Photon energy redshift from a tensor metric perturbation
= Photon energy redshift from a tensor metric perturbation
{title2=$d\log\epsilon/d\eta=-\dot h_{ij}e^ie^j/2$}
For a <tensor cosmological perturbation> $h_{ij}$, the time <geodesic equation> in a local <orthonormal tetrad> gives $d\log\epsilon/d\eta=-\dot h_{ij}e^ie^j/2$. The photon comoving energy removes the background redshift; the dot is a partial time derivative, whereas the energy derivative follows the ray.