# Difference between revisions of "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.

## 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.

## 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.

## 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.

## 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).

## 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.