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Robust forecasts on fundamental physics from the foreground-obscured, gravitationally-lensed CMB polarization

These forecasts are based on the framework developed in This formalism first performs a Fisher estimate of a given experimental configuration (sky fraction, frequencies, bandwidths, white noise levels and beams) to clean foregrounds (one- or two-component dust and synchrotron) from the CMB using a parametric maximum-likelihood method. Here, we take cleaning foregrounds to constitute estimating their spectral indices. The residual foregrounds and increased CMB noise level are propagated self-consistently to a delensing forecast (EBEB [iterative or otherwise], CMBxCIB or CMBxLSS); the resulting delensing residuals and lensing deflection noise are propagated to a standard CMB parameter Fisher code in which we marginalize over the amplitude and multipole dependence of any remaining foreground residuals. This formalism can combine pairs of experiments with different sky coverage, and can constrain numerous extensions to the standard model, namely M_\nu, N_{\rm eff}, \Omega_k, r, n_t, \alpha_s, Y_{\rm He}, w_0 and w_a. A schematic of the formalism is plotted below.

Schematic forecast.png

A web interface to the code is available on NERSC: The tool allows you to look at specific instrumental configurations (sensitivities, frequencies, bandpasses, FWHM), choose dust and synchrotron spectral indices, sky components, delensing options (CMBxCMB, CMBxCIB), marginalization for cosmological constraints, and many other options. A NERSC account tied to the mp107 user group is needed, but is simple to obtain.

I. Forecast on inflation: \sigma(r)

These forecasts are based on the optimized experimental configurations provided by Victor Buza here. In summary, there are six configurations, assuming three values of f_{\rm sky} (0.01, 0.05 and 0.1) and two values of r (0 and 0.01). The experiment is broken down into a multi-frequency "degree-scale" effort aimed at cleaning foregrounds and a single-frequency (assumed 145 GHz, 1' FHWM) "arcmin-scale" effort aimed at delensing; both efforts are assumed to have access to a multipole range of 30 \le \ell \le 4000. We combine all of these bands together and pass to our component-separation, delensing and Fisher formalism, assuming dust and synchrotron are present and using iterative CMB EBEB delensing (we can also provide constraints for no/CIB/LSS delensing). We perform the same procedure for Planck (we don't use the WMAP channels), and combine the two Fisher matrices together. We assume a simple \LambdaCDM+r model, and constrain it using T, E, B and d information.

f_{\rm sky} = 0.01 f_{\rm sky} = 0.05 f_{\rm sky} = 0.1
\sigma(r=0) \times 10^{-4} 5.50 6.65 6.81
\sigma(r=0.01) \times 10^{-3} 1.73 1.24 1.12

Clearly we have more optimistic results than Victor. This may be because we're using polarization noise levels rather than temperature [updated numbers now assume temperature noise values were quoted]; we also consider fewer foreground parameters than Victor does. There could also be differences in the way we're delensing. A further possibility is that we are using different foreground inputs: our foreground templates are extrapolated from Planck results, which specify the amplitude of the dust power in the cleanest 24, 33, 42, 53, 63 and 72% of the sky. As a result, the level of the foregrounds changes with f_{\rm sky}. Essentially, we should discuss!


I have corrected our noise values to reflect the fact that they're polarisation rather than temperature. I have also modified our code to allow for a pure delensing channel. This channel is not used for foreground cleaning or parameter constraints: it is solely used to delens the B mode (and measure the lensing deflection). It is, however, affected by component separation: I assume that the noise in this channel is boosted, and include foreground residuals. I obtain the following results with (without) iterative EBEB delensing.

f_{\rm sky} = 0.01 f_{\rm sky} = 0.05 f_{\rm sky} = 0.1
\sigma(r=0) \times 10^{-4} 10.4 (34.4) 6.99 (16.5) 6.26 (12.3)
\sigma(r=0.01) \times 10^{-3}

I'll fill in the r=0.01 values ASAP, but immediately we can see some interesting behaviour, notably that we see f_{\rm sky} as having the opposite effect on our constraints. This is something like the results we expect with fixed \ell_{\rm min} and no delensing. I'm wondering therefore exactly how delensing is performed in Victor's code. In particular, is the noise in the delensing channel boosted to reflect the effects of component separation?

UPDATED RESULTS (31/05/2016):

I have updated our code to allow for the case in which the dedicated delensing channel can be used “raw”, i.e., without boosting the noise or including foreground residuals. In this case, we obtain the following results for the 1% f_{\rm sky} experiment with r = 0 (apologies for the formatting, I don't have time to make this prettier!).

siv_fc_r_0_fsky_0.01 x Planck | del: CMBxCMB | components: sync+dust
>>> marginalized $\sigma$( r = 0.0 ) = 0.000937807170105

Note that the constraints have hardly changed from the case in which the delensing channel has been cleaned assuming the same penalties as cleaning the degree-scale experiment. This implies that the results tabulated above are not limited by noise (or indeed foreground residuals), but something else.

I’ve therefore had a look into the effects of \ell_{\rm min}, as it's the only other thing to have changed. I’ve been assuming that multipoles in the range 300--4000 are available for delensing. If instead I assume \ell_{\rm min} = 200, I see the following, where I’ve now compiled results for all three of Victor's experimental configurations.

siv_fc_r_0_fsky_0.01 x Planck | del: CMBxCMB | components: sync+dust
>>> marginalized $\sigma$( r = 0.0 ) = 0.000618893367485
siv_fc_r_0_fsky_0.05 x Planck | del: CMBxCMB | components: sync+dust
>>> marginalized $\sigma$( r = 0.0 ) = 0.000492305638963
siv_fc_r_0_fsky_0.1 x Planck | del: CMBxCMB | components: sync+dust
>>> marginalized $\sigma$( r = 0.0 ) = 0.000490317485246

Note the improvement, especially in the 1% f_{\rm sky} case. The trend with f_{\rm sky} is still inverted with respect to Victor’s, but the dependence is shallower.

If I drop \ell_{\rm min} to 30, the f_{\rm sky} relation flips to that expected when delensing is efficient: see below. I am, however, consistently a factor of around 2.6 more optimistic than Victor.

siv_fc_r_0_fsky_0.01 x Planck | del: CMBxCMB | components: sync+dust
>>> marginalized $\sigma$( r = 0.0 ) = 0.000218912039016
siv_fc_r_0_fsky_0.05 x Planck | del: CMBxCMB | components: sync+dust
>>> marginalized $\sigma$( r = 0.0 ) = 0.00030512915036
siv_fc_r_0_fsky_0.1 x Planck | del: CMBxCMB | components: sync+dust
>>> marginalized $\sigma$( r = 0.0 ) = 0.000358516699929

This dependence of delensing efficiency on \ell_{\rm min} makes sense, as we need access to patches of size ~2 degrees to be able to measure their coherent arc-minute deflections. I’ve made a plot of delensing residuals vs \ell_{\rm min} that might prove helpful. This assumes a single one-arcmin-resolution delensing channel with polarisation noise per beam-sized pixel of 0.38 muK (as per Victor’s r=0, f_{\rm sky} = 1% experiment), and clearly shows the requirement for measuring large/intermediate-scale polarisation modes.

Siv delensing vs ell min.png

II. Forecast on other cosmological parameters  \sigma( \Sigma m_\nu), \sigma( N_{eff}), \sigma( \alpha_s) & \sigma( \Omega_K)

We derive here results which aim at being compared to Erminia’s forecasts: Some discrepancies might appear due to different assumptions, priors, polarized vs. total intensity sensitivity, etc.

We look at the variation of cosmological constraints (neutrino mass, Neff, running and curvature) as a function of polarized sensitivity or resolution. We combine the one-channel CMB-S4 with Planck and/or DESI BAO measurements. Results are summarized in this figures below, which can also be downloaded as the following presentation

5/27/2016 update: use the same assumptions for Planck as described in this page:

IIa. Neutrinos

Neff Mnu vs uK arcmin updated planck v05272016.png

Neff Mnu vs uK FWHM updated planck v05272016.png

IIb. Curvature & Running

OmK alphas vs uK arcmin updated planck v05272016.png

OmK alphas vs FWHM updated planck v05272016.png