Third peak detected in Microwave Backround?
In May 2001, the experiments
all reported new (or extended) measurements of the angular power spectrum of
the cosmic microwave background. All data sets appear to show both second
and third peaks. Many in the cosmological community gave a sigh of relief,
as the third peak appears too large to be consistent with the previously
successful no-CDM prediction I had made:
The new data from DASI (blue) and BOOMERanG (green)
together with LCDM (left panel) and no CDM (right panel) models. [The
Maxima-1 data have been excluded because the addition of more points
and error bars overwhelms the eye.] The solid red line is the best
constrained fit of the
(from the last line of their Table 4). The dotted red line is the
pre-existing LCDM model
which comes closest to the data. The purple line is the pre-existing
no-CDM model of
McGaugh (1999), unmodified from the
fit to the
[old, first release] combined BOOMERanG and Maxima-1 data (which, except
for a very slight tweak to the geometry, is identical to the no-CDM models
At first glance, it does appear that the there is more power in the third
peak than predicted by the no-CDM model. This is, as emphasized by
McGaugh (1999), the simplest
expression of a possible MOND
model. Reality could be, and at some level must be, more complicated.
However, it is not yet necessary to invoke this
to "save" the no-CDM model, which actually still does quite well:
A close up of the first two peaks detected by BOOMERanG and DASI,
together with the pre-existing
The model has not been adjusted in any way from what was previously
published. [Not even the amplitude has been adjusted: the BOOMERanG
recalibration agrees eerily well with the old fit to the MAXIMA-1
Goodness of fit with no attempt to re-fit model and
accounting only for tabulated errors. Systematic errors start
to dominate at large l, and completely dominate l > 700.
*chi^2 budget dominated by point at L=147. Without it, chi^2=1.25
+chi^2 budget dominated by point at L=289. Without it, chi^2=1.19
&chi^2=0.85 excluding above 2 points (remaining N=26)
Note that the chi^2 budget is dominated by points with small error bars
at low l. Any model which fits the first peak as defined by the
remainder of those points will pay a comparable penalty.
The only "problem" is with the putative third peak, where the uncertainties
are still quite large.
In addition to the random errors in the above figures, there is also a
systematic error due to the uncertainty in the BOOMERanG beam size.
This dominates at large l, and can cause a tilt of the spectrum:
The BOOMERanG data with the tilt resulting from the
effects of a +/- 1 sigma error in the beam size
(the little triangles in their Fig. 2).
The data have been tilted by 1 sigma in the direction favorable to CDM
in the left panel and by 1 sigma in the opposite direction in the right
panel. The untilted data are shown by small green dots.
As a result of this beam uncertainty, the data are consistent with
either LCDM or no-CDM models. The model lines are identical to those in the
figure above except that the normalization of the red lines has been
adjusted to better match the tilted data.
As a result of the systematic beam uncertainty, the simple no-CDM model
remains quite viable. Indeed, it is only because of this uncertainty that
any model provides a decent fit. Without it, the chi^2 of the
"best" fit LCDM model is quite horrid.
So, where are we?
Unfortunately, I don't think the new data shed any additional light on
the issue of the existence of CDM. It still appears that the second
peak is smaller than had been expected by LCDM models, roughly consistent
with no-CDM expectations. But even this may now be in doubt, as the beam
uncertainty does begin to play a role even here. The amplitude of the
third peak remains too poorly constrained to be of any use.
So, what'll it take?
In principle, a good measurement of the first three peaks ought to do it.
Ideally, this should come from the same experiment so as to minimize issues of
should certainly nail the first two peaks, which will help
a lot. It is not clear how much it will help with the third. Perhaps
enough by itself; or perhaps in combination with other experiments.
So, what will happen?
Some further predictions of the no-CDM model:
These are all expectations within the framework of a purely baryonic, CDM-free
universe. This, in turn, is only the first-order approximation of a MOND
prediction. Ultimately, MOND must require some deviation from this.
For example, if MOND is a modifcation of intertia, the effective mass of
the baryons may be less at low accelerations, resulting in less baryonic drag.
If instead MOND is a modification of gravity, then the
integrated Sachs-Wolfe effect is probably underestimated and the pure baryon
model which fits the peaks will underpredict the COBE data. Maybe
there will be a clear signature of physics beyond the existence or nonexistence
of CDM in the MAP data, but that in itself should be a wonderful thing!
- The universe will remain "closed."
MAP will put the first peak in
very nearly the same place it is now, which will be close to but (if the
errors are as expected) significantly on the closed side of Omega_total = 1.
That is, Omega_total > 1 at high confidence, like 1.04 +/- 0.01 or some
such. The interpretation in CDM will be a dash of reionization to nudge
the position of the first peak to lower l.
- The first-to-second peak ratio will remain around what the BOOMERanG
data currently suggest. One needs very accurate data for the CMB
to become competitive with BBN in constraining the baryon density. CDM
models will start pushing the baryon density higher again.
- The third peak, when adequately resolved, will be smaller than the second.
The interpretation should be that CDM does not exist. But that is what the
second peak is already telling us, so who knows what will be concocted...
© Stacy McGaugh, May 8, 2001;
last edited July 18, 2001
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