contents=  Submitted to the Proceedings of the US Community Study on the
Future of Particle Physics (Snowmass 2021) ,
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# Snowmass 2021 Cosmic Frontier White Paper:
Cosmology with Millimeter-Wave Line Intensity Mapping

Kirit S. Karkare  Kavli Institute for Cosmological Physics, University of
Chicago, Chicago, IL 60637, USA  Fermi National Accelerator Laboratory,
Batavia, IL 60510, USA  Azadeh Moradinezhad Dizgah  Département de Physique
Théorique, Université de Genève, 1211 Genèva 4, Switzerland  Garrett K.
Keating  Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA 02138,
USA
Patrick Breysse  Center for Cosmology and Particle Physics, New York
University, New York, NY 10003, USA  Dongwoo T. Chung  Canadian Institute for
Theoretical Astrophysics, University of Toronto, Toronto, ON M5S 3H8, Canada
Dunlap Institute for Astronomy and Astrophysics, University of Toronto,
Toronto, ON M5S 3H4, Canada
for the Snowmass 2021 Cosmic Frontier 5 Topical Group
Endorsers: James Aguirre  University of Pennsylvania, Philadelphia, PA 19104,
USA  Zeeshan Ahmed  Kavli Institute for Particle Astrophysics and Cosmology,
Stanford University, Stanford, CA 94305, USA  SLAC National Accelerator
Laboratory, Menlo Park, CA 94025, USA  Adam Anderson  Fermi National
Accelerator Laboratory, Batavia, IL 60510, USA  Pete S. Barry  Argonne
National Laboratory, Lemont, IL 60439, USA  Ritoban Basu Thakur  California
Institute of Technology, Pasadena, CA 91125, USA  Bradford Benson  Fermi
National Accelerator Laboratory, Batavia, IL 60510, USA  Kavli Institute for
Cosmological Physics, University of Chicago, Chicago, IL 60637, USA  José Luis
Bernal  Johns Hopkins University, Baltimore, MD 21218, USA  Federico Bianchini
Kavli Institute for Particle Astrophysics and Cosmology, Stanford University,
Stanford, CA 94305, USA  SLAC National Accelerator Laboratory, Menlo Park, CA
94025, USA  Simeon Bird  University of California, Riverside, Riverside, CA
92521, USA  C. Matt Bradford  Jet Propulsion Laboratory, Pasadena, CA 91109,
USA  California Institute of Technology, Pasadena, CA 91125, USA  John E.
Carlstrom  Kavli Institute for Cosmological Physics, University of Chicago,
Chicago, IL 60637, USA  Argonne National Laboratory, Lemont, IL 60439, USA
Emanuele Castorina  University of Milan, 20122 Milano MI, Italy  Andrea Caputo
Tel Aviv University, Ramat Aviv 69978, Israel  Clarence Chang  Argonne
National Laboratory, Lemont, IL 60439, USA  Kavli Institute for Cosmological
Physics, University of Chicago, Chicago, IL 60637, USA  Tzu-Ching Chang  Jet
Propulsion Laboratory, Pasadena, CA 91109, USA  California Institute of
Technology, Pasadena, CA 91125, USA  Yun-Ting Cheng  California Institute of
Technology, Pasadena, CA 91125, USA  Cyril Creque-Sarbinowski  Johns Hopkins
University, Baltimore, MD 21218, USA  Abigail T. Crites  Cornell University,
Ithaca, NY 14850, USA  Oliver Doré  Jet Propulsion Laboratory, Pasadena, CA
91109, USA  California Institute of Technology, Pasadena, CA 91125, USA
Jacques Delabrouille  Centre Pierre Binétruy International Research
Laboratory, CNRS, 75016 Paris, France  University of California, Berkeley,
Berkeley, CA 94720, USA  Lawrence Berkeley National Laboratory, Berkeley, CA
94720, USA  Simone Ferraro  Lawrence Berkeley National Laboratory, Berkeley,
CA 94720, USA  Jeffrey Filippini  University of Illinois, Urbana-Champaign,
Champaign, IL 61801, USA  Yan Gong  National Astronomical Observatories,
Chinese Academy of Sciences, Beijing, China  Ely Kovetz  Ben-Gurion University
of the Negev, Be’er Sheva, Israel  Guilaine Lagache  Aix Marseille University,
CNRS, CNES, LAM, Marseille, France  Adam Lidz  University of Pennsylvania,
Philadelphia, PA 19104, USA  Abhishek S. Maniyar  Center for Cosmology and
Particle Physics, New York University, New York, NY 10003, USA  Daniel P.
Marrone  University of Arizona, Tucson, AZ 85721, USA  Jeff McMahon  Kavli
Institute for Cosmological Physics, University of Chicago, Chicago, IL 60637,
USA  Zhaodi Pan  Argonne National Laboratory, Lemont, IL 60439, USA  Emmanuel
Schaan  Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA  Erik
Shirokoff  Kavli Institute for Cosmological Physics, University of Chicago,
Chicago, IL 60637, USA  Sara M. Simon  Fermi National Accelerator Laboratory,
Batavia, IL 60510, USA  Gordon Stacey  Cornell University, Ithaca, NY 14850,
USA  Eric R. Switzer  Goddard Space Flight Center, Greenbelt, MD 20771, USA
Peter Timbie  University of Wisconsin, Madison, Madison, WI 53715, USA
Joaquin Vieira  University of Illinois, Urbana-Champaign, Champaign, IL 61801,
USA  Gensheng Wang  Argonne National Laboratory, Lemont, IL 60439, USA  W. L.
Kimmy Wu  SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA
Michael Zemcov  Rochester Institute of Technology, Rochester, NY 14623, USA

###### Abstract

Next-generation tests of fundamental physics and cosmology using large scale
structure require measurements over large volumes of the Universe, including
high redshifts inaccessible to present-day surveys. Line intensity mapping, an
emerging technique that detects the integrated emission of atomic and
molecular lines without resolving sources, can efficiently map cosmic
structure over a wide range of redshifts. Observations at millimeter
wavelengths detect far-IR emission lines such as CO/[CII], and take advantage
of observational and analysis techniques developed by CMB experiments. These
measurements can provide constraints with unprecedented precision on the
physics of inflation, neutrino masses, light relativistic species, dark energy
and modified gravity, and dark matter, among many other science goals. In this
white paper we forecast the sensitivity requirements for future ground-based
mm-wave intensity mapping experiments to enable transformational cosmological
constraints. We outline a staged experimental program to steadily improve
sensitivity, and describe the necessary investments in developing detector
technology and analysis techniques.

##  1 Introduction

Over the past few decades, thanks to the increasing volume and precision of
cosmological surveys—in particular measurements of the cosmic microwave
background (CMB) and large-scale structure (LSS)—we have established a high-
precision, “concordance” model of cosmology: the $\Lambda$CDM paradigm.
Nevertheless, we are still left with fundamental open questions. What was the
mechanism that set the seeds of cosmic structure in the very early universe?
What is the nature of dark energy (DE) and dark matter (DM)? What are the
properties of neutrinos and other possible light relics? High-precision maps
of the three-dimensional LSS provide a rich trove of information about the
origin, evolution and composition of the Universe, probing deviations from the
standard cosmological model and potentially hinting at new physics. The line
intensity mapping (LIM) technique offers a means to map LSS over a wide range
of scales and across many redshift epochs, complementing upcoming wide-field
galaxy surveys at redshifts $z\leq 2$, and providing a spectroscopic probe of
LSS at $z>2$.

In contrast to typical galaxy surveys, which directly image large numbers of
resolved galaxies, LIM measures the aggregate emission of all galaxies in a
chosen spectral line [1]. Spatial fluctuations in the resulting intensity
field and spectral emission information can be combined to generate a smoothed
three-dimensional map of the galaxy distribution. As illustrated in Figure 1,
the clustering component traces the underlying DM while the shot noise
contribution arises from the discrete nature of the sources. Emission lines
originating from different phases of the interstellar medium can be used
individually and in synergy with each other to constrain cosmology and
astrophysics [2, 3, 4]. Since the LIM technique does not require resolving
individual galaxies, it is an efficient probe of LSS over large comoving
volumes, enabling measurements over large scales and over long redshift lever
arms, including the high-redshift regime. The promise of LIM surveys for
testing fundamental cosmology is therefore multifold:

  1. 1.

Wide redshift coverage mitigates degeneracies between cosmological parameters
due to different degeneracy directions at low and high redshifts.

  2. 2.

Measuring very large-scale modes allows extraction of key information about
physics at the scale of the cosmological horizon, including imprints of
multiple degrees of freedom during inflation and general relativistic effects
that probe the theory of gravity.

  3. 3.

Probing higher redshifts provides access to an order of magnitude more linear
and semi-linear density modes, which are less affected by nonlinearities and
astrophysical processes that decorrelate the modes from the initial
conditions, and can be described accurately with perturbative theoretical
models; see the dedicated Snowmass 2021 white paper on cosmology at high
redshift for further details [5].

Figure 1: Left: Schematic image of a 100 deg2 line intensity map. Individual
layers indicate the three-dimensional information obtained by mapping at
different frequencies $\nu_{\rm obs}$. Center: Zoom-in on a small segment of
an individual frequency channel, showing the correspondence between the large-
scale structure seen in the underlying galaxy population and the lower-
resolution intensity map. Right: Schematic of a LIM power spectrum (solid
black), showing the large-scale clustering component (dashed blue) driven by
the dark matter distribution and the shot noise component (dot-dashed orange)
due to the Poisson statistics of individual objects.

LIM at millimeter wavelengths has garnered significant experimental interest
in recent years. These measurements target atomic and molecular lines with
rest-frame wavelengths in the far-IR. Lines such as the CO(J$\rightarrow$J-1)
rotational transitions and the [CII] ionized carbon fine structure line are
bright in dusty, star-forming galaxies that are abundant in the early
Universe, and have been observed in individual sources out to the epoch of
reionization [6, 7]. Observations from cm to THz frequencies are capable of
detecting emission from redshifts $0<z<10$ using a combination of lines.
Figure 2 shows the mean brightness temperatures of spectral lines detectable
by mm-wavelength ground-based surveys, in addition to representative
atmospheric transmission. These observations operate in a region of frequency
space with much less Galactic foreground contamination than LIM efforts
targeting the 21 cm line [8], and build on the extensive heritage of CMB
observations at similar frequencies. Current experiments, including CCAT-p
[9], COMAP [10], CONCERTO [11], EXCLAIM [12], mmIME [13], SPT-SLIM [14], TIM
[15], and TIME [16], are demonstrating the technologies and analysis
techniques to probe cosmology, but so far lack the necessary scale and
sensitivity to place competitive cosmological constraints.

The goal of this white paper is to illustrate that next-generation mm-wave LIM
experiments are capable of testing fundamental physics and cosmology,
particularly at higher redshifts and over larger volumes than possible with
current probes of LSS. After describing the motivating science cases, we
forecast the measurement requirements needed to cross critical target
thresholds. We outline a staged experimental program that reaches these
thresholds by gradually increasing the sensitivity and volume of LIM
observations. We then describe the needed investments in technology to improve
experimental sensitivity, and summarize the challenges in extracting cosmology
from LIM measurements and the investments in analysis techniques that would
address them.

Figure 2:  Spectral lines detectable by a ground-based mm-wavelength survey
(reproduced from Ref. [17]). Shown above are model predictions for the
brightness temperatures of individual lines, their sum (dashed black), and the
median atmospheric transmission at the South Pole (light thin blue). Colors
correspond to observed redshifts of the lines.

##  2 Science Summary

Wide-field LIM surveys would advance our understanding of open fundamental
questions in cosmology, and in several cases cross physically-motivated
theoretical thresholds. Measuring clustering statistics of line intensity
fluctuations over the redshift range $0<z<10$ would allow us to:

  1. 1.

Decipher the origin of cosmic structure: The simplest models of single-field,
slow-roll inflation predict primordial fluctuations with a nearly scale-
invariant power spectrum and Gaussian distribution, in agreement with CMB and
LSS observations [18]. Deviations from either prediction, e.g., features in
the primordial power spectrum [19, 20] or primordial non-Gaussianity (PNG)
[21], would probe fundamental physics at the highest energy scales and shed
light on the mechanism that set the seeds of cosmic structure; see the
dedicated Snowmass 2021 white paper on Inflation [22]. High-precision
measurements of the line power spectrum can significantly improve current
bounds on inflaton features [18, 23, 24] by detecting, e.g., sinusoidal
modulation of the power spectrum [25] with enhanced sensitivity to lower
amplitudes and a broader range of feature frequencies. The amplitude of the
local-type PNG, $f_{\rm NL}^{\rm loc}$, can be constrained by measuring the
scale-dependent line bias on large scales [26]. Furthermore, measurement of
the line bispectrum improves limits on the local shape and constrains other
types of PNG, such as the equilateral [27, 28, 29], orthogonal [30], and
folded [31, 32] shapes (which do not leave distinguishable imprints on the
power spectrum [33]). Detection of local-type PNG is considered a “smoking
gun” for multi-field inflation, which generically predicts $f_{\rm NL}^{\rm
loc}={\mathcal{O}}(1)$. Therefore, crossing the critical threshold of
$\bm{\sigma(f_{\rm NL}^{\rm loc})\sim 1}$ would rule out single-field models
of inflation, which obey the consistency relation enforcing $f_{\rm NL}^{\rm
loc}\ll 1$ [34, 35]. Reaching similar thresholds on other shapes is also
desirable: detecting $\bm{f_{\rm NL}^{\rm eq}\geq 1}$ would imply that
inflation is a strongly-coupled phenomenon [36, 37] and considerably limit
inflation model space. CMB data from Planck provide the current tightest
constraints [38], but recent results from galaxy surveys [39, 40, 41] point to
the potential of LSS to exceed the current CMB limits of $f_{\rm NL}^{\rm
loc}=-0.9\pm 5.1,\ f_{\rm NL}^{\rm eq}=-26\pm 47,f_{\rm NL}^{\rm orth}=-38\pm
24$. Advantages of LIM: First, LIM measurements of large comoving volumes
compared to galaxy surveys would access very large-scale modes, which are
crucial in constraining $f_{\rm NL}^{\rm loc}$ using scale-dependent bias.
Second, since the signal-to-noise ratio for PNG in the bispectrum sharply
increases as a function of the smallest scale [42], probing $z>2$ and
accessing a large number of linear and semi-linear modes make LIM surveys
particularly powerful compared to lower-redshift surveys. Third, using cross-
correlations between multiple lines observable in a LIM survey in addition to
auto spectra can further improve constraints by mitigating cosmic variance
[43].

  2. 2.

Measure the sum of neutrino masses: When neutrinos become non-relativistic,
their masses contribute to the matter content of the universe and modify the
expansion history and growth of structure [44]. They can thus be constrained
by measurements of line clustering statistics such as the power spectrum. The
mass splitting measured by neutrino oscillation experiments sets a minimum for
the sum of neutrino masses, $M_{\nu}=0.059\ {\rm eV}$ in the normal and
$M_{\nu}=0.10\ {\rm eV}$ in the inverted mass hierarchies [45, 46]. This sets
a critical threshold of $\bm{\sigma(M_{\nu})\sim 0.012\ {\rm eV}}$ for a
$\bf{5\sigma}$ detection of the minimum neutrino mass [47]. Improving on the
current best constraints of $\sigma(M_{\nu})\leq 0.12\ {\rm eV}$ from CMB and
LSS data [48, 49] would indirectly distinguish between the two mass orderings,
with implications for determining the nature of neutrinos (Dirac vs.
Majorana), understanding mixing in the lepton sector, and discriminating
between flavor models [50]; see the dedicated Snowmass 2021 white paper on
synergies between cosmological and laboratory probes of neutrinos [51].
Advantages of LIM: By mapping LSS over a long redshift lever arm, LIM surveys
capture the redshift evolution of the scale-dependent suppression of the
matter power spectrum and growth rate due to neutrino masses. Furthermore,
wide redshift coverage breaks parameter degeneracies in the CMB and low-
redshift LSS probes [52], most notably between $M_{\nu}$ and the large-scale
amplitude of the matter power spectrum, optical depth, and DE equation of
state [53, 54, 55].

  3. 3.

Search for new light particles: The Standard Model (SM) of particle physics
predicts three species of massless neutrinos contributing to the radiation
content of the Universe at early times, corresponding to $N^{\rm SM}_{\rm
eff}=3.046$. Changing $N_{\rm eff}$ modifies the amplitude of the matter power
spectrum and the phase and amplitude of the baryon acoustic oscillations [56],
and thus can be constrained by measuring the power spectra of biased tracers
of DM. Detection of excess light relic abundance offers discovery space for
new physics, as many extensions to the SM predict extra light relics. The spin
states and decoupling temperatures determine the minimum excess $\Delta N_{\rm
eff}$ values: $\Delta N_{\rm eff}>0.027$ for a single scalar, $0.047$ for a
Weyl fermion, and $0.054$ for a vector boson [57, 58]. Therefore, reaching
$\bf{\sigma(N_{\rm eff})\lesssim 0.02-0.03}$ would constrain excess light
relics with non-zero (zero) spin at $\bf{2\sigma}$ ($\bf{1\sigma}$), probing a
wide range of models—including those with axions, axion-like particles,
thermal populations of gravitinos, and dark photons [59]; see the dedicated
Snowmass 2021 white paper on light relics [60]. Advantages of LIM: By probing
extremely large comoving volumes, LIM surveys could significantly improve on
current limits from CMB and LSS data, $\sigma(N_{\rm eff})\simeq 0.17$ [48].
Since LIM is not affected by the degeneracy between $N_{\rm eff}$ and the
primordial Helium fraction, $Y_{\rm He}$—one of the limiting factors in CMB
constraints on light relics—these measurements will be highly complementary to
CMB-S4 [61].

  4. 4.

Test the physics of dark energy and gravity: Although the current accelerated
expansion is well-modeled by a cosmological constant which begins to dominate
the cosmic energy density at late times, $z\lesssim 2$, it unclear whether
this is the correct model of DE, or if the acceleration is due to
modifications to General Relativity. “Tracking”-type behavior, where DE
behaves like matter at high redshift with equation of state $w\simeq 0$, and
then transitions to a cosmological constant with $w\simeq-1$ at low redshift,
is a generic prediction of scalar-tensor theories with second-order equations
of motion (Horndeski theories) [62, 63]. Another class of models, which has
received attention as a solution to the Hubble tension [64, 65, 66], assumes
an early dark energy (EDE) component that behaves like a cosmological constant
before some critical pre-recombination redshift $z_{c}$, and afterwards
dilutes faster than radiation. LSS surveys can test these models by precisely
characterizing the expansion history during both the matter- and DE-dominated
eras [67]. At the same time, LSS probes models of gravity by tracing their
imprints on the growth of structure [68, 69]; while modifications to gravity
and dynamic DE are largely indistinguishable in the expansion history, their
effects are distinct in the fluctuations probed by clustering statistics [70].
Advantages of LIM: High-precision LIM measurements would significantly improve
current constraints on dynamical and EDE models due to wide redshift access.
[71, 72, 73]. Measurements at high redshift probe the EDE fraction out to very
high pre-recombination redshifts [25], and constrain EDE where its effect on
the matter power spectrum is more prominent since nonlinearities reduce the
difference between EDE and $\Lambda$CDM [74].

  5. 5.

Explore dark matter candidates: High-precision measurements of line clustering
statistics constrain various dark matter scenarios, including those that act
like an additional contribution to $N_{\rm eff}$ [75] and those that leave
features in the clustering statistics of DM tracers, such as self-interacting
DM [76], ultra-light axion DM [77], and models with DM-baryon scattering [78];
see the dedicated Snowmass 2021 white papers on dark matter constraints from
cosmic surveys [79, 80, 81]. Advantages of LIM: By probing the faintest
galaxies, which are not detected by galaxy surveys, LIM can uniquely constrain
DM models that suppress small-scale structure [82]. LIM surveys can also be
sensitive to radiative decays/annihilations of a broad range of beyond-the-
Standard-Model particles which decay to photons at a specific frequency. If
the density of these exotic species traces the DM, they will appear in LIM
data as an emission line with no known atomic or molecular frequency. Models
that can be probed using this signature include axion or sterile neutrino dark
matter which decays to photons [83, 84], or an enhanced decay rate of the
cosmic neutrino background [85].

Beyond the fundamental physics goals outlined above, a wide-field high-
redshift LIM survey would also be a valuable tool for a broader range of
astrophysical studies; see e.g., [1, 86]. LIM surveys provide a unique window
into the aggregate properties of faint, distant galaxies unobservable by
traditional surveys, probing galaxy growth and evolution [87, 88, 13, 89, 10,
90] as well as the process of cosmic reionization [91].

##  3 Measurement Requirements and Staged Experimental Program

Focusing on a subset of science goals described above, in this section we
forecast the experimental sensitivity that LIM surveys targeting CO/[CII]
require to cross the critical thresholds for $f_{\rm NL}^{\rm loc},M_{\nu}$,
and $N_{\rm eff}$. We also use the Chevallier-Polarski-Linder parametrization
of the DE equation of state ($w_{0},w_{a}$) to illustrate LIM’s potential to
constrain dynamic DE models [92, 93].

Rather than focusing on a single survey design, we perform Fisher forecasts to
determine the optimal design of ground-based mm-wave LIM surveys in achieving
the best constraints on parameters of interest by measuring CO/[CII]. We
present constraints as a function of spectrometer-hours: the product of
spectrometer count and integration time, which is a reasonable proxy for
sensitivity and the “effort level” of an experiment. Based on these results,
we then outline a staged experimental approach that builds up sensitivity,
enabled by technical advances discussed in Section 4.

We use only the line power spectra in our forecasts. Exploiting information in
the observed intensity field beyond the power spectrum, e.g., higher-order
statistics, one-point statistics, and synergies between LIM and future CMB and
galaxy surveys [94] would not only improve constraints, but also offer a means
to overcome degeneracies with nuisance astrophysical parameters, and to
improve mitigation of systematics and foregrounds.

###  3.1 Sensitivity required to cross critical thresholds

Our forecasts consider power spectrum measurements of several CO rotational
lines (from J=2-1 to J=6-5) and the [CII] fine-structure line combined with
Planck primary CMB data [48]. As the best- and worst-case scenarios, we show
constraints with and without interloper lines as a source of noise in our
analysis [95, 96]. We use a linear model of the line power spectrum, and
assume that the line biases and mean brightness temperatures are well-
constrained. We choose a conservative bound on the small-scale cutoff ($k_{\rm
max}$) to stay in the regime where the linear model of the line power spectrum
is accurate to $\sim 20\%$ [97]. The large-scale cutoffs—most relevant for
$f_{\rm NL}^{\rm loc}$—are set by the angular extent of the survey and the
atmospheric transmission as a function of frequency in the angular and line-
of-sight directions, respectively. For each line, we split the survey into
redshift bins with mean redshifts $z_{i}$ and widths of 0.1 dex to account for
the cosmic evolution of the line-emitting population, as well as variations in
noise levels caused by the atmospheric transmission. The constraints are
obtained using a unified Fisher Forecast pipeline described in Ref. [17],
where further details about the signal and interloper modeling, instrument
noise, and forecasting assumptions are outlined.

The instantaneous sensitivity of an instrument is determined by spectrometer
count. Each “spectrometer” consists of a single spatial pixel that fully
samples the 80–310 GHz range with frequency channels of width
$\Delta\nu=\nu/R$; we assume resolving power $R=300$. Millimeter-wave
detectors are now routinely fabricated with device noise that is subdominant
to the atmospheric background at excellent sites [98]—even at the $R\sim
100-1000$ spectral resolution needed for LIM science—so we assume that the
instrument noise is dominated by thermal emission from the atmosphere.

Figure 3: Projected 1$\sigma$ constraints on several extensions to
$\Lambda$CDM (blue) and optimal sky coverage to achieve these constraints
(red), as a function of a mm-wave LIM experiment’s sensitivity parametrized by
spectrometer-hours. A spectrometer is assumed to measure 80–310 GHz with
$R=300$ from excellent mm-wave observing sites. The dashed lines correspond to
the case where interloper lines are neglected (i.e., perfect line separation),
while the solid lines include the interlopers as noise terms. In all cases
$\Lambda$CDM parameters are marginalized over and Planck priors are imposed.

Figure 3 shows projections for one-parameter extensions to $\Lambda$CDM
varying $f_{\rm NL}$, $N_{\rm eff}$, and $M_{\nu}$, and for a three-parameter
extension varying $w_{0}$, $w_{a}$, and $M_{\nu}$, in blue. The sky fraction
that minimizes parameter uncertainties at each value of spectrometer-hours is
shown in red, and limits from Planck are shown with horizontal gray lines. In
all cases, significant improvements over current constraints are possible; the
projected uncertainties generally plateau after $\sim 10^{8}-10^{9}$
spectrometer-hours, when the observable sky fraction hits a maximum of $f_{\rm
sky}=0.4$. In all cases except $f_{\rm NL}^{\rm loc}$, the “interloper” worst-
case scenario is not significantly less constraining than the best-case
scenario111Without a Planck prior, the impact of interlopers is more relevant
[17].. The degradation of the $f_{\rm NL}^{\rm loc}$ constraint agrees with
the findings of Ref. [99], which showed that while interloper contamination
increases the uncertainty and biases the best-fit value of $f_{\rm NL}^{\rm
loc}$, using cross-correlations between lines of interest and interlopers can
largely remove the contamination.

Our forecasts indicate that future mm-wave LIM surveys can deliver
cosmological constraints that are comparable to or exceed contemporary and
planned CMB/LSS experiments. LIM experiments in the $\sim 10^{7}$
spectrometer-hour range can deliver constraints from the clustering power
spectrum that are competitive with those from the upcoming generation of
spectroscopic galaxy surveys [100], such as EUCLID [101] and DESI [102].
Experiments with $\sim 10^{8}$ spectrometer-hours would improve constraints on
most parameters by an additional factor of 2–4. For $N_{\rm eff}$, such a
survey would provide comparable constraints to baseline forecasts for CMB-S4
[59], while for $M_{\nu}$, a $\sim 10^{7}$ spectrometer-hour survey gives
similar constraining power to CMB-S4. Projected constraints on $f_{\rm
NL}^{\rm loc}$ surpass those from the proposed PUMA 21 cm experiment at
$10^{7}$–$10^{8}$ spectrometer-hours depending on the degree of interloper
mitigation [33]; we also note that our forecasts for PNG are based only on the
power spectrum and that significant additional constraining power will come
from the bispectrum.

Projections for several of the science targets outlined in Section 2 rely on
effects observable in the DM fluctuations in the linear regime, i.e., the
initial conditions of structure formation. Therefore, the number of measurable
linear (or weakly nonlinear) modes is a useful metric for comparing the
potential of different LSS surveys. The decorrelation of the observed
fluctuations from their initial conditions due to nonlinear evolution and
instrumental noise is accounted for in defining the number of modes. As in
Ref. [5], we compute the primordial physics Figure of Merit (FoM) to
characterize the “effective” number of observed modes correlated with the
initial conditions (see Appendix A for further details). Sensitivity to
several parameters of interest—such as primordial features, local-shape PNG,
and EDE—scale as $1/\sqrt{{\rm FoM}}$. Ambitious future LIM surveys could
achieve a FoM up to 170, with the exact value depending on how well interloper
lines can be suppressed. For comparison, the expected FoM for DESI is 0.16,
while PUMA expects 26–85 depending on foreground mitigation; see [5] for more
extended comparison across various LSS surveys.

When interpreting the forecasted parameter constraints and FoM, it is
important to note that the LIM technique is still in an early stage of
development compared to the CMB and galaxy surveys, and several major caveats
exist. First, while we assume perfect knowledge of the nuisance astrophysical
parameters (i.e., the mean brightness temperature and line bias, which are
degenerate with cosmological parameters), their current uncertainties are
large. We anticipate that taking cross-correlations, both internally in multi-
line intensity maps and with other probes such as galaxy surveys and CMB
lensing, will significantly reduce these uncertainties [103]. Second, we
assume linear theory for the line power spectrum; marginalizing over nonlinear
parameters could degrade constraints, with the of impact depending on the
choice of small-scale cutoff [25]. Finally, we assume that large angular and
line-of-sight scales can be recovered without a significant $1/f$ component
above the $k_{\rm min}$ cutoffs. The degree to which this is possible is
uncertain and depends on the scan strategy and atmospheric noise—techniques to
recover large scales will be tested on pathfinder experiments.

Although our forecasts are performed specifically for mm-wave measurements
from 80–310 GHz, we also anticipate and advocate for measurements of rest-
frame far-IR lines outside of this range. Generally, cm-wave or THz
measurements employ technology and observation strategies similar to mm-wave,
and will improve the statistical power and redshift range of LIM measurements.
Ground-based cm-wave surveys of low-J CO lines with $10^{7}$–$10^{8}$
spectrometer-hours would complement mm-wave measurements by independently
providing percent-level determination of the high-redshift expansion history
[104, 105, 106] and PNG constraints from multiple tracers [107, 108, 109].
Since CO(1-0) and CO(2-1) at $z\gtrsim 2$ have no interloper lines to contend
with, these measurements will also aid in attributing mm-wave signals to
specific lines. Surveys of [CII], [NII], [OI], [OIII], and other lines
extending to higher frequencies should enable similar synergies.

###  3.2 Experimental program

We envision a staged experimental approach in which increasing numbers of
spectrometers are deployed on ground-based mm-wave telescopes to achieve the
science goals outlined in the previous section. This strategy follows the
approach used to develop similar technology for current mm-wave observatories
measuring the CMB. It offers a natural path to increasing technical readiness
and scale, and by the mid-2030s, this program could position mm-wave LIM as a
successor to current CMB surveys.

Table 1 outlines possible experimental stages and forecasts for the science
cases in Section 2, in addition to the primordial physics Figure of Merit.
Each stage corresponds to a different experimental scale and is differentiated
by the instrumentation and platform used—while current experiments employ a
wide array of spectrometer technologies, we anticipate that future projects
will converge on high-density on-chip spectrometers deployed at existing CMB
facilities. Once the transition to CMB-style instruments is made, we assume
that densely-packed spectrometer wafers will be deployed in receivers with
multiple “optics tubes,” as envisioned for SO, SPT-3G+, and CMB-S4. An optics
tube is assumed to hold an array of 400 on-chip spectrometers on a 6” wafer in
the same formfactor as the SO-LAT optics tubes; note that this requires a
significant increase in packing density over current on-chip spectrometers
(see Section 4).

Spec- hrs |  Example |  Time- scale |  $\sigma(f_{\rm NL})$ |  $\sigma(M_{\nu})$ (meV) |  $\sigma(N_{\rm eff})$ |  $\sigma(w_{0})\times 10^{2}$ |  $\sigma(w_{\rm a})\times 10^{2}$ |  FoM
---|---|---|---|---|---|---|---|---
$10^{5}$ |  TIME, CCAT-p, SPT-SLIM | 2022 | 5.1 (5.1) | 61 (65) | 0.1 (0.11) | 13 (14) | 51 (52) | 0.0015
$10^{6}$ |  TIME-EXT | 2025 | 4.7 (5) | 43 (47) | 0.082 (0.087) | 5.3 (6.3) | 21 (26) | (0.09-0.1)
$10^{7}$ |  SPT-like 1 tube | 2028 | 3.1 (4.2) | 23 (28) | 0.043 (0.051) | 2 (2.2) | 8.5 (9.7) | (1.7-3.1)
$10^{8}$ |  SPT-like 7 tubes | 2031 | 1.2 (3) | 9.7 (13) | 0.02 (0.023) | 0.93 (1) | 3.8 (4.3) | (9.5-28)
$10^{9}$ |  CMB-S4-like 85 tubes | 2037 | 0.48 (2.4) | 4.1 (6.8) | 0.013 (0.016) | 0.61 (0.73) | 2.1 (2.8) | (21-108)
Planck | 5.1 | 83 | 0.187 | 41 | 100 | —

Table 1: Stages of future mm-wave LIM experiments and projected constraints
for cosmological science cases, with optimistic (pessimistic) assumptions
about the ability to suppress the impact of interloper emission. For each
stage we provide an approximate example of the class of instrument required
for such a survey. The timescale is a rough estimate of when such a survey
could begin operations. All forecasts include Planck priors.

While this program outlines an ambitious scaling up from current-generation
experiments, we note that over the last 10 years similar progress has been
made with CMB experiments. Moreover, this progression is feasible using
existing 5–10m class CMB facilities, which are well-suited to the degree-to-
arcminute scales necessary for these LIM science cases. Experimental
techniques for extracting power spectra from extended, low surface brightness
emission are mature and large classes of instrumental systematics relevant to
the measurement are well-understood and quantified.

##  4 Investments Needed

###  4.1 Technology Developments

While first-generation mm-wave LIM instruments are now being demonstrated,
several advances are still needed to enable the sensitivity required to cross
the aforementioned science thresholds. The following hardware-related
investments in detectors, readout, and facilities would leverage the
considerable investment made in CMB experiments over the last few decades:

  * •

On-Chip Spectrometer Packing Density: Current approaches to mm-wave
spectroscopy (diffraction gratings, Fourier Transform or Fabry-Perot
spectroscopy, heterodyne detection) are difficult to scale to large
spectrometer counts. On-chip spectroscopy, in which the detector and
spectrometer are integrated on a silicon wafer, offers a natural path to
maximizing the sensitivity of mm-wave receivers. However, while prototype on-
chip spectrometers are now being demonstrated [110, 111], their spatial
packing density is still significantly lower than CMB focal planes (primarily
due to the physical extent of the spectrometer on the wafer). Innovation in
focal plane geometry and layout will be key to enabling high-density close-
packed arrays. Our forecasts assume that a 6” diameter wafer holds $\sim 400$
spectrometers, which fully samples the available focal plane area.

  * •

On-Chip Spectrometer Spectral Resolution: On-chip spectrometers have
demonstrated spectral resolution of $R\sim 300-500$ [110, 112]. Improving this
to $R\sim 1000$ would move LIM experiments into the regime of spectroscopic
surveys. Higher $R$ increases the number of available modes and significantly
improves the measurement of redshift-space distortions [113, 25]. When
mitigating astrophysical systematics, higher $R$ enables higher-fidelity line
separation, either by allowing finer application of anisotropic projection
effects [95, 96] or phase-space templates [114, 115], or by requiring less
volume to be excised when masking foreground lines [116, 117, 118]. Increasing
the spectral resolution of on-chip spectrometers requires development of new
low-loss dielectric materials.

  * •

Multiplexed Readout: Spectroscopic pixels require significantly more detectors
than their broadband counterparts; a 1000-spectrometer array with $R\sim 300$
would have a detector count approaching that of the entire CMB-S4 experiment.
Readout development will be essential to the success of future spectroscopic
instruments. New technologies based on state-of-the-art FPGA platforms, such
as the RF system-on-chip, promise to dramatically reduce overall readout costs
to $1–2 per channel [119].

  * •

Telescopes and Facilities: The science goals outlined above can all be
accomplished with 5–10 m class telescopes, with unobstructed optics optimized
for measurements of extended, low surface brightness emission and minimal
instrumental systematics. Several such facilities exist or will be built in
the next decade, including SPT, ACT, SO, CCAT-p, and CMB-S4 [120, 9, 121].
Reusing these telescopes for the LIM measurement represents a natural step
that would extend their lifetime in service of cosmological science similar to
CMB.

###  4.2 Analysis Techniques

Controlling astrophysical, instrumental, and modeling systematics will also be
critical for LIM cosmology. Investments in analysis techniques, which can be
validated by pathfinder experiments, will enable future surveys to take
advantage of the sensitivity enabled by hardware advances:

  * •

Astrophysical systematics: Both astrophysical continuum and spectral line
emission induce systematics in the LIM measurement. Continuum
foregrounds/backgrounds can be orders of magnitudes stronger than the signal
of interest [122]. However, they generally vary smoothly with frequency,
affecting modes at low spectral wavenumber (i.e., where $k_{\rm z}\sim 0$).
Furthermore, mm-wave continuum emission has been extensively studied at the
angular scales of interest by CMB experiments. Spectral line sources—typically
referred to as interlopers—are another potential source of systematics. This
is particularly true at mm-wave, where CO rotational transitions from a range
of redshifts could be present at any given frequency, along with other
potential lines [123, 117]. Mitigating interloper lines remains an active area
of research with several methods under investigation, including masking [116,
117, 118], leveraging differential effects in projection from angular/spectral
dimensions to physical space (i.e., the Alcock-Paczyński effect [124, 95,
96]), coherently removing power [114, 115], and using machine learning
techniques [125, 126]. Preliminary work suggests that these methods should be
highly effective in suppressing the effects and biases of interloper emission,
but more effort is needed, along with validation on data from pathfinder
experiments.

  * •

Instrumental systematics: Instrumental systematics can arise from a variety of
mechanisms, including calibration errors, detector gain variations, and
reflections in optics. Of particular concern are effects that induce
frequency-dependent structure on otherwise-smooth spectral response [127,
128]. At millimeter wavelengths the atmosphere presents an additional
challenge for ground-based experiments, since the telluric lines of ozone,
water, oxygen, and other chemical species could imprint frequency-dependent
structure in the data. Although these systematics are both site- and
instrument-specific, mm-wave LIM will benefit from observational techniques
developed by CMB experiments, in addition to strategies tested on pathfinder
instruments [87, 129].

  * •

Modeling systematics: Realizing LIM’s full potential requires accurate
theoretical models of the signal, matching the measurement sensitivity. Like
galaxy redshift surveys, this requires both state-of-the art numerical
simulations and analytical tools, the latter usually validated by the former.
Developments on both fronts are needed for LIM observables. On the analytic
side, existing models based on the halo-model framework [130, 131] require two
ingredients: relating the line intensity to DM halos, and relating the halo
properties to the underlying DM distribution. While the latter can be modeled
accurately using perturbative models of LSS, there are large uncertainties on
the former, primarily driven by lack of observational constraints [97, 132,
133, 134]. Ongoing and future LIM experiments [16, 135, 136, 137, 138, 139]
will inform this poorly-constrained theory space. The combination of
observational data and small-volume simulations of hydrodynamical galaxy
formation and radiative transfer can be used to construct “effective” models
of line luminosity, which are simple enough to be incorporated into semi-
analytic simulations (based on N-body simulations) over cosmological volumes,
and into analysis of future LIM data [140, 141, 142]. A consistent theoretical
framework for the line emission is needed to fully take advantage of multi-
line observational capability [3].

##  5 Conclusions

Line intensity mapping at millimeter wavelengths is a powerful tool for
testing fundamental physics and cosmology by measuring large-scale structure
over large volumes and at high redshift. Far-IR emission lines such as CO and
[CII] trace galaxies through most of the history of the Universe, and are
redshifted to the mm-wave atmospheric windows where they can be detected from
the ground. Observations from proven observing sites, mapping out the Universe
from $0<z<10$, could measure an order of magnitude more primordial modes than
contemporary galaxy surveys and provide transformational constraints on
numerous cosmological science cases, including inflation, dark energy, dark
matter, and neutrinos and relativistic species. To develop this new
observational technique, we recommend support for mm-wave LIM projects as they
transition from pathfinders to experiments with significant cosmological
constraining power. This transition will be enabled by investments in the
following technical areas:

  * •

Instrumentation: Development in mm-wave detectors, spectrometers, and readout
will significantly increase instantaneous sensitivity.

  * •

Analysis: Development of techniques to mitigate astrophysical, instrumental,
and modeling systematics will enable robust extraction of the cosmological
signal.

All of these efforts leverage decades of investment and experience from CMB
and LSS experiments in detector technology, facilities, observing strategy,
and analysis.

##  6 Acknowledgements

We thank Adam Anderson, José Luis Bernal, Matt Bradford, Clarence Chang,
Jacques Delabrouille, Dan Marrone, Gabriela Sato-Polito, Sara Simon, and
Michael Zemcov for helpful comments.

##  Appendix A Primordial Physics Figure of Merit

To quantify the information content of the LIM power spectrum in constraining
primordial physics, we calculate the primordial physics FoM as defined in [5].
We compute the linear matter power spectrum using the CLASS Boltzmann
code222https://github.com/lesgourg/class_public [143], and model the nonlinear
line power spectrum using redshift-space Eulerian perturbation theory at one-
loop level, including the effective field-theory terms and infrared
resummation, using the velocileptors package
333https://github.com/sfschen/velocileptors [144]. The line biases are
computed by assuming Sheth-Tormen halo biases and co-evolution predictions as
in [97]. We set the small-scale cut ($k_{\rm max}$) according to instrument
resolutions in the angular and line-of-sight directions, and further impose
the cutoff of $k_{\rm max}<1\ h{\rm Mpc}^{-1}$. The same large-scale cut is
set as in the parameter forecasts. Instrumental noise is computed as in [17],
and interlopers are accounted for as additional noise terms.

Figure 4: Primordial physics FoM as a function of maximum observed redshift,
for a survey with $\sim 4\times 10^{9}$ spectrometer-hours. The shaded blue
region is excluded by cosmic variance for a full-sky survey probing all six
lines. The solid (dashed) lines assume best- (worst-) scenario of perfect (no)
cleaning of interlopers. The red lines show the combined FoM.

Figure 4 shows the FoM as a function of maximum observed redshift for $\sim
4\times 10^{9}$ spectrometer-hours, for each individual line and their
combination. The solid and dashed lines correspond to including or neglecting
the interloper lines in the noise. The blue shaded region is the cosmic
variance limit for a full-sky survey. It is important to recognize that an
experiment’s constraining power cannot be fully condensed in a single FoM. For
instance, while the total FoM (in red) appears to saturate at high redshift,
access to the high-redshift regime is particularly powerful in breaking
parameter degeneracies, as illustrated by our parameter forecasts.

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