- 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?

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.

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

- 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**

- a noiseless case
- 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)

- 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

- Starobinsky model:
- Linde, Inflationary Cosmology after Planck 2013?

I | Attachment | History | Action | Size | Date | Who | Comment |
---|---|---|---|---|---|---|---|

png | beam_spectrum_lownoise_withEEsansprefactor.png | r1 | manage | 51.3 K | 2016-01-22 - 14:02 | KimmyWu | |

png | ns_vs_fsky.png | r1 | manage | 59.5 K | 2016-01-21 - 11:57 | KimmyWu | |

png | ns_vs_fsky_noiseless_vs_1uk.png | r1 | manage | 100.6 K | 2016-01-22 - 14:50 | KimmyWu |

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