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A scalar-tensor theory of gravity is formulated in which $G$ and particle masses are allowed to vary. The theory yields a globally static cosmological model with no evolutionary timescales, no cosmological coincidences, and no flatness and…
We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-deSitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the…
Alternative scenarios to the Big Bang singularity have been subject of intense research for several decades by now. Most popular in this sense have been frameworks were such singularity is replaced by a bounce around some minimal…
The origin of negative pressure fluid (the dark energy) is investigated in the quantum model of the homogeneous, isotropic and closed universe filled with a uniform scalar field and a perfect fluid which defines a reference frame. The…
The evolution of the universe is studied in exactly solvable dynamical quantum model with the Robertson-Walker metric. It is shown that the equation of motion which describes the expansion or contraction of the universe can be represented…
We review the field of collisionless numerical simulations for the large-scale structure of the Universe. We start by providing the main set of equations solved by these simulations and their connection with General Relativity. We then…
An essential aspect of cosmic voids is that these underdense regions provide complementary information about the properties of our Universe. Unlike dense regions, voids are avoided by matter and are less contaminated by baryonic processes.…
The prevailing cosmological model with the lambda-term, in which the space is flat, is studied (section 1). The corresponding age of the Universe (t0) is calculated (assuming a Hubble constant consistent with the measurements of the Hubble…
We study the cosmological evolution of a type-0 string theory by employing non-criticality, which may be induced by fluctuations of the D3 brane worlds. We check the consistency of the approach to O(alpha ') in the corresponding…
A spherically symmetric comoving fluid solution of Einstein's equations is adapted for cosmological application by extending the geometry of standard FRW cosmology using a generalised curvature term. The resulting model retains many of the…
Observations of distant supernovae indicate that the Universe is now in a phase of accelerated expansion the physical cause of which is a mystery. Formally, this requires the inclusion of a term acting as a negative pressure in the…
The Friedman equation for the universe with arbitrary curvature $(k = 0, \pm 1)$, filled with mutually noninteracting pressureless dust, radiation, cosmological constant, and strings is considered. We assume the string domination scenario…
An overview is presented of a recently proposed "radically conservative" solution to the problem of dark energy in cosmology. The proposal yields a model universe which appears to be quantitatively viable, in terms of its fit to supernovae…
The Cauchy-Kowalevski theorem is applied to the solutions of Einstein's equations and to cosmology. Three fundamental requirements of the theorem: the use of analytic series; the existence of the boundary surfaces; and the setting of the…
The possibility of an expanding decelerating Universe in the distant future is investigated in the context of a quintessence scalar field cosmology. Such a conceivable evolution is tested against SNe Ia and $H(z)$ cosmic chronometers data,…
The standard cosmological model, now strongly constrained by direct observation at early epochs, is very successful in describing the structure of the evolved universe on large and intermediate scales. Unfortunately, serious contradictions…
We consider the cosmological models for the higher dimensional spacetime which includes the curvatures of our space as well as the curvatures of the internal space. We find that the condition for the integrability of the cosmological…
In this paper, observational constraints on the cosmic equation of state of dark energy ($p = w \rho$) have been investigated using gravitational lensing statistics. A likelihood analysis of the lens surveys has been carried out to…
One of the biggest mysteries in cosmology is Dark Energy, which is required to explain the accelerated expansion of the universe within the standard model. But maybe one can explain the observations without introducing new physics, by…
This paper reviews statistical methods recently developed to reconstruct and analyze dark matter mass maps from weak lensing observations. The field of weak lensing is motivated by the observations made in the last decades showing that the…