A priori, if we ignore the last few comments above, there is a
reasonable chance that Liu and Li could have made a human error and
accidentally made an assumption in their analysis method that
happened to anti-correlate with the cosmological component of the
quadrupole, mostly cancelling it out. It is clear from
0907.2731
that in July 2009, they were not aware of what they did differently
from the WMAP team regarding the spacecraft attitude.
However, in that case, it would be reasonable that the strongest
anti-correlation would be for an offset a little further away. So, by
considering the timing offset to be a free parameter, it should be
possible to find an optimal offset that anti-correlates with the
cosmological quadruole even more strongly. The argument should then
shift to more first principle methods - which offset should in principle
be correct (e.g. as in the last few comments)?
But have a look at Table 1 and Figure 3 of v2 of the paper! The following
graph shows the 10 values explicit in Table 1 and the 1 value implicit
in it, assuming that I have understood correctly.
As stated in the paper, the two halves of the plot appear to be very
linear, with slope [tex]14.6\pm 0.2 \mu K [/tex] / full_offset, and the minimum
appears to occur very sharply at the point that Liu and Li used. It
seems to be stretching the limits of credibility that Liu and Li
happened by chance to find a very sharp optimal point for
anti-correlating the cosmic quadrupole signal.
Is it reasonable that this is so linear? Wouldn't we expect some more
complicated mix of e.g. trigonometric functions etc? The obvious answer
is that getting a Taylor expansion that is linear to first order happens
in many situations. A plot of [tex]|sin(\delta)|[/tex], where [tex]-7' < \delta < 7'[/tex],
gives a plot identical to the above, apart from scaling.
A formal statistical exercise would be to calculate more and more
offsets closer and closer to the minimum, until the level where noise
(and doing things correctly like sidereal day vs WMAP-day vs
Earth-day) make it difficult to get a preciser estimate of the minimal
offset. At the moment, if we ignore our intuition that the minimum is
very sharp, we could presumably say that if Liu and Li chose an
arbitrary offset in their initial (July 2009) analysis, then they had
a 10% chance of finding this minimum (that they were not looking for).
That's not (yet) a strong rejection. Ten more calculations with
[tex]\delta = \pm 0.01 i, i \in \{1, 2, 3, 4, 5\}[/tex], where [tex]\delta[/tex] is the
timing offset fraction as before, should get to a 99\% rejection of
Liu & Li finding the minimum by chance.
Another extension would be to go around and beyond [tex]\pm 0.5[/tex], e.g.
[tex]\delta[/tex] = 0.45, 0.48, 0.5, 0.52, 0.55, 0.6, 0.7, 0.8, 0.9, 1.0, 2.0,
3.0 to see if at least some sort of feature occurs at the value of
the WMAP team's offset (the sign convention is [tex]+0.5[/tex] in Fig. 3).
If this function turns out to be linear with no sign of
anything at all except at [tex]\delta = 0[/tex], then I suspect that the "Axis
of Evil" problem will be replaced by the WMAP
Evil Attitude
effect: WMAP's spacecraft attitude evilly hid itself from the WMAP
team and from many other cosmologists for seven years...