Essay

SAKHAROV OSCILLATIONS

Adapted from P. Coles, 1999, The Routledge Critical Dictionary of the New Cosmology, Routledge Inc., New York. Reprinted with the author's permission. To order this book click here: http://www.routledge-ny.com/books.cfm?isbn=0415923549

The large-scale pattern of angular fluctuations (ripples) in the temperature of the cosmic microwave background radiation detected by the Cosmic Background Explorer (COBE) satellite is thought to have been generated by the Sachs-Wolfe effect. On smaller angular scales, we would expect to see a different behaviour. In fact, the level of anisotropy seen on angular scales of a degree or less should be much higher than that detected by the 10° resolution of the COBE satellite. The characteristic increase in the fluctuation amplitude on these smaller scales is usually called the Doppler peak, but this is an extremely inappropriate name for the effect. The physical origin of the enhanced temperature fluctuations was originally worked out by Andrei Sakharov (though in a different context) during the 1960s. A more fitting description of this phenomenon is therefore Sakharov oscillations.

Only a brief description of the physics behind these oscillations is given here. What happens is essentially that, during the plasma era of the thermal history of the Universe, fluctuations on intermediate length scales oscillated like longitudinal compression waves because they were smaller than the relevant Jeans length defined in the theory of gravitational Jeans instability. These waves were similar to sound waves in air, except that the medium in which they were oscillating was a two-component fluid of matter and radiation. The cosmological compression waves were also standing waves, acting as if they were in a cavity whose size was fixed by the scale of the cosmological horizon at the time.

When such a wave is oscillating there are basically two effects that can cause it to alter the temperature of the radiation as seen by an observer. If a region of such a wave is undergoing a compression, then both matter and radiation are squeezed together. Not only is the region then denser, it is also hotter. But during the oscillations, matter and radiation also move into and out of the compressed region, thus inducing a Doppler effect and a consequent increase (or decrease) in the observed temperature according to whether the fluid is moving towards (or away from) the observer. These two effect both contribute, but they are not generally in phase with each other: the phase of maximum compression corresponds to the phase of minimum velocity.

Calculating the net result for waves of different wavelengths is quite complicated, but it is clear chat the degree to which the velocity and density effects tend to reinforce each other varies from wave to wave. Some waves would therefore have produced relatively high temperature fluctuations, and others lower fluctuations. When we look at the pattern of temperature fluctuations seen on the sky we see a series of bumps in the angular power spectrum corresponding to this complicated phase effect: the Sakharov oscillations.