# Neutrino Mass WG Telecon

## October 10

• Review of draft of neutrino mass section of DSR

## Call 4 - September 18

• Introductions from new members of the group (and plans for contributions)
• Updates on the consistency between forecasts from different groups -- please post results and updates to the wiki
• Discussion of neutrino mass scheme (Martina)

• Updates on choice for the neutrino mass scheme (Martina writing)

The 1massive+2massless (1massive hereafter) mass scheme is a good approximation to the normal hierarchy (NH). Correct for Mnu=0.06eV, less correct for Mnu>0.06eV. From File:Nu mass frac.pdf, you see that the mass fractions fnu become comparable already for mlight>~5e-3eV for NH. The corresponding value of mnu is Mnu>~0.065eV (see blue line in File:S4 mnu.pdf, where it is also clear that mlight(Mnu) is a rapidly varying function of Mnu for the values of Mnu under consideration for S4). Therefore, for Mnu>0.06eV, the degenerate scheme is a better approximation to NH. Plot3: ratio of matter power spectra at fixed Mnu and different mass schemes. Solid is degenerate/NH, dashed is 1massive/NH. A similar plot can be found in Lesgourgues et al

This is also clear if one looks at how comsological observables compare in different mass schemes. Plot3 shows the ratio between the matter power spectrum computed with 1massive or degenerate approximation and the matter power spectrum computed with exact NH, for different values of mnu. For Mnu=0.06eV, 1massive is a better proxy. For Mnu>0.06eV, 1massive progressively fails in approximating the exact scenario. In contrast, the degenerate scheme is progressively closer to NH, as one might expect (fnu,i->1/3 for Mnu>0.06eV). The physical reason is based on the fact that the free-streaming length, and the corresponding power suppression, depends on the individual neutrino masses. Plot4: posterior probability for Mnu for different mass schemes. Fiducial model: Mnu=0.06eV, NH.

Although the differences are very small (permille effects), they might affect parameter estimation. Plot4 shows the posterior probability on mnu obtained for a S4-like survey in 3 cases: 1massive, degenerate and NH. The fiducial model is always Mnu=0.06eV with exact NH. The main messages are the following:

• degenerate is a fairly good approximation to the exact NH;
• 1massive systematically biases low the posterior distribution (both shifting the peak of the distribution and under-estimating the variance). One can naively gauge this effect by looking at Plot3: imagine you want to reproduce the purple dashed curve starting from the purple solid curve and using the degenerate scheme. The only way to get closer to the dashed curve is to increase the total mass and going from the purple solid to the green solid, then to the blue solid etc…In your analysis, this means that to obtain the same physical effects on cosmological probes you have to sample higher values of mnu, therefore you get the difference in the posteriors shown by Plot4.

For comparison, the 1sigma c.l. are:

• exact NH: [0.059-0.120]eV
• degenerate: Mnu=0.078(+0.038)(-0.056)eV
• 1massive: Mnu=0.061(+0.032)(-0.041)eV

Similar results holds for currently available data as well, see e.g. Giusarma et al

## Call 3 - August 28

Updates on forecasting efforts - questions on efforts

Plots for S4 meeting

• (Joel) Update on lensing-derived neutrino mass with non-white noise (atmosphere and point sources) with Planck co-added and included for low-ell and extra sky coverage, including DESI BAO. All numbers are 1-σ constraints on Mnu in units of meV. Lensed spectra including lensing-induced non-Gaussian covariances were used. (Updated 9-18-2018 to fix bug with noise, all constraints shift by 0 or 1 meV)
σ(τ) = 0.001 σ(τ) = 0.002 σ(τ) = 0.003 σ(τ) = 0.004 σ(τ) = 0.005 σ(τ) = 0.006 σ(τ) = 0.007 σ(τ) = 0.008 σ(τ) = 0.009 σ(τ) = 0.010
S4 Noise 13 14 16 18 20 22 24 26 28 29
S4 Noise / 4 12 13 15 17 19 21 23 25 27 28
S4 Noise / 2 12 14 15 17 20 22 24 25 27 29
S4 Noise * 2 13 14 16 18 20 23 24 26 28 30

Same as above, but with current BAO rather than DESI (taken from File:Bao desi.pdf)

σ(τ) = 0.001 σ(τ) = 0.002 σ(τ) = 0.003 σ(τ) = 0.004 σ(τ) = 0.005 σ(τ) = 0.006 σ(τ) = 0.007 σ(τ) = 0.008 σ(τ) = 0.009 σ(τ) = 0.010
S4 Noise 35 36 38 39 42 44 46 49 51 53
S4 Noise / 4 34 35 37 39 41 43 45 48 50 52
S4 Noise / 2 35 36 37 39 41 43 46 48 51 53
S4 Noise * 2 36 37 38 40 42 44 47 49 51 54

Same as above, but no BAO

σ(τ) = 0.001 σ(τ) = 0.002 σ(τ) = 0.003 σ(τ) = 0.004 σ(τ) = 0.005 σ(τ) = 0.006 σ(τ) = 0.007 σ(τ) = 0.008 σ(τ) = 0.009 σ(τ) = 0.010
S4 Noise 49 50 52 55 58 61 64 68 72 75
S4 Noise / 4 46 48 50 52 55 58 62 66 70 73
S4 Noise / 2 48 49 51 53 56 60 63 67 70 74
S4 Noise * 2 51 52 54 56 59 62 66 69 73 77

CMB-S4 with atmospheric noise, co-added with Planck, with point sources, and lensing reconstruction noise available here (Updated 9-10-2018 to fix bug): File:CMB S4 noise coadd.txt

## Call 2 - August 23

Agenda for call:

- Theory/pheno discussion: how can science book treatment be improved / added to but also shortened? https://arxiv.org/pdf/1610.02743.pdf

- Forecasting: any updates or questions?

- Plans for meeting slides.

## Call 1

Agenda for call:

0) general charge

1) discussion of plan

2) feedback?

3) volunteers for forecasting

Input for forecasts (will later have a link from Tom Crawford that will be maintained with up-to-date info):

• This is the link. For now it basically says what is stated below, but it will be updated if/when things change.

As a starting point for forecasts, for the large aperture wide-field survey let's go with the numbers from the CDT (Table 1 from https://www.nsf.gov/mps/ast/aaac/cmb_s4/report/CMBS4_final_report_NL.pdf). For the small-area (r-focused) survey, things are not quite settled.

That means (via Tom Crawford and Matt Hasselfield): area of sky: 40% of the full sky frequencies: 40 90 150 220 270 map depths (T, in units of uK-arcmin): 5.6 1.35 1.81 9.1 17.1 [assumed detector effort in physical det-yrs]: 24268 349455 349455 124251 124251

For beams, baseline would be to assume a diffraction-limited 6m telescope. To be concrete, let's say a 1.4' beam at 150 GHz that then scales as (1/freq).

To include the effects of atmosphere and 1/f, the recommendation is to use the ell scaling at https://cmb-s4.org/CMB-S4workshops/index.php/Update_on_Neff_Forecasts. That means putting in a knee at ell=3400 in TT and at 340 in EE (and presumably BB):

NlTT= N0TT(1+ (l /3400)-4.7)

NlEE= N0EE(1+ (l /340)-4.7)

Neutrino Mass Analysis Working Group Plan Through December 2018

Outline of Science Chapter

To be modeled off of the Science Book chapter, with updates and some new ingredients

• Brief Intro
• CMB Lensing / forecasting
```    Goals:
```
```   -Add updates with new noise levels
```
```   -What can we say about CMB lensing vs RSD, weak lensing, Lyman-alpha, cluster abundance?
```
```   -Add discussion of systematics and why the measurement should be robust
```
```   -Expand on tau limitation. What you actually need to know about foregrounds and noise given the tau limits. Options for improving tau?
```
```   -Discuss model independence with cross-correlations
```
```   -Discuss influence of priors on conclusions about hierarchy, mass scale
```
• Additional CMB - S4 probes
```    Goals:
```
```   - Add cluster based forecasts, add cross-correlation based forecasts
```
• S4 constraints in context with lab experiments and neutrino model-building
```   Goals:
```
```   -Include input from neutrino phenomenologists and experimentalists
```
```   -Potentially add: updates regarding Miniboone results? Updates regarding stronger hints of Normal Hierarchy or delta?
```
```   -Detection scenarios: expand on Section 3.5 and Table 3-2 in Science Book
```
```   -Discussion of how Mnu constraints inform model building
```

To-do before September Meeting:

-Preliminary forecasts on neutrino mass for each key observable

-Have conclusions in hand OR identify specific outstanding issues for what we can say about CMB lensing vs other methods

-Tau limitation and prospects for improvement

-Impact of priors

-Summary of content for context with lab experiments / model-building for comments

To-do by November:

-Draft of chapter available for circulation