Coherent Phase Argument for Inflation

TL;DR

The paper argues that phase coherence of primordial perturbations is the strongest smoking-gun evidence for inflation. It explains how inflation imprints identical phases on all modes, producing a characteristic sequence of acoustic peaks in the CMB and a distinctive temperature-polarization cross-correlation. Using WMAP data, it shows that a flat, inflation-based model tightly constrains cosmological parameters, implying dark matter and dark energy dominance. It further discusses viable alternatives and emphasizes that any viable theory must reproduce the coherent-phase condition that inflation naturally affords.

Abstract

Cosmologists have developed a phenomenally successful picture of structure in the universe based on the idea that the universe expanded exponentially in its earliest moments. There are three pieces of evidence for this exponential expansion -- {\it inflation} -- from observations of anisotropies in the cosmic microwave background. First, the shape of the primordial spectrum is very similar to that predicted by generic inflation models. Second, the angular scale at which the first acoustic peak appears is consistent with the flat universe predicted by inflation. Here I describe the third piece of evidence, perhaps the most convincing of all: the phase coherence needed to account for the clear peak/trough structure observed by the WMAP satellite and its predecessors. I also discuss alternatives to inflation that have been proposed recently and explain how they produce coherent phases.

Figures (11)

• Figure 1: Outline of the evolution of structure in the universe. Perturbations are generated at very early times during inflation (determined by the potential $V$ of the field $\phi$ which drives inflation), start to evolve under the combined influence of pressure and gravity when the universe is of order $10^5$ years old, and then bifurcate into inhomogeneities in matter (which continue to grow due to gravity) and anisotropies in the radiation (which remain constant).
• Figure 2: Evolution of the amplitudes of two Fourier modes with the same wavelength. After inflation, modes remain constant until they re-enter the horizon. After re-entry, they evolve under the competing influences of pressure and gravity.
• Figure 3: Evolution of four Fourier modes of the temperature of the radiation as a function of conformal time $\eta$ ($=\eta_*$ at recombination). Largest scale mode (labeled "Super-Horizon") is still constant at recombination. A slightly smaller scale mode (labeled "First peak") has begun its acoustic oscillation, and has maximal amplitude at recombination. An even smaller scale mode began oscillating earlier; its amplitude is zero at recombination. The smallest scale mode shown here ("Second Peak") has gone through one full oscillation, so its amplitude will be at a maximum. From mc.
• Figure 4: The evolution of an infinite number of modes all with the same wavelength. Left panel shows the wavelength corresponding to the first peak, right to the first trough. Although the amplitudes of all these different modes differ from one another, since they start with the same phase, the ones on the left all reach maximum amplitude at recombination; the ones on the right all go to zero at recombination.
• Figure 5: Modes corresponding to the same two wavelengths ( First Peak and First Trough) as in Fig. \ref{['fig:many']}, but this time with initial phases scrambled. The anisotropies at the angular scales corresponding to these wavelengths would have identical rms's if the phases were random.