Gravitational secondaries arise from two sources: the
differential redshift from time-variable metric perturbations [Sachs & Wolfe, 1967] and gravitational
lensing. There are many examples of the former, one of which we have
already encountered in §3.8 in the
context of potential decay in the radiation dominated era. Such gravitational
potential effects are usually called the integrated Sachs-Wolfe
(ISW) effect in linear perturbation theory (§4.2.1),
the Rees-Sciama (§4.2.2)
effect in the non-linear regime, and the gravitational
wave effect for tensor perturbations (§4.2.3).
Gravitational waves and lensing also produce -modes in the polarization (see §3.7)
by which they may be distinguished from acoustic polarization.
Plate 5a: Secondary anisotropies (a) Gravitational secondaries: ISW, lensing and Rees-Sciama (moving halo) effects