Radiation Driving Force

Key Concepts:

The series of higher acoustic peaks is sensitive to the energy density ratio of dark matter to radiation in the universe.  Because the amount of radiation is known from the measured temperature of the CMB and the thermal history, under normal assumptions the higher acoustic peaks are sensitive to the dark matter density in the universe.

Let's see how that works.

What happens is that if the energy density of the radiation dominates the matter density, we can no longer consider the photon-baryon fluid to be oscillating in a fixed gravitational potential well.  In fact, the potential decays away at just the right time to drive the amplitude of the oscillations up:

This timing is not a coincidence.  What happens is that if the radiation dominates the density, it is also what is making the gravitational potential in the first place.  Mathematically, the Poisson equation relates the overdensity of photons to the gravitational potential.  As pressure stops the radiation from further compression, the density fluctuation stabilizes leaving the gravitational potential to decay with the expansion of the universe. The decay happens when the fluid is in its most compressed state.  The fluid now sees no gravitational potential to fight against as it bounces back and the amplitude of the oscillations goes way up (beyond the edge of your browser! about a factor of 5).

Because, this driving effect does not come into play once the density of the universe is dominated by the dark matter, we expect there to be a distinction between modes that started oscillating when the universe was radiation dominated and those that started oscillating when the universe was already matter dominated.  Because the density in radiation redshifts faster than matter due to the stretching of the photon wavelengths, the universe was radiation dominated only at its earliest epochs.  Finally, because modes of smaller wavelength start oscillating first, it is the small scale modes, or higher acoustic peaks, that feel this driving effect.

The upshot is that we expect a ramp up of the amplitude of the peaks as we cross from low multipoles to high multipoles. Where this transition occurs tells us the energy density ratio of matter to radiation in the universe.