Cumulative gravitational lensing in Newtonian perturbations of Friedman-Robertson-Walker cosmologies

It is a common assumption amongst astronomers that, in the determination of the distances of remote sources from their apparent brightness, the cumulative gravitational lensing due to the matter in all the galaxies is the same, on average, as if the matter were uniformly distributed throughout the cosmos. The validity of this assumption is considered here by way of general Newtonian perturbations of Friedman-Robertson-Walker (FRW) cosmologies. The analysis is carried out in synchronous gauge, with particular attention to an additional gauge condition that must be imposed. The mean correction to the apparent magnitude-redshift relation is obtained for an arbitrary mean density perturbation. In the case of a zero mean density perturbation, when the intergalactic matter has a dust equation of state, then there is indeed a zero-mean first order correction to the apparent magnitude-redshift relation for all redshifts. Point particle and Swiss cheese models are considered as particular cases.Comment: 28 pages. LaTeX2e. Uses the following packages: amsmath, amsthm, amssymb, amsfonts, mathrsf

Apparent magnitudes in an inhomogeneous universe: the global viewpoint

Apparent magnitudes are important for high precision cosmology. It is generally accepted that weak gravitational lensing does not affect the relationship between apparent magnitude and redshift. By considering metric perturbations it is shown that objects observed in an inhomogeneous universe have, on average, higher apparent magnitudes than those observed at the same redshift in a homogeneous universe.Comment: 2 pages, Latex, with aastex and emulateapj