Three distinct low-redshift nonlinear contributions are:
- The thermal Sunyaev-Zeldovich effect arises when hot cluster electrons inverse-Compton scatter the cosmic microwave background. Photons receive energy from the thermal electron distribution. With , the thermodynamic-temperature equivalent is , with Compton y parameter . This is a spectral distortion: a low-frequency decrement, a high-frequency increment, and a nonrelativistic null at , about217GHz for the present CMB temperature. Relativistic electron corrections shift the detailed spectrum and null.
- The kinetic Sunyaev-Zeldovich effect is the Doppler shift caused by scattering off the bulk motion of an electron cloud. At lowest order, . It can have either sign. Unlike the thermal effect, it has the spectrum of a small blackbody temperature shift: frequency independent in thermodynamic temperature units, or proportional to in intensity units.
- The Rees-Sciama effect arises from potentials changing during nonlinear collapse, accretion or motion of structures. Energy gained when a photon enters a well need not equal energy lost on departure. Its gravitational line-of-sight source is the nonlinear evolving-potential counterpart of the Integrated Sachs-Wolfe effect. It too is achromatic in thermodynamic temperature units, not a Compton spectral distortion. Linear potentials can be constant in a matter era while nonlinear potentials still evolve.
Gravitational lensing supplies another nonlinear modification by remapping pre-existing temperature and polarization patterns. It preserves the local blackbody spectrum; it does not generate temperature differences by lensing a perfectly isotropic background.
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