One would like to know not only the nature of the fluctuations, but also the means by which they are generated. We assume of course that they are not merely placed by fiat in the initial conditions. Let us first divide the possibilities into broad classes. In fact, the distinction between isocurvature and adiabatic fluctuations is operationally the same as the distinction between conventional causal sources (e.g. defects) and those generated by a period of superluminal expansion in the early universe (i.e. inflation). It can be shown that inflation is the only causal mechanism for generating superhorizon size density (curvature) fluctuations ([Liddle] 1995). Since the slope of the power spectrum in E can be traced directly to the presence of ``superhorizon size'' temperature, and hence curvature, fluctuations at last scattering, it represents a ``test'' of inflation ([Hu & White] 1997, [Spergel & Zaldarriaga] 1997). The acoustic phase test, either in the temperature or polarization, represents a marginally less robust test that should be easily observable if the former fails to be.
These tests, while interesting, do not tell us anything about the detailed physics that generates the fluctuations. Once a distinction is made between the two possibilities one would like to learn about the mechanism for generating the fluctuations in more detail. For example in the inflationary case there is a well known test of single-field slow-roll inflation which can be improved by using polarization information. In principle, inflation generates both scalar and tensor anisotropies. If we assume that the two spectra come from a single underlying inflationary potential their amplitudes and slopes are not independent. This leads to an algebraic consistency relation between the ratio of the tensor and scalar perturbation spectra and the tensor spectral index. However information on the tensor contribution to the spectrum is limited by cosmic variance and is easily confused with other effects such as those of a cosmological constant or tilt of the initial spectrum. By using polarization information much smaller ratios of tensor to scalar perturbations may be probed, with more accuracy, and the test refined (see [Zaldarriaga et al.] 1997 for details). In principle, this extra information may also allow one to reconstruct the low order derivatives of the inflaton potential.
Similar considerations apply to causal generation of fluctuations without inflation. Two possibilities are a model with ``passive evolution'' where initial stress fluctuations move matter around and ``active evolution'' where exotic but causal physics continually generates stress-energy perturbations inside the horizon. All cosmological defect models bear aspects of the latter class. The hallmark of an active generation mechanism is the presence of vector modes. Vector modes decay with the expansion so in a passive model they would no longer be present by recombination. Detection of (cosmological) vector modes would be strong evidence for defect models. Polarization is useful since it provides a unique signature of vector modes in the dominance of the B-mode polarization.
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