3.2. Sachs-Wolfe Effect
The simplest contribution to the CMB anisotropy from density fluctuations is just a gravitational redshift, known as the Sachs-Wolfe effect . A photon coming from a region which is slightly overdense will have a slightly larger redshift due to the deeper gravitational well at the surface of last scattering. Conversely, a photon coming from an underdense region will have a slightly smaller redshift. Thus we can calculate the CMB temperature anisotropy due to the slightly varying Newtonian potential from density fluctuations at the surface of last scattering:
where the factor 1/3 is a general relativistic correction. Fluctuations on large angular scales (low multipoles) are actually larger than the horizon at the time of last scattering, so that this essentially kinematic contribution to the CMB anisotropy is dominant on large angular scales.