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We investigate non phantom tracker scalar field models as dynamical dark energy scenario. These models can alleviate the cosmic coincidence problem and transition to a cosmological constant-like behaviour at late times. Focusing on the…
We find new classes of exact solutions of the initial momentum constraint for vacuum Einstein's equations. Considered data are either invariant under a continuous symmetry or they are assumed to have the exterior curvature tensor of a…
We establish the inequality for Henneaux-Teitelboim's total energy-momentum for asymptotically anti-de Sitter initial data sets which are asymptotic to arbitrary $t$-slice in anti-de Sitter spacetime. In particular, when $t=0$, it…
In order to deal with a large cosmological constant a relaxation mechanism based on modified gravity has been proposed recently. By virtue of this mechanism the effect of the vacuum energy density of a given quantum field/string theory (no…
We formulate and prove the stability statement associated with the spacetime Penrose inequality for $n$-dimensional spherically symmetric, asymptotically flat initial data satisfying the dominant energy condition. We assume that the ADM…
The majority of renormalizable field theories possessing the scale invariance at the classical level exhibits the trace anomaly once quantum corrections are taken into account. This leads to the breaking of scale and conformal invariance.…
We study formal expansions of asymptotically flat solutions to the static vacuum field equations which are determined by minimal sets of freely specifyable data referred to as `null data'. These are given by sequences of symmetric trace…
The competition between CDM and MOND to account for the `missing mass' phenomena is asymmetric. MOND has clearly demonstrated that a characteristic acceleration $a_0$ underlies the data and understanding what gives rise to $a_0$ is an…
Advantages of inhomogeneous cosmological models that are exact solutions of Einstein's equations over linearised perturbations of homogeneous models are presented. Examples of effects that can be described in the inhomogeneous ones are…
In a continuum setting, the energy-momentum tensor embodies the relations between conservation of energy, conservation of linear momentum, and conservation of angular momentum. The well-defined total energy and the well-defined total…
It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. This…
We find five fundamental reasons demanding that any gravitational mass m, and the speed of light c, vary with cosmological time such that mc remains constant. This is required by the universal condition of conservation of momentum in a…
We give a definition and derive the equations of motion for the center of mass and angular momentum of an axially symmetric, isolated system that emits gravitational and electromagnetic radiation. A central feature of this formulation is…
We construct asymptotically flat, scalar flat extensions of Bartnik data $(\Sigma, \gamma, H)$, where $\gamma$ is a metric of positive Gauss curvature on a two-sphere $\Sigma$, and $H$ is a function that is either positive or identically…
We investigate axially symmetric asymptotically flat vacuum self-gravitating system. A class of initial data with apparent horizon was numerically constructed. The examined solutions satisfy the Penrose inequality. The prior analysis of a…
There exists some tension on large scales between the Planck data and the LCDM concordance model of the Universe, which has been amplified by the recently claimed discovery of non-zero tensor to scalar ratio $r$. At the same time, the…
The inhomogeneous distribution of matter in the non-linear regime of galaxies, clusters of galaxies and voids is described by an exact, spherically symmetric inhomogeneous solution of Einstein's gravitational field equations, corresponding…
The fact that the LambdaCDM model fits the observations does not necessarily imply the physical existence of `dark energy'. Dropping the assumption that cold dark matter (CDM) is a perfect fluid opens the possibility to fit the data without…
Based on scale critical initial data, we construct smooth asymptotically flat Cauchy initial data for the Einstein vacuum system that does not contain Marginally Outer Trapped Surfaces (MOTS) but whose future evolution contains a trapped…
An alternative to the postulate of dark energy required to explain the accelerated expansion of the universe is to adopt an inhomogeneous cosmological model to explain the supernovae data without dark energy. We adopt a void cosmology…