CosmoCoffee

Anze Slosar · Posted: April 20 2014

I am having arguments with some colleagues of mine about the following:

To me, the fact that ExB and TxB are (mostly) consistent with zero is a good argument in favour of BICEP2 seeing primordial fluctuations rather than foregrounds. One would expect that a generic foreground would push roughly the same amount of power into all cross-correlations. However, some people insist that ExB=0 by construction because of this paragraph:

Antony Lewis · Posted: April 22 2014

I think I would agree that if they've just changed a constant rotation angle by a degree, that will not significantly change any foreground argument at low L - as they say it doesn't have a big affect at L~100 anyway where most of their interesting signal is.

However I think having TB and EB consistent with zero is a pretty weak check - T must be dominated by primordial CMB temperature so the sensitivity to a small foreground contamination in T must be small compared to cosmic variance from the primary signal and their B noise (might be more interesting if they correlated their B with high- and low-frequency T from Planck in the same patch of sky with CMB projected out -did they try that?). Likewise even for E: If we assume as an extreme case that observed E is

E o = E + f

, and observed

B o = f

, so $\langle E_o B_o\rangle= \langle ff\rangle= C_f$ , the number of sigmas at which you could expect to see the EB in the null hypothesis of zero B is something like
$\sigma \sim \sqrt{\frac{n C_f^2}{C_E N}}$
where

n

is the number of modes observed and

N

the (lensing+) noise power. If O(f)~O(E)/6 is the case you are trying to check against (where all the excess B is foregrounds), then

C f

~

C E / 36

, so for

N

~

C E / 100

you'd need at least 50 modes to be able to tell at

σ > 2

. I don't think they say exactly how many modes they have, but for L~100 with 2% of the sky, it's not much bigger than 50 (and certainly not per L bin), and this was a very extreme back-of-the-envelope toy case (if I did it right).

Anze Slosar · Posted: April 23 2014

I see, I didn't appreciate just how much more power there is in EE. BB at ell=100 is something like 0.015+−0.003, while EB point there is around 0.01+−0.01. Averaged over all bins, you might actually get a better competitive error, but then there is this 2sigma point at l=50. Thanks.