Related papers: Beyond the Thin Lens Approximation
Consider radar ranging of a distant galaxy in a Friedman-Lemaitre cosmological model. In this model the comoving coordinate of the galaxy is constant, hence the equations of null geodesics for photons travelling to the distant galaxy and…
When angular objects in lensing are considered as linear objects, interesting phenomena start happening. Tachyonic caustics are one example. We review that the intrinsic variables of the lens equation are angular variables. We argue that…
Weak gravitational lensing (WL) has been established as one of the most promising probes of cosmology. So far, most studies have exploited the shear effect of WL leading to coherent distortions of galaxy shapes. But WL also introduces…
Strong field (exact) solutions of the gravitational field equations of General Relativity in the presence of a Cosmological Constant are investigated. In particular, a full exact solution is derived within the inhomogeneous Szekeres-Szafron…
In these lecture notes I review the theory of the non--linear evolution of cosmological perturbations in a self--gravitating collisionless medium, with vanishing vorticity. The problem is first analyzed in the context of the Newtonian…
We derive a set of equations monitoring the evolution of covariant and gauge-invariant linear scalar perturbations of Friedman-Lema\^itre-Robertson-Walker models with multiple interacting non-linear scalar fields. We use a dynamical…
The accelerated expansion of the Universe remains one of the central open problems in modern cosmology. While the $\Lambda$CDM model successfully describes a wide range of observations, the physical nature of dark energy is still unknown,…
We study the evolution of linear perturbations in a Lema\^itre-Tolman-Bondi (LTB) void model with realistic cosmological initial conditions. Linear perturbation theory in LTB models is substantially more complicated than in standard…
It is shown how certain observations interpreted in the background of the Friedmann model with $\Lambda < 0 = k$ (the $\Lambda$CDM model) can be re-interpreted using the $\Lambda = 0$ Lema\^{\i}tre - Tolman (L-T) model so as to do away with…
Model-independent constraints on the spatial curvature are not only closely related to important problems such as the evolution of the Universe and properties of dark energy, but also provide a test of the validity of the fundamental…
We investigate gauge invariant cosmological perturbations in a spatially flat Friedman-Robertson-Walker universe with scalar fields. It is well known that the evolution equation for the gauge invariant quantities has exact solutions in the…
We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes…
The spacetime evolution of massless spinning particles in a Robertson-Walker background is derived using the deterministic system of equations of motion due to Papapetrou, Souriau and Saturnini. A numerical integration of this system of…
We clarify the procedure for expressing the Friedmann equation in terms of directly measurable cosmological scalars constructed out of higher derivatives of the scale factor. We carry out this procedure for pure dust, Chaplygin gas and…
Gravitational field equations in Randers-Finsler space of approximate Berwald type are investigated. A modified Friedmann model is proposed. It is showed that the accelerated expanding universe is guaranteed by a constrained Randers-Finsler…
Solutions to flat space Friedmann-Robertson-Walker cosmologies in Brans-Dicke theory with a cosmological constant are investigated. The matter is modelled as a $\gamma$-law perfect fluid. The field equations are reduced from fourth order to…
This paper presents an analytical study of the behavior of radial free-geodesics in the Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime within the Lambda Cold Dark Matter ({\Lambda}CDM) model. Using the radial free motion solutions,…
In 1988 Bardeen has suggested a pragmatic formulation of cosmological perturbation theory which is powerful in practice to employ various fundamental gauge conditions easily depending on the character of the problem. The perturbation…
Cosmological simulation of gravitational weak lensing in open models is treated using the direct integration method, which is independent of the mult-lens-plane method. Statistical averages of optical quantuties (the convergencen shear and…
We provide a new extension of general relativity (GR) which has the remarkable property of being more constrained than GR plus a cosmological constant, having one less free parameter. This is implemented by allowing the cosmological…