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

Abstract

Abstract. 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.

Evaluating backreaction with the peak model of structure formation

“…The effect of inhomogeneities on the passage of light was first discussed by Zel'dovich in 1964 [32] (early literature on the topic also refers to an unpublished colloquium by Feynman in the same year). This and the work which followed [33][34][35] studied the passage of light in the case when the deviation from the FRW models is in some sense small (see [36][37][38][39][40][41][42] for later studies of perturbed FRW universes).…”

Calculation of distances in cosmological models with small-scale inhomogeneities and their use in observational cosmology: a review

“…Somewhat confusingly, it is claimed that they 'therefore have a higher apparent magnitude', which is correct if 'higher' means 'brighter', but of course larger magnitudes correspond to fainter objects. However, this is a second-order effect; to first order, small deviations from homogeneity do not change the average magnification (Claudel 2000).…”

Lensing Effects on Gravitational Waves in a Clumpy Universe: Effects of Inhomogeneity on the Distance‐Redshift Relation

“…Ω Λ0 = 0, Ω m0 = 1 Ω Λ0 = 0.7, Ω m0 = 0.3 n = 100 × y max y max = 5 n = 100 × y max y max = 5 y max error n error y max error n error 0.5 12 10 11791 0. the gravitational wave observations, since we can observe the only amplitude of superposed waves, although it is observable in optical observations, e.g., the observation of Type Ia supernovae. As mentioned in §3, several works have discussed the equality between µ and µ F (Weinberg 1976;Ellis et al 1998;Claudel 2000;Rose 2001;Kibble & Lieu 2005). However, in practical sense, µ is not an observable quantity and thus µ E might be more important.…”

“… (29) and the average magnification in the clumpy universe. Sevral previous works have discussed this issue(Weinberg 1976;Ellis et al 1998;Claudel 2000;Rose 2001;Kibble & Lieu 2005).…”