Listening for the Size of the Universe

The baryon acoustic oscillations that produce the peaks and troughs in the CMB angular power spectrum can also be seen in the distribution of galaxies in space. Before the electrons and protons combine to form hydrogen, a transparent gas, the free electrons strongly scattered the photons of the CMB. The photons form a high pressure fluid, and if there is a pressure gradient, the electrons will be pushed down the pressure gradient. But if the electrons move, the protons must follow or else a large electric field will be set up, which then pulls the protons along to follow the electrons. Thus the normal matter ("baryons ") and the CMB photons are tied together to make a "baryon-photon" fluid. This fluid has a high sound speed since the photons provide most of the density and almost all of the pressure. As a result the sound speed in the baryon-photon fluid is about 170,000 km/sec. In a region with high initial density, there will be a high pressure in the baryon-photon fluid which will propagate as an expanding spherical sound wave. The animation at right shows a cross-section of this process. In this figure dark matter is blue, baryons are green, and photons are red. Both recombination the baryon-photon fluid is red plus green which is yellow. After recombination the photons go off at the speed of light and baryons are left sitting in a spherical shell around the initial excess density of dark matter. The sound wave travels for about 400,000 years before recombination, at a large fraction of the speed of light, and the distances covered before recombination expand along with the Universe, so at recombination the shell has a radius of about 450,000 light years. This expands after recombination to a current size of 500 million light years. Thus we expect to see an enhanced number of galaxy pairs separated by 500 million light years.

This effect was first detected in Eisenstein et al. (2005). The latest results from BOSS, the Baryon Oscillation Spectroscopic Survey, which is working to get redshifts for 1.5 million Luminous Red Galaxies out to redshift z = 0.7, are detailed in a paper by Anderson et al.. They have a strong 10σ detection of the BAO signal and measurements of the acoustic scale length in two redshift bins centered at z = 0.32 and 0.57.

A cartoon produced by the BOSS project showing the spheres of baryons around the initial dark matter clumps.

Astronomers calculate a function ξ(s), which is the fraction of excess pairs at a separation s. This function falls rapidly with distance, so the graph above plots s2ξ(s) which is much flatter, versus the distance s. The distance is measured in funny units: h-1Mpc, where h is the Hubble constant divided by 100 km/sec/Mpc. The secondary peak due to the baryon shells is seen at about 105 h-1Mpc, or about 500 million light years.

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The thumbnail on the right is my simplified way of showing how these data, combined with the CMB measurement of the acoustic scale length at z = 1089, and the supernova measurement of the acceleration of the expansion of the Universe, provide enough information to simultaneously determine the current matter density, the current dark energy density and the rate of change of the dark energy density. The figure is labeled with the "Equation of State" w = P/ρc2 but I think a better way to think of this is in terms of the "cosmic interest rate" on dark energy density. The percentage change per unit time in the dark energy density is less than 1/3 of the Hubble rate and could well be zero, as expected for a cosmological constant.

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© 2014 Edward L. Wright. Last modified 24 Jan 2014