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3.1 The physics of the anisotropy spectrum and its implications

The physics of stellar distance calibrators is very complicated, because it comes from the era in which the Universe has had time to evolve complicated astrophysics. A large class of alternative approaches to cosmological parameters in general involve going back to a substantially astrophysics-free zone, the epoch of recombination. Although none of these tests uniquely or directly determine H0, they provide joint information about H0 and other cosmological parameters which is improving at a very rapid rate.

In the Universe’s early history, its temperature was high enough to prohibit the formation of atoms, and the Universe was therefore ionized. Approximately 3 × 105 yr after the Big Bang, corresponding to a redshift zrec ∼ 1000, the temperature dropped enough to allow the formation of atoms, a point known as “recombination”. For photons, the consequence of recombination was that photons no longer scattered from ionized particles but were free to stream. After recombination, these primordial photons reddened with the expansion of the Universe, forming the cosmic microwave background (CMB) which we observe today as a black-body radiation background at 2.73 K.

In the early Universe, structure existed in the form of small density fluctuations (δρ∕ ρ ∼ 0.01) in the photon-baryon fluid. The resulting pressure gradients, together with gravitational restoring forces, drove oscillations, very similar to the acoustic oscillations commonly known as sound waves. At the same time, the Universe expanded until recombination. At this point, the structure was dominated by those oscillation frequencies which had completed a half-integral number of oscillations within the characteristic size of the Universe at recombination; this pattern became frozen into the photon field which formed the CMB once the photons and baryons decoupled. The process is reviewed in much more detail in [60].

The resulting “acoustic peaks” dominate the fluctuation spectrum (see Figure 4View Image). Their angular scale is a function of the size of the Universe at the time of recombination, and the angular diameter distance between us and zrec. Since the angular diameter distance is a function of cosmological parameters, measurement of the positions of the acoustic peaks provides a constraint on cosmological parameters. Specifically, the more closed the spatial geometry of the Universe, the smaller the angular diameter distance for a given redshift, and the larger the characteristic scale of the acoustic peaks. The measurement of the peak position has become a strong constraint in successive observations (in particular Boomerang, reported in [30] and WMAP, reported in [146Jump To The Next Citation Point] and [145Jump To The Next Citation Point]) and corresponds to an approximately spatially flat Universe in which Ωm + Ω Λ ≃ 1.

View Image

Figure 4: Diagram of the CMB anisotropies, plotted as strength against spatial frequency, from the WMAP 3-year data [145Jump To The Next Citation Point]. The measured points are shown together with best-fit models to the 1-year and 3-year WMAP data. Note the acoustic peaks, the largest of which corresponds to an angular scale of about half a degree.

But the global geometry of the Universe is not the only property which can be deduced from the fluctuation spectrum10. The peaks are also sensitive to the density of baryons, of total (baryonic plus dark) matter, and of dark energy (energy associated with the cosmological constant or more generally with w < − 13 components). These densities scale with the square of the Hubble parameter times the corresponding dimensionless densities (see Equation (5View Equation)) and measurement of the acoustic peaks therefore provides information on the Hubble constant, degenerate with other parameters, principally the curvature energy Ωk and the index w in the dark energy equation of state. The second peak strongly constrains the baryon density, ΩbH20, and the third peak is sensitive to the total matter density in the form ΩmH20.

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