254 The cosmic microwave background
7.6.2 Coherent acoustic oscillations
If a series of peaks equally spaced inlis observed in the microwave background
temperature power spectrum, it strongly suggests we are seeing the effects
of coherent acoustic oscillations at the time of last scattering. Microwave
background polarization provides a method for confirming this hypothesis.
As explained in section 7.3.2, polarization anisotropies couple primarily to
velocity perturbations, while temperature anisotropies couple primarily to density
perturbations. Now coherent acoustic oscillations produce temperature power
spectrum peaks at scales where a mode of that wavelength has either maximum
or minimum compression in potential wells at the time of last scattering. The
fluid velocity for the mode at these times will be zero, as the oscillation is
turning around from expansion to contraction (envision a mass on a spring.) At
scales intermediate between the peaks, the oscillating mode has zero density
contrast but a maximum velocity perturbation. Since the polarization power
spectrum is dominated by the velocity perturbations, its peaks will be at scales
interleaved with the temperature power spectrum peaks. This alternation of
temperature and polarization peaks as the angular scale changes is characteristic
of acoustic oscillations (see Kosowsky (1999) for a more detailed discussion).
Indeed, it is almost like seeing the oscillations directly: it is difficult to
imagine any other explanation for density and velocity extrema on alternating
scales. The temperature-polarization cross-correlation must also have peaks with
corresponding phases. This test will be very useful if a series of peaks is detected
in a temperature power spectrum which is not a good fit to the standard space of
cosmological models. If the peaks turn out to reflect coherent oscillations, we
must then modify some aspect of the underlying cosmology, while if the peaks
are not coherent oscillations, we must modify the process by which perturbations
evolve.
If coherent oscillations are detected, any cosmological model must include a
mechanism for enforcing coherence. Perturbations on all scales, in particular on
scales outside the horizon, provide the only natural mechanism: the phase of the
oscillations is determined by the time when the wavelength of the perturbation
becomes smaller than the horizon, and this will clearly be the same for all
perturbations of a given wavelength. For any source of perturbations inside the
horizon, the source itself must be coherent over a given scale to produce phase-
coherent perturbations on that scale. This cannot occur without artificial fine-
tuning.
7.6.3 Adiabatic primordial perturbations
If the microwave background temperature and polarization power spectra reveal
coherent acoustic oscillations and the geometry of the universe can also be
determined with some precision, then the phases of the acoustic oscillations
can be used to determine whether the primordial perturbations are adiabatic