Related papers: Geometric distances between closed universes
The strongest evidence for dark energy comes presently from geometric techniques such as the supernova distance-redshift relation. By combining the measured expansion history with the Friedmann equation one determines the energy density and…
This is a written version of a talk given at the Fifth Friedmann Seminar on recent work in Observational Cosmic Topology done in partial collaboration with Armando Bernui. We address three relevant questions related to the search for the…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
Non commutative geometry is creating new possibilities for physics. Quantum spacetime geometry and post inflationary models of the universe with matter creation have an enormous range of scales of time, distance and energy in between. There…
A classical model for the extension of singular spacetime geometries across their singularities is presented. The regularization introduced by this model is based on the following observation. Among the geometries that satisfy Einstein's…
We propose a (physical)-geometrical method to measure the present rates of the density cosmological parameters for a Friedmann-Lemaitre universe. The distribution of linear separations between two interacting galaxies,when both of them…
A metric-field approach to gravitation is presented. It is based on an idea of dependency of space-time properties on measuring instruments. Some bimetric equations that realize this idea are considered. They were tested by the binary…
We study the possibility to probe the spatial geometry of the Universe by supernova measurement of the cubic correction to the luminosity distance. We illustrate with an accelerating universe model with infinite-volume extra dimensions, for…
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
We investigate structure formation in a one dimensional model of a matter-dominated universe using a quasi-newtonian formulation. In addition to dark matter, luminous matter is introduced to examine the potential bias in the distributions.…
A phenomenological approach is proposed to the problem of universe accelerated expansion and of the dark energy nature. A general class of models is introduced whose energy density depends on the redshift $z$ in such a way that a smooth…
It is demonstrated how a convenient choice of the mathematical structure of the quantum cosmology superspace, precisely the definition of a convenient regular state superspace and the restriction of the dynamics to this space, yields…
In the Friedmann equations, an infinite initial density is avoided only when the universe is spatially flat. With such equations being then valid when the scale factor $a=0$, the universe must also be in the state of vacuum when $a$ is…
A duality between spacetime manifolds, the geodesic duality, is introduced. Two manifolds are geodesic dual, if the transformation between their metrics is also the transformation between their geodesics. That is, the transformation that…
Various astronomical observations have been consistently making a strong case for the existence of a component of dark energy with negative pressure in the universe. It is now necessary to take the dark energy component(s) into account in…
The Hilbert-Einstein equations are insufficient to describe the geometry of the Universe, as they only constrain a local geometrical property: curvature. A global knowledge of the geometry of space, if possible, would require measurement of…
In the multiverse, the universes can be created in entangled pairs with spacetimes that are both expanding in terms of the time variables experienced by internal observers in their particle physics experiments. The time variables of the two…
In this essay we discuss the difference in views of the Universe as seen by two different observers. While one of the observers follows a geodesic congruence defined by the geometry of the cosmological model, the other observer follows the…
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field…
Graphs are interesting structures: extremely useful to depict real-life problems, extremely easy to understand given a sketch, extremely complicated to represent formally, extremely complicated to compare. Phylogeny is the study of the…