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n_s constraints from 30m telescope


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)
    • 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


  • 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.



-- Kimmy Wu - 2016-01-21

Topic attachments
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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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Topic revision: r2 - 2016-01-22 - KimmyWu
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