Cosmic Microwave Background Anisotropies

TL;DR

This paper surveys the physical origin, measurement, and interpretation of CMB anisotropies, focusing on how acoustic peaks encode the pre- and post-recombination physics of a flat, dark-matter–dark-energy universe with inflationary initial conditions. It presents a coherent framework linking photon–baryon fluid oscillations, gravitational driving, baryon loading, diffusion damping, and polarization, to the angular power spectra $C_\\ell$ and their sensitivity to key parameters like $\Omega_b h^2$, $\Omega_m h^2$, and the angular diameter distance $D_*$. It extends the discussion beyond the primary peaks to secondary anisotropies (ISW, lensing, SZ) and non-Gaussian signatures, detailing data-analysis pipelines (mapmaking, bandpowers, parameter estimation) essential for current and future CMB experiments. The work demonstrates how CMB observations constrain cosmology, test inflation, and provide probes of dark energy and structure formation, highlighting the interplay between theory, observation, and statistical inference in precision cosmology.

Abstract

Cosmic microwave background (CMB) temperature anisotropies have and will continue to revolutionize our understanding of cosmology. The recent discovery of the previously predicted acoustic peaks in the power spectrum has established a working cosmological model: a critical density universe consisting of mainly dark matter and dark energy, which formed its structure through gravitational instability from quantum fluctuations during an inflationary epoch. Future observations should test this model and measure its key cosmological parameters with unprecedented precision. The phenomenology and cosmological implications of the acoustic peaks are developed in detail. Beyond the peaks, the yet to be detected secondary anisotropies and polarization present opportunities to study the physics of inflation and the dark energy. The analysis techniques devised to extract cosmological information from voluminous CMB data sets are outlined, given their increasing importance in experimental cosmology as a whole.

Figures (5)

• Figure 1: Idealized acoustic oscillations. (a) Peak scales: the wavemode that completes half an oscillation by recombination sets the physical scale of the first peak. Both minima and maxima correspond to peaks in power (dashed lines, absolute value) and so higher peaks are integral multiples of this scale with equal height. Plotted here is the idealization of Equation (\ref{['eqn:gravityoscillator']}) (constant potentials, no baryon loading). (b) Baryon loading. Baryon loading boosts the amplitudes of every other oscillation. Plotted here is the idealization of Equation (\ref{['eqn:baryonoscillator']}) (constant potentials and baryon loading $R=1/6$) for the third peak.
• Figure 2: Angular diameter distance. In a closed universe, objects are further than they appear to be from Euclidean (flat) expectations corresponding to the difference between coordinate distance $d$ and angular diameter distance $D$. Consequently, at a fixed coordinate distance, a given angle corresponds to a smaller spatial scale in a closed universe. Acoustic peaks therefore appear at larger angles or lower $\ell$ in a closed universe. The converse is true for an open universe.
• Figure 3: Radiation driving and diffusion damping. The decay of the potential $\Psi$ drives the oscillator in the radiation dominated epoch. Diffusion generates viscosity $\pi_\gamma$, i.e. a quadrupole moment in the temperature, which damps oscillations and generates polarization. Plotted here is the numerical solution to Equation (\ref{['eqn:continuity']}) and Equation (\ref{['eqn:Euler']}) for a mode with wavelength much smaller than the sound horizon at decoupling, $ks_* \gg 1$.
• Figure 4: Gravitational waves and the energy scale of inflation $E_i$. Left: temperature and polarization spectra from an initial scale invariant gravitational wave spectrum with power $\propto E_i^4=(4 \times 10^{16} {\rm GeV})^4$. Right: 95% confidence upper limits statistically achievable on $E_i$ and the scalar tilt $n$ by the MAP and Planck satellites as well as an ideal experiment out to $\ell=3000$ in the presence of gravitational lensing $B$-modes.
• Figure 5: Data pipeline and radical compression. Map are constructed for each frequency channel from the data timestreams, combined and cleaned of foreground contamination by spatial (represented here by excising the galaxy) and frequency information. Bandpowers are extracted from the maps and cosmological parameters from the bandpowers. Each step involves a substantial reduction in the number of parameters needed to describe the data, from potentially $10^{10} \rightarrow 10$ for the Planck satellite.