 Synchronous Sachs-Wolfe line-of-sight formula

With instantaneous photon decoupling and tight-coupling initial brightness, integrate the synchronous photon brightness equation along the unperturbed ray $\mathbf{x}(\tau )={\mathbf{x}}_0-\mathbf{n}({\tau }_0-\tau )$. The direction $\mathbf{n}$ here is photon propagation, opposite to the observer-to-source sky direction. Emission terms are evaluated at the emitter, not the observer. The synchronous metric integral combines endpoint gravitational redshifts and evolving-potential effects when expressed in Newtonian gauge; it is not solely the Integrated Sachs-Wolfe effect.

// Target: cosmology.bigb