Models of inhomogeneous universes constructed with exact solutions of Einstein's General Relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides large scale inhomogeneity models spherically symmetric around the observer, Swiss-cheese models have also been studied. Among them, Swiss-cheeses where the inhomogeneous patches are modeled by different particular Szekeres solutions have been used for reproducing the apparent dimming of the type Ia supernovae (SNIa). However, the problem of fitting such models to the SNIa data is completely degenerate and we need other constraints to fully characterize them. One of the tests which is known to be able to discriminate between different cosmological models is the redshift-drift. This drift has already been calculated by different authors for Lemaître-Tolman-Bondi (LTB) models. We compute it here for one particular axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese which has previously been shown to reproduce to a good accuracy the SNIa data, and we compare the results to the drift in the ΛCDM model and in some LTB models that can be found in the literature. We show that it is a good discriminator between them. Then, we discuss our model's remaining degrees of freedom and propose a recipe to fully constrain them. 98.65.Dx PACS

The Lambda-CDM model is the best fit to cosmological data, and to the observed galactic rotation curves. However, in the absence of a direct detection of dark matter one should explore theories such as MOND, and perhaps also modified gravity theories like fourth order gravity and Scalar-Tensor-Vector Gravity [STVG] as possible explanations for the non-Keplerian behaviour of galaxy rotation curves. STVG has a modified law for gravitational acceleration which attempts to fit data by fixing two free parameters. We show that, remarkably, the biharmonic equation which we get in the weak field limit of the field equations in a fourth order gravity theory implies a modification of Newtonian acceleration which is precisely of the same repulsive Yukawa form as in the STVG theory, and the corrections could in principle be large enough to try and explain the observed rotation curves. We also explain how our model provides a first principles understanding of MOND. We also show that STVG and fourth order gravity predict an acceleration parameter a0 whose value is of the same order as in MOND.

Flat galaxy rotation curves and the accelerating Universe both imply the existence of a critical acceleration, which is of the same order of magnitude in both the cases, in spite of the galactic and cosmic length scales being vastly different. Yet, it is customary to explain galactic acceleration by invoking gravitationally bound dark matter, and cosmic acceleration by invoking a 'repulsive' dark energy. Instead, might it not be the case that the flatness of rotation curves and the acceleration of the Universe have a common cause? In this essay we propose a modified theory of gravity. By applying the theory on galactic scales we demonstrate flat rotation curves without dark matter, and by applying it on cosmological scales we demonstrate cosmic acceleration without dark energy.

Binary black holes have been in limelight off late due to the detection of a gravitational waves from coalescing compact binaries in the events GW150914 and GW151226. In this paper we study gravitational lensing by the binary black holes modelled as an equal mass Majumdar-Papapetrou di-hole metric and show that this system displays features that are quite unprecedented and absent in any other lensing configuration investigated so far in the literature. We restrict our attention to the light rays which move on the plane midway between the two identical black holes, which allows us to employ various techniques developed for the equatorial lensing in the spherically symmetric spacetimes. If distance between the two black holes is below a certain threshold value, then the system admits two photon spheres. As in the case of single black hole, infinitely many relativistic images are formed due to the light rays which turn back from the region outside the outer (unstable) photon sphere, all of which lie beyond a critical angular radius with respect to the lens.However in the presence of the inner (stable) photon sphere, the effective potential after admitting minimum turns upwards and blows up for the smaller values of radii and the light rays that enter the outer photon sphere can turn back, leading to the formation of a new set of infinitely many relativistic images, all of which lie below the critical radius from the lens mentioned above. As the distance between the two black hole is increased, two photon spheres approach one another, merge and eventually disappear. In the absence of the photon sphere, apart from the formation of a finite number of discrete relativistic images, the system remarkably admits a radial caustic, which has never been observed in the context of relativistic lensing before. Thus the system of binary black hole admits novel features both in the presence and absence of photon spheres. We discuss possible observational signatures and implications of the binary black hole lensing.

It has been argued in the literature that in order to make a matter dominated Friedmann-Lemaitre-Robertson-Walker universe compatible with the generalized second law of thermodynamics, one must invoke dark energy, or modified gravity. In the present article we investigate if in a similar spirit, inhomogeneous cosmological models can be motivated on thermodynamic grounds. We examine a particular minimal void Lemaitre-Tolman-Bondi inhomogeneous model which agrees well with observations. While on the one hand we find that the entropy associated with the apparent horizon is not well-behaved thermodynamically, on the other hand the canonical Weyl curvature entropy shows satisfactory thermodynamic behavior. We suggest that evolution of canonical Weyl curvature entropy might be a useful way to evaluate the thermodynamic viability of inhomogeneous cosmologies.Comment: This version: one paragraph added at the end, acknowledgements and references added, matches published versio

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