science goals
number of elements	5,000	32,000
10 σ single transit sens.	8.7μJy	1.3μJy
Array element	Parabolic on-axis 6m dish with 1D pointing		Small for short baselines, D ≫ λ_min for systematics
construction	on-site fiber glass production, mm surface accuracy		Better beam control than Stage I for systematics
OMT	ultra-wide band, dual-pol
front-end	amplifiers and digitizers integrated with OMT		alternative arrangement to be explored
channelizer	one per 10-100 dishes		helps with corner-turning, alternatives possible
Correlator	FFT correlator with partial N² correlations		Individual baseline correlation mode for calibration.
FRB capability	real-time FRB search engine
real-time beam-forming	10⁴ concurrent tracking beams		pulsar, transients, multi-messenger

Survey
area	50%
observing time	5 years on sky, wall-time 7-10 years
Calibration
complex amplitude	sky sources
primary beam	per antenna calibration using fixed wing drones
clock distribution	sub ps clock distribution for phase stability

Table 2: Basic instrumental parameters.

Figure 2: A collage of scientific possibilities offered by PUMA. Upper left plot is for *petite* array, others are for full array. *Upper Left*: Forecasted BAO errors compared with current and planned experiments. *Upper Right*: Forecasted one-sigma errors on growth parameters compared with current and planned experiments. *Middle Left*: Forecasted errors on non-Gaussanity parameters compared with current and planned experiments. *Middle Right*: Forecasted errors on linear oscillation features. *Lower Left*: FRB plot *Lower Right*: Pulsar plot

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