Photon monopole (${\Theta }_0$)

The photon monopole is the direction-averaged fractional temperature perturbation. In Newtonian gauge its gravitationally observable effective temperature is the Sachs-Wolfe combination ${\Theta }_0+\Psi$.

In Newtonian gauge, ${\Theta }_0+\Psi$ combines the intrinsic photon temperature perturbation with the gravitational redshift at emission. With constant potentials and negligible baryon loading it oscillates as $\cos (k{r}_s)$ for adiabatic initial conditions.