This is a simple posting in which I put up for discussion some plots for Chapter 2 of the S4 Science Book. There are two new types of plots: \(r-n_s\) and \(r-n_t\), and two old types of plots: "\(\sigma_r\) vs Effort" and "\(\sigma_r\) vs \(f_{sky}\)," which have been updated to include decorrelation, and to have an extra panel depicting the "fraction rms of the lensing residual" and "the fraction of total effort going towards delensing."

For this plot, I assume that the \(n_s\) constraint comes from \(TT, TE, EE\) and the \(r\) constraint comes from \(BB\). Under this assumption, I can take the \(\sigma_{n_s}\) achieved by the large survey, and the \(\sigma_r\) achieved by the small survey, and form a perfectly non-degenerate ellipse. For the large survey, I was guided by this posting, and picked \(n_s=0.9655\) and \(\sigma_{n_s}=0.002\). For the small survey, I was guided by the decorrelation section of this posting, and picked \(r=[0,0.01]\) and the minima \(\sigma_r=[0.00075, 0.00159]\) for \(f_{sky}=[0.01, 0.10]\).

In this section, I extend our model to include \(n_t\) as a parameter. I run CAMB with the same Cosmology as before (w/ \(n_t=0\)), but now pick the pivot scale -- \(k_t\) to break the \(r-n_t\) degeneracy, and calculate \(\frac{\partial C_l^{BB}}{\partial n_t}\) for the extra dimension in the Fisher Matrix. The two cases I consider are \(r=0.01\) and \(r=0.10\), though the second one is mostly out of curiosity. Both cases are using the \(r=0.01\) optimized distribution, and an \(f_{sky}=0.1\), meaning that the \(r=0.10\) is quite non-optimal.

Some literature I found making \(n_t\) forecasts:

- Robust forecasts on fundamental physics from the foreground-obscured, gravitationally-lensed CMB polarization
- Forecasting sensitivity on tilt of power spectrum of primordial gravitational waves after Planck satellite
- How much can we learn about the physics of inflation?