Cosmological fluctuations on the light cone

In studying temperature fluctuations in the cosmic microwave background Weinberg has noted that some ease of calculation and insight can be achieved by looking at structure perturbed light cone on which photons propagate. his approach worked a specific gauge specialized to around standard Robertson-Walker cosmological model with vanishing spatial three-curvature. this paper we generalize analysis providing invariant treatment no choice is made, considering geometries non-vanishing By using scalar, vector, tensor fluctuation basis find relevant combinations appear have explicit dependence curvature even if geometry nonvanishing. We not previously considered, albeit too consequential, observer included order enforce invariance. As well as working comoving time also work conformal metric any given three-curvature written time-dependent factor (the expansion radius time) times static same For drops out identically. Thus photon either or all.