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waynehu

Professor, Department of Astronomy and Astrophysics
University of Chicago

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Adiabatic vs. Isocurvature Perturbations

 

The scalar component is interesting to isolate since it alone is responsible for large scale structure formation. There remain however two possibilities. Density fluctuations could be present initially. This represents the adiabatic mode. Alternately, they can be generated from stresses in the matter which causally push matter around. This represents the isocurvature mode.

The presence or absence of density perturbations above the horizon at last scattering is crucial for the features in both the temperature and polarization power spectrum. As we have seen in §3.3.1, it has as strong effect on the phase of the acoustic oscillation. In a typical isocurvature model, the phase is delayed by tex2html_wrap_inline1106 moving structure in the temperature spectrum to smaller angles (see Fig. 13). Consistency checks exist in the E-polarization and cross spectrum which should be out of phase with the temperature spectrum and oscillating at twice the frequency of the temperature respectively. However, if the stresses are set up sufficiently carefully, this acoustic phase test can be evaded by an isocurvature model ([Turok] 1996). Perhaps more importantly, acoustic features can be washed out in isocurvature models with complicated small scale dynamics to force the acoustic oscillation, as in many defect models ([Albrecht et al.] 1996).

Even in these cases, the polarization carries a robust signature of isocurvature fluctuations. The polarization isolates the last scattering surface and eliminates any source of confusion from the epoch between last scattering and the present. In particular, the delayed generation of density perturbations in these models implies a steep decline in the polarization above the angle subtended by the horizon at last scattering. The polarization power thus hits the asymptotic limits given in the previous section in contrast to the adiabatic power spectra shown in Fig. 14 which have more power at large angles. To be more specific, if the E-power spectrum falls off as tex2html_wrap_inline1700 and or the cross spectrum as tex2html_wrap_inline1702 , then the initial fluctuations are isocurvature in nature (or an adiabatic model with a large spectral index, which is highly constrained by COBE).

Of course measuring a steeply falling spectrum is difficult in practice. Perhaps more easily measured is the first feature in the adiabatic E-polarization spectrum at twice the angular scale of the first temperature peak and the first sign crossing of the correlation at even larger scales. Since isocurvature models must be pushed to the causal limit to generate these features, their observation would provide good evidence for the adiabatic nature of the initial fluctuations ([Hu, Spergel & White] 1997).

Next: Inflation vs. Defects