n_s constraints from 30m telescope
Background
Questions to be answered:
- If we have a 30m telescope geared with a polarization sensitive receiver at Advanced ACTPol sensitivity (7-8 uK-arcmin at 90/150GHz, from arXiv: 1510.02809), we can measure really high ell E-modes. Does that improve the constraints on n_s?
Big picture:
- For the Starobinsky model (R^2 inflation) on fig. 12 of the Planck 2015 Constraints on Inflation paper (arXiv: 1502.0211), aside from further constraining r, tightening the n_s constraint will be more effective in ruling it out in the near future before constraints on r gets below 1e-3.
- So the question is, how quickly would measuring more high ell E-modes tighten the constraint on n_s?
Current constraints on n_s
From Planck's 2015 XIII. Cosmological parameters (arXiv: 1502.01589), XI. CMB power spectra, likelihoods, and robustness of parameters (arXiv: 1507.02704), and Planck's 2013 XVI Cosmological parameters paper ((arXiv: 1303.5076), the basic 6-parameter LCDM constraints are:
parameter |
Planck TT + lowP |
Planck TT+TE+EE+lowP |
Planck TT only (2013) |
ombh2 |
0.02222 ± 0.00023 |
0.02225 ± 0.00016 |
0.02207 ± 0.00033 |
omch2 |
0.1197 ± 0.0022 |
0.1198 ± 0.0015 |
0.1196 ± 0.0031 |
100theta |
1.04085 ± 0.00047 |
1.04077 ± 0.00032 |
1.04132 ± 0.00068 |
tau |
0.078 ± 0.019 |
0.079 ± 0.017 |
0.097 ± 0.038 |
ln(1e10 A_s) |
3.089 ± 0.036 |
3.094 ± 0.034 |
3.103 ± 0.072 |
n_s |
0.9655 ± 0.0062 |
0.9645 ± 0.0049 |
0.9616 ± 0.0094 |
|
H_0 |
67.31 ± 0.96 |
67.27 ± 0.66 |
67.4 ± 1.4 |
I added the row for H_0 because I use H_0 instead of 100*theta in my fisher code.
Cosmology and Inputs for the forecast
fiducial cosmology:
The fiducial cosmology I use in this forecast based on the LCDM best fit from Planck's 2013 XVI cosmological parameter (arXiv: 1303.5076) as listed in the last column in the previous section. In addition, I assume a minimal neutrino mass of ~60meV (and r = 0)
Inputs for the 30m telescope:
- Beam = 0.33' ( 1 deg is about ell~200, lmax*0.33 = 200*60, lmax~36000)
- Polarization noise (T noise is 1/sqrt(2) of this): 1, 3, 7.5, 10 uK-arcmin
- lmaxEE = 4000, 10000, 20000; stepping through to see how much of a difference lmax makes
- fsky = 0.0125, 0.125, 0.5; 0.0125 is 500 sq deg.
- lmaxTT = 3000; any higher is contaminated by foregrounds
- lmin various with fsky
- use only the TT, TE, and EE lensed spectra -- not using phi (C^dd)
Planck prior inputs:
- For the fsky = 500 sq deg, sample variance degrades the constraints by a significant amount, it is essential to have some large area survey prior (e.g. Planck)
- We take the lower foreground freqs (100, 143, 217 GHz)
- noise (T) = [6.8,6.0,13.1] uK-arcmin
- noise (P) = [10.9,11.4,26.7] uK-arcmin
- beam = [ 9.5,7.1,5.0] arcmin
- lmax = 2500
- lmin = 30
- fsky = I tweak the fsky input so that the TT only constraints match the 2013 parameter constraints and the TT/TE/EE constraints match the 2015 parameter constraints to within about 10%; and fsky = 0.12
sigma(n_s) vs fsky using lensed TT/TE/EE (no delensing)
- the solid lines are without Planck priors; the points at fsky=0.0125 has Planck prior
- practically no difference going from ell=4000 to ell=20000. Perhaps expected given how smooth the peaks are beyond the 9th peak at ell~3000 (see e.g. fig 5 of SPTpol 100 sq deg EE spectrum paper arXiv: 1411.1042)
- Also, sensitivity isn't a big driver. A 10uK-arcmin experiment is almost as good as a 1uK-arcmin experiment. Also expected because E-modes are much brighter.
- The improvement of adding high ell EE over the Planck prior for the fsky=0.0125 case is about 7%
parameter | Planck prior alone (TT+TE+EE) | Planck + 10uK-am, lmax=4000 | Planck + 10uK-am, lmax=10000 |
sigma(n_s) | 0.0051 | 0.00474 | 0.00474 |
Next: one would expect that the peaks to be sharper in its unlensed (de-lensed) state. So perhaps one can extract more information/tighter constraints on n_s after delensing the E-modes. The ideal case would be fully delensed T and E-modes, i.e. with unlensed TT, TE, and EE. This will be the best case scenario on n_s constraint given CMB TT/TE/EE spectra.
sigma(n_s) vs fsky using unlensed TT/TE/EE
References
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Kimmy Wu - 2016-01-21
Topic revision: r1 - 2016-01-21
- KimmyWu