Figures 4-6

Figure 4

Analytic decomposition ($\Omega_0=1$ scale invariant adiabatic model). The effective temperature after gravitational redshift dominates the primary anisotropy. Peak heights are enhanced and modulated by baryon-photon ratio $R$ as well as experience a boost crossing the equality scale at $\ell \approx \sqrt{3} (2 \Omega_0 H_0^2/a_{eq})^{1/2} \eta_0 \approx 400$. The Doppler effect is smaller and out of phase with the temperature. The ISW effect due to potential decay after recombination is small here but can be significant for low matter content universes. Diffusion damping cuts off the acoustic spectrum at small scales.

Figure 5

Driving effects. The time evolution of the potential can enhance the amplitude of the acoustic oscillation by driving effects. In the adiabatic case [(a) solid lines, numerical results and (b) heuristic picture], the potential enhances the first compression through infall and decays leaving the oscillator strongly displaced from the zero point. In the (baryon) isocurvature case [(a) dashed line], the potential grows from zero and stimulates a sine mode. The first extrema here is suppressed due to the fact that the gravitation driving begins near sound horizon crossing. Notice that for the first cycle of the adiabatic and isocurvature oscillations, the gravitational force mimics a driving force of approximately twice the natural period.

Figure 6
Heights of the peaks in a scale invariant adiabatic model. The heights of the peaks is determined by the baryon drag and acoustic driving effects and so are sensitive to $\Omega_b h^2$ and $\Omega_0 h^2$. Baryons increase compression in potential wells causing the peak heights to alternate. Lower matter content causes more potential decay driving the oscillation.