# The first acoustic peak in CMB

1. Feb 23, 2011

Dear all,
Searching proofs for Dark energy, people always mention "the first acoustic peak in CMB".
can anyone tell me what exactly is that?
how long did we expect it to be and now -having Dark energy- how long do we see it?

2. Feb 23, 2011

### bapowell

The first acoustic peak is seen in the CMB temperature power spectrum:

Consider the graph formed by the red line. This is the best fit WMAP temperature power spectrum. It measures the fluctuations in temperature as a function of multipole moment, $\ell$. The multipole moment corresponds to the angular separation, $\theta$ of the correlated fluctuations on the sky: $\ell \approx \pi/\theta$. So in this plot, scales on the order of the present-day horizon are at the far left, and smaller length scales are at the far right. The broad central peak is the first acoustic peak.

What you are looking at in this plot is the Fourier transform of the spatial density correlation function -- in English, what you are seeing are acoustic waves oscillating in the baryon-photon plasma of the early universe. It's a snapshot of the universe when it was some several hundred thousand years old. As the universe cooled, the photons decoupled from the baryons, and no longer participated in these oscillations -- they instead began free streaming across the universe making up what we know of today as the CMB, forever locking in these intricate patterns of primordial oscillation.

The first peak corresponds to an acoustic wave that had just enough time to compress once before this decoupling. The higher order peaks have gone through more oscillations (and hence, are damped somewhat relative to the first.) Scales to the left of the first peak were actually 'superhorizon' at the time of decoupling -- they subtended length scales that were causally disconnected -- and so oscillations could not be set up on these scales.

Anyway, so back to the first peak. The first peak corresponds to a very special length scale in the early universe -- namely, its angular separation gives the size of the horizon at the time of decoupling. Astronomers measure distances by measuring the angle subtended by an object of known size. In our case, theory tells us how big the horizon was at the time of decoupling, and we know how long ago the CMB was emitted. From the figure above, it's simple geometry to relate the angle, $\theta$, to the horizon distance at decoupling. If the geometry is flat, well, you get the usual Euclidean result. However, if there is appreciable spatial curvature you'll measure a smaller angle for a given length scale (see left figure). And so, the angular diameter of the central peak -- it's position along the x-axis -- helps to determine the geometry of the universe. For example, an open universe would give the gray curve in the figure. WMAP has discovered that the universe indeed is very close to flat, to about 1%.

So what does all this mean for dark energy?? If the universe is flat, then it must have a density equal to the critical density. But we know that ordinary matter and dark matter only account for roughly 25% of the critical density. We know this from several data sources, but perhaps most notably, by measuring the locations and sizes of the higher order peaks in the CMB. So there is another source of energy that contributes about 75% to the overall budget. It needs to be smooth and uniform, and we call it dark energy.

The fact that dark energy causes the universe to undergo accelerated expansion can also be seen in the CMB, although the evidence for this is most notable in supernovae redshift measurements.

Last edited: Feb 23, 2011
3. Feb 23, 2011

### skydivephil

What a fabulously lucid answer, thansk for answering my red tilt question as well. I salute you .

4. Dec 9, 2012

5. Dec 9, 2012

### bapowell

Hrm. That is odd. The first peak is indeed located at l=200, so I'm not sure why they obtain a different acoustic scale. I will need to look more closely at how they define their quantitites; in the meantime, check out http://background.uchicago.edu/~whu/araa/node7.html and see if it helps.

6. Dec 10, 2012