# Putting Together the CMB-S4 Science Book Requirements Table

The Concept Definition Task Force has been tasked with writing down science requirements, with three suggested levels (sky's the limit, minimum worth doing, something in between). John C. has, in turn, asked the Science Book chapter leads to create a summary table of requirements from the book. Below are notes and discussions for each Science Book "science goal" chapter (intro, CMB lensing, and analysis/sims/forecasting not included). Chapter leads are particularly encouraged to contribute material and collate into a final recommendation. As per John C.'s email (and the recommendation of Jo Dunkley and others to the CDT), there is also an "astrophysics chapter" included in the discussions.

## INFLATION

From Raphael:

Theorist’s dream: σ(r)=1×10−6

Aspirational goal: σ(r)=5×10−4

Minimal goal: σ(r)=1×10−3

Both are for a fiducial value of r = 0 and must include foreground removal and systematics.

From Tom C.:

I am only considering constraints on r (tensor-to-scalar ratio) here, as I think all other inflation science from S4 only adds marginally to the science case.

Sky's The Limit: sigma(r) = 5 x 10^{-4). This would result in a >5-sigma detection of Higgs or Starobinsky inflation or strongly rule out all but one of the classes of models discussed in the Science Book.

Minimum Worth Doing: sigma(r) = 1 x 10^{-3}. This is a factor of two better than the projected r constraint from the full BICEP/Keck program. It's also the default case in the Science Book. There's not much room between this and "sky's the limit," so I won't give an in-between case.

From John K.: I essentially agree with Raphael's numbers: sky's the limit σ(r)=1e-6, medium goal σ(r)=5e-4, minimum worth doing σ(r)=1e-3. I feel most strongly that the minimum worth doing for S4 should be set no worse than σ(r)=1e-3, since I think existing Stage 3 experiments are already on track to get with a factor of 3 of that, and it also aligns with theoretical benchmarks, as Tom says above. For the "sky's the limit" number I think we might want to discuss what we really mean by that...I can believe 1e-4 might be possible with a combination of the most ambitious version of a ground-based CMB program I can easily imagine, and good luck on foreground complexity. But strictly from the theory side, σ(r)=1e-6 is a reasonable thing to wish for, if one is going to go much beyond the medium goal.

I think we should also consider "confidence of detection" goals for scenarios where there is evidence for "r" at various levels above σ(r). For example, I'd suggest these should include: for 3x σ(r) high S/N component-separated B-mode maps, and additionally for 5x σ(r) replication of this evidence in several regions of sky, and additionally for 10x σ(r) some specification for characterizing the shape of the primordial BB angular spectrum.

From Jo D

High sigma(r)=0.0002 (5 sigma detection of 0.001)

Medium sigma(r)=0.001

Low sigma(r) = 0.002 (5 sigma detection of 0.01). I am not yet convinced that stage 3 are fully on track for a convincing detection at this level yet, given number of frequencies being fielded.

## NEUTRINOS

From Raphael:

Theorist’s dream: σ(\sum mν)=8meV

Aspirational goal: σ(\sum mν)=15meV

Minimal goal: σ(\sum mν)=20meV

Both are for a normal mass hierarchy with \sum mν = 58 meV, rely on the lensing power spectrum, and include a prior from DESI BAO measurements and assume an external measurement of the optical depth with σ(τ) = 0.006.

One area not covered by these requirements is cluster science. No clear targets were identified in the science book, but it is qualitatively clear that cluster science significantly benefits from higher resolution. For example at ”a 99% purity threshold, the 3, 2 and 1 arc- minute configurations would identify approximately 45,000, 70,000 and 140,000 clusters.” Furthermore, at 1 arcmin resolution one could begin to resolve clusters and study pressure profiles, learn about baryonic physics, etc. Clusters can also be used to constrain neutrino mass. To my knowledge sufficiently reliable forecasts for this do not exist.

From Tom C.:

I am only considering neutrino mass constraints here; N_eff constraints will go under Light Relics.

Assuming the S4 neutrino mass constraints come from CMB lensing only, the constraints are only weakly sensitive to the instrument noise and resolution and much more dependent on priors from external data sets (e.g., Science Book, Figures 15 and 16). Since we have no control over the galaxy survey data, the "external prior" that could influence S4 design is optical depth (tau). Whether S4 gets an independent constraint on tau is the main difference between "sky's the limit" and anything else for neutrinos.

Sky's The Limit: sigma(\summnu) = 15 meV (4-sigma detection of minimum neutrino mass). No extant tau constraint will get us this, so this scenario requires S4 to be statistics-limited (not dominated by systematics) down to \ell = 10 (e.g., Allison et al. arXiv:1509.07471). Note this still requires combination with DESI BAO.

Minimum Worth Doing: sigma(\summnu) = 30 meV (2-sigma detection of minimum neutrino mass). Can do this with current Planck tau constraint and 5uK-arcmin / 5 arcmin beam (Science Book, Figure 15). Note this requires DESI BAO and is little if any improvement over DESI BAO alone.

Something In Between: Baseline S4 design (~1 uK-arcmin, < 3-arcmin beams) gives sigma(\summnu) = 26 meV with Planck tau and DESI BAO.

From Jo D

High: 5 sigma detection of minimum mass, sigma(mnu)=0.012 (including e.g. BAO data)

Medium: 3 sigma measurement of minimum mass, sigma(mnu)=0.02

Low: 2 sigma measurement of minimum mass, sigma(mnu)=0.03

## LIGHT RELICS

From Raphael:

Theorist's dream: σ(Neff)=0.005

Aspirational goal: σ(Neff)=0.027

Minimal goal: σ(Neff)=0.035

Some of these goals involve other data sets. It might be a natural to convert these requirements to map-level requirements on noise-levels, foreground residuals, and systematics.

From Tom C.:

Sky's The Limit: sigma(N_eff) = 0.013, giving a 2-sigma detection of any light particle that was ever in equilibrium with the Standard Model. This requires something like 0.5 uK-arcmin over 80% of the sky out to \ell=5000 in temperature (Science Book, Figure 24).

Minimum Worth Doing: sigma(N_eff) = 0.05, giving 1-sigma evidence for light scalars that were ever in equilibrium with the Standard Model.

Something In Between: Baseline S4 design (~1 uK-arcmin, < 3-arcmin beams, 40% of the sky) gives sigma(N_eff) ~= 0.03-0.04.

From Jo D

High: sigma(Neff)=0.0009, 3 sigma measurement of 0.027, 1 extra boson

Medium: sigma(Neff)=0.03, in between

Low: sigma(Neff)=0.054, 3 sigma measurement of 0.162, prediction of 3 extra families of fermions

(I don't think it is worth talking about targeting 1-sigma measurements. 1-sigma will not tell us anything)

## DARK ENERGY

From Tom C.:

If we assume the Dark Energy / Modified Gravity constraints come from CMB lensing only, then the constraints are weakly dependent on noise and beam. If we include the tSZ and kSZ constraints and CMB-lensing-based cluster mass measurements, resolution becomes very important.

Sky's The Limit: A <0.2% constraint on GR at z~0.5 from pairwise kSZ, >10,000 clusters at z>1 from tSZ, a 2% constraint on the mean mass of every 1000-cluster stack from CMB-cluster lensing. This requires ~1uK-arcmin noise and 1 arcmin beams.

Minimum Worth Doing: At least get the nominal DE constraints from combining CMB lensing and cosmic shear (Science Book, Figure 38). This requires a few uK-arcmin noise over 40% of the sky and <5-arcmin beams.

Something In Between: 1 uK-arcmin noise and < 3-arcmin beams gives a ~0.5% constraint from pairwise kSZ, >~1000 clusters at z>1, and a <~4% constraint on the mean mass of a 1000-cluster stack.

Jo D

Significant improvement on w0-wa, and/or w(z) at z=1-2, and/or growth function, compare to what DESI+LSST can achieve. E.g. Medium = 0.5% measurement of growth function.

I think we need to do some more forecasting work to determine what these targets are.

## DARK MATTER

From Tom C.:

The most clearly stateable DM science goal is detecting DM annihilation in the CMB power spectra, and this is weakly dependent on noise and beam and most strongly dependent on sky fraction (Science Book, Figure 32).

'From Jo D'

High: p_ann < 0.5e-7 m3/s/kg (we'd like to do better, but this is CV limit)

Medium: p_ann<0.9

Low: p_ann< 1.5

I don't think this is a strong science driver

## ASTROPHYSICS

From Raphael:

One area not covered by these requirements is cluster science. No clear targets were identified in the science book, but it is qualitatively clear that cluster science significantly benefits from higher resolution. For example at ”a 99% purity threshold, the 3, 2 and 1 arc- minute configurations would identify approximately 45,000, 70,000 and 140,000 clusters.” Furthermore, at 1 arcmin resolution one could begin to resolve clusters and study pressure profiles, learn about baryonic physics, etc. Clusters can also be used to constrain neutrino mass. To my knowledge sufficiently reliable forecasts for this do not exist.

From Jo D [Using some numbers from Nick B and David S]

Tau High: sigma(tau)=0.0002 Low: sigma(tau)=0.0005 I don't think we can do this from the ground, but we should track CLASS's success

Delta-z Medium: sigma(deltaz) = 0.1 More work needed to understand how well this will be measured by 21cm, i.e. how competitive our kSZ measurement could be

Cluster feedback efficiency: <1% Cluster non-thermal pressure support: <1%

These last two will significantly improve our ability to model non-linear baryonic effects. This will connect directly to how well we can recover dark energy parameters from the LSST WL survey. Reaching mass limits of 1e14 in the cluster catalog will also be good target to remove non-linear clusters from LSS surveys sufficiently to recover the small-scale WL information content. More studies would be useful here.