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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)

ns_vs_fsky.png

  • 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)
    • The peaks fading out should not matter. It is the overall tilt of the spectrum
  • 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.

Next: Run

  1. a noiseless case
  2. an extremely low noise case 1e-5 uK-arcmin, so that beam contribution will be present in N_ell = noise^2 exp (ell(ell+1)*beam^2/8log2)

Compare noiseless/1e-5uK-arcmin/1uK-arcmin cases

ns_vs_fsky_noiseless_vs_1uk.png

  • The 1e-5uK-arcmin lines completely overlaps with the noiseless case (see next section for explanation)
  • The 1uK-arcmin case with lmax = 4000, 10000, 24700 all overlap with the lmax=4000 case with noiseless/1e-5uK-arcmin case

Beam cross-over

At 1 uK-arcmin, the cross-over of the noise due to beam with the EE spectrum is around ell~3000-4000. To make even higher ell measurements of the EE spectrum sensitive to the tilt of the spectrum. One needs to push the noise level lower.

beam_spectrum_lownoise_withEEsansprefactor.png

References

-- Kimmy Wu - 2016-01-21

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PNGpng beam_spectrum_lownoise_withEEsansprefactor.png r1 manage 51.3 K 2016-01-22 - 14:02 KimmyWu  
PNGpng ns_vs_fsky.png r1 manage 59.5 K 2016-01-21 - 11:57 KimmyWu  
PNGpng ns_vs_fsky_noiseless_vs_1uk.png r1 manage 100.6 K 2016-01-22 - 14:50 KimmyWu  
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