Speaker
Dr
Hao Liu
(NBI)
Description
For an orthogonal integral transform with complete dataset, any two components
are linearly independent; however, when some data points are missing, there is
going to be leakage from one component to another, which is referred to as the
``leakage in integral transforms'' in this work. A special case of this kind
of leakage is the EB-leakage in detection of the cosmological gravitational
wave background (CGWB). We first give the general solutions for all integral
transforms, prove that they are the best solutions, and then apply them to the
case of EB-leakage and detection of the CGWB. In the upcoming decade,
\blue{most likely, new cosmic microwave background (CMB) data are from
ground/balloon experiments}, so they provide only partial sky coverage. Within
this context, the EB-leakage becomes inevitable. We show how to use the
general solutions to achieve the minimal error bars of the EB-leakage, and use
it to find out the maximum ability to detect the CGWB through CMB. The results
show that, \blue{when focusing on the tensor-to-scalar ratio $r$ (at a pivot
scale of 0.05 Mpc$^{-1}$)}, $1\%$ sky coverage ($f_{sky}=1\%$) is enough for a
$5\sigma$-detection of $r\ge 10^{-2}$, but is barely enough for $r=10^{-3}$.
If the target is to detect $r\sim 10^{-4}$ or $10^{-5}$, then $f_{sky}\ge
10\%$ or higher is strongly recommended to enable a $5\sigma$-detection and to
reserve some room for other errors.
Primary author
Dr
Hao Liu
(NBI)
