Related papers: Cosmic Divergence, Weak Cosmic Convergence, and Fi…
The presently accelerating universe may keep accelerating forever, eventually run into the event horizon problem, and thus be in conflict with the superstring idea. In the other way around, the current accelerating phase as well as the fate…
Continuity is one of the most central notions in mathematics, physics, and computer science. An interesting associated topic is decompositions of continuity, where continuity is shown to be equivalent to the combination of two or more weak…
It is argued that when the dimension of space is a constant integer the full set of Einstein's field equations has more information than the spatial components of Einstein's equation plus the energy conservation law. Applying the former…
The strong equivalence principle is extended in application to averaged dynamical fields in cosmology to include the role of the average density in the determination of inertial frames. The resulting cosmological equivalence principle is…
In this work, a convergence lemma for function $f$ being finite compositions of analytic mappings and the maximum operator is proved. The lemma shows that the set of $\delta$-stationary points near an isolated local minimum point $x^*$ is…
In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use…
We have found that the conformally coupled induced gravity can be an infrared fixed point of induced gravity with Yukawa couplings with matter. The late time cosmology with a uniform mean matter distribution can be described by the…
Firmly nonexpansive operators arise naturally as resolvents of monotone operators and as generalizations of projections and proximal mappings in convex optimization and fixed point theory. While their iterates are known to converge weakly…
We observe the past and present of the universe, but can we predict the far future? Observations suggest that in thousands of billions of years from now most matter and radiation will be absorbed by the cosmological horizon. As it absorbs…
Recent cosmological observations suggest that nearly seventy per cent of the energy density in the universe is unclustered and has negative pressure. Several conceptual issues related to the modeling of this component (`dark energy'), which…
The discovery that the cosmic expansion is accelerating has been followed by an intense theoretical and experimental response in physics and astronomy. The discovery implies that our most basic notions about how gravity work are violated on…
Although previous results have ruled out the possibility of a static horizon in cosmology, we present black hole and white hole metrics that retain static horizons while reproducing cosmological behavior at large distances. Using an…
How much matter is there in the universe? Does the universe have the critical density needed to stop its expansion, or is the universe underweight and destined to expand forever? We show that several independent measures, especially those…
The interplay between cosmological expansion and local attraction in a gravitationally bound system is revisited in various regimes. First, weakly gravitating Newtonian systems are considered, followed by various exact solutions describing…
The dynamics of a minimally coupled scalar field in the expanding universe is discussed with special reference to phantom cosmology. The evolution of the universe with a phantom field vis-a-vis a quintessence field is compared. Phantom…
Let $H$ be a Hilbert space. We investigate the properties of weak limit points of iterates of random projections onto $K\geq 2$ closed convex sets in $H$ and the parallel properties of weak limit points of residuals of random greedy…
Observations suggest that nearly seventy per cent of the energy density in the universe is unclustered and exerts negative pressure. Theoretical understanding of this component (`dark energy'), which is driving an accelerated expansion of…
Some fixed point results of classical theory, such as Banach's Fixed Point Theorem, have been previously extended by other authors to asymmetric spaces in recent years. The aim of this paper is to extend to asymmetric spaces some others…
The cosmic crystallography method of Lehoucq et al. [1] produces sharp peaks in the distribution of distances between the images of cosmic sources. But the method cannot be applied to universes with compact spatial sections of negative…
The basic hypothesis of a post-Copernican Cosmological theory is that {\em all the points} of the Universe have to be essentially equivalent: this hypothesis is required in order to avoid any privileged {\em observer}. This assumption has…