NonGaussianities

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Tensor non-Gaussianities

Forecasting observational limits for a CMBS-4 type experiment for non-Gaussianities associated with sourced of the form  \langle h\zeta\zeta\rangle . We use correlations of the form \langle BTT\rangle,  \langle BTE\rangle and  \langle BEE \rangle . Some notes can be found here :File:CMBS4 hss.pdf.

DeltaFNL equilateral local2.jpg

The main result is shown in the Figure on the left. We show the error bar  f_{\rm NL} ,  \sigma(f_{\rm NL}^{h\zeta\zeta}) for various values of the maximum multipole in temperature  \ell_{\rm max}^T . In a recent paper (1603.02243), we considered the shape predicted by single field slow-roll inflation. Here we took a more general approach, taking the symmetrized shapes for local and equilateral non-Gaussianities as defined for scalar bispectra (see notes File:CMBS4 hss.pdf). The bound on equilateral non-Gaussianities is reached when the B-modes have decayed; after this no equilateral triangles can be measured. The local type does not have this problem since the signal comes from configurations that have a large B-mode correlate with small T-modes. We expect this shape to be constrained better as we increase the maximum multipole in temperature (while keeping the B-mode multipole fixed to a max. Fig. 5 in our power shows that all power comes from  \ell^B < 100 ).

Plot on the left is assuming (for the colored lines) a noise dominated B-mode. The gray bands shows what happens if we detect r at some level through BB.

Interesting observation is that the error bar on equilateral up  \ell_{\rm max}^T \sim 500 is only 5 times as high as that of local type NGs. This can be compared to current bounds on equilateral which have  \sigma(f_{\rm NL}^{\rm equal}) and  \sigma(f_{\rm NL}^{\rm local}) \sim 5 . So for TTT, the ratio is more like 10, as opposed to 5. Not sure why (maybe limitations of the code as well as noise modeling?). Most likely explanation would be the additional power at low  \ell for local type NGs.

Putting numbers into context, in order to measure e.g.  r through the BTT correlation function, we need a coupling that is about a factor >10 times as large as predicted by SFSR (i.e.  \sqrt{r} ). This is very crude, and should be made more explicit. It also depends on whether the signal is in the local limit or in the equilateral limit (as the figure shows).

Things to do:

- On request (Raphael): forecasts for TTT (running, should be done next week).

- Carefully check normalization of local and equilateral shapes with scalar equivalent.

- Current analysis is based on flat sky, with  \ell_{\rm min} = 10 . Should check if it is actually accurate all the way down to this low l. Otherwise, consider same  \ell_{\rm min} as done for power spectra (i.e. 30).

- Other shapes: again, for sake of comparison, e.g. orthogonal, folded.

- Nose modeling: very simple right now. Just white noise (see arXiv 1603.02243).

- Science case: what models? Massive higher order spin fields (see e.g. arXiv 1503.08043 and upcoming work by Creminelli et al and Hayden, Pimentel and Baumann ).

- Extend to BTE and BEE.

- Include parity violating models.


Other possible things (these can be publications by themselves)

- Foregrounds. These are not included in this simple forecast. Dust? What shape? Can it be cleaned by choosing the right estimator?

- CMB map making to predict error bars on  f_{\rm NL} correctly (see e.g. arXiv 0711.4933 for scalars)

- Other sources, e.g. lensing. Do they contribute to the signal? What shape?