Secondary anisotropies of the CMB

TL;DR

The paper reviews the full landscape of secondary CMB anisotropies, focusing on reionisation and large-scale structure as dominant late-time sources of temperature and polarization fluctuations. It synthesizes the physics of Thomson scattering, ISW/RS effects, gravitational lensing, and the Sunyaev–Zel'dovich phenomenon, linking them to ionisation history, halo formation, and gas physics. It then surveys observational status, modeling approaches (notably the halo model and mass functions), and the cosmological leverage of SZ cluster counts and the SZ power spectrum, including relativistic and non-thermal corrections and non-Gaussian signatures. The work underscores the dual role of secondary anisotropies as both challenging foregrounds and powerful probes of dark energy, structure formation, and the growth of cosmic velocity and density fields, with planed and upcoming experiments (Planck, SPT, ACT, LOFAR, etc.) poised to exploit these signals.

Abstract

The Cosmic Microwave Background fluctuations provide a powerful probe of the dark ages of the universe through the imprint of the secondary anisotropies associated with the reionisation of the universe and the growth of structure. We review the relation between the secondary anisotropies and and the primary anisotropies that are directly generated by quantum fluctuations in the very early universe. The physics of secondary fluctuations is described, with emphasis on the ionisation history and the evolution of structure. We discuss the different signatures arising from the secondary effects in terms of their induced temperature fluctuations, polarisation and statistics. The secondary anisotropies are being actively pursued at present, and we review the future and current observational status.

Figures (19)

• Figure 1: From Spergel et al. (2006): The compilation of the small scale CMB measurements from ground-based and balloon experiments (Ruhl et al. 2003, Abroe et al. 2004, Kuo et al. 2004, Readhead et al. 2004, Dickinson et al. 2004). The red, dark orange and light orange lines represent the predictions from the $\Lambda$CDM model fit to the WMAP data for the best fit, the 68% and 95% confidence levels respectively. Excess of power is seen at the largest $l$ values.
• Figure 2: From Hu & Dodelson (2002): The power spectrum of the secondary temperature anisotropies arising from gravitational effects (panel a) and scattering effects (panel b). The power spectrum of primary anisotropies is shown for comparison. The calculations use a flat universe with $\Omega_\Lambda = 0.67, \Omega_{\rm b}h^2 = 0.02, \Omega_{\rm m}h^2 = 0.16, n=1$. Acronyms are defined in the text. $\delta$- and i-mod refer to density and ionisation fraction modulation respectively (Sect. \ref{['sec:reion']}). "Suppression" and "Doppler" refer to the damping and anisotropy generation at reionisation (Sect. \ref{['sec:reion']}).
• Figure 3: Left panel, from Zhang, Pen & Trac (2004): The Doppler effect induced temperature anisotropies (kinetic SZ) from numerical simulations. The results include non-linear regime and are obtained by assuming universe was reionised at $z=16.5$ and remained ionised after that. The contribution from the linear regime, OV effect, (dashed line) is plotted for comparison, together with primary power spectrum and thermal SZ spectrum in the R-J region (see Sect. \ref{['sec_SZ']}). Right panel, from Santos et al. (2003): Analytic computation of the secondary anisotropies produced by reionisation. Top thick lines are for the inhomogeneous reionisation-induced fluctuations. Bottom lines are for density-induced fluctuations where the solid thin line is for the linear OV effect and the dashed for the non-linear contribution to OV.
• Figure 4: From Iliev et al. (2007b): Doppler effect induced temperature fluctuation maps from numerical simulations including radiative transfer (right panel). The left panel shows the result after correcting for the missing large-scale velocities.
• Figure 5: Left panel, from Liu et al. (2001): Reionisation-induced polarisation (dashed, dotted and thin solid lines) with the first-order $E$-mode power spectrum (thick solid line). The second order reionisation-induced polarisation is computed from numerical simulations with different escape fractions of ionising photons $f_{\rm esc}$. Right panel, from Santos et al. (2003): $B$-mode polarisation with contributions from lensing (thin solid line) and tensor modes (thin-dashed). The contribution, at reionisation, from density (thick dashed) and ionisation (thick solid) modulated scattering is also shown. The density modulated contribution uses the halo model for non-linear corrections. Also shown for comparison is the first-order $E$-mode power spectrum (dot-dashed line).