Related papers: The nearly flat universe
The Universe is a physical object. Physical objects have shapes and sizes. General relativity is insufficient to describe the global shape and size of the Universe: the Hilbert-Einstein equations only treat limiting quantities towards an…
Distance measurement provide no constraints on curvature independent of assumptions about the dark energy, raising the question, how flat is our Universe if we make no such assumptions? Allowing for general evolution of the dark energy…
Geometry of the universe has always intrigued mathematicians and cosmologists. Recent results from the Wilkinson Microwave Anisotropy Project (WMAP) indicate that the visible universe is incredibly flat. This apparent flatness could be due…
What does it mean to be flat? We propose to define it by measuring the maximal variation around a point, or from a dual perspective, the distance to neighboring level sets. After developing some calculus rules, we show how flat minima,…
We introduce the notion of almost finite dimensionality of algebras and study its connection with the classical finiteness conditions.
The paper uses geometrical arguments to derive equations with relevance for cosmology; 5-dimensional spacetime is assumed because it has been shown in other works to provide a setting for significant unification of different areas of…
The properties of the quantum universe on extremely small spacetime scales are studied in the semi-classical approach to the well-defined quantum model. It is shown that near the initial cosmological singularity point quantum gravity…
The belief that three dimensional space is infinite and flat in the absence of matter is a canon of physics that has been in place since the time of Newton. The assumption that space is flat at infinity has guided several modern physical…
The Cosmological Principle states that the universe is both homogeneous and isotropic. This, alone, is not enough to specify the global geometry of the spacetime. If we were able to measure both the Hubble constant and the energy density we…
Recent observational results suggest that our universe is nearly flat and well modelled within a $\Lambda$CDM framework. The observed values of $\Omega_{m}$ and $\Omega_{\Lambda}$ inevitably involve uncertainties. Motivated by this, we make…
Recent observations suggest that the ratio of the total density to the critical density of the universe, $\Omega_0$, is likely to be very close to one, with a significant proportion of this energy being in the form of a dark component with…
This short paper proposes an alternative theory to Anthropic Principle. According to our interpretation, the Universe is not "fine-tuned" for life, but "roughly-tuned" for computation and its biofilness is only a phenomenon. This standpoint…
One can make the very simple hypothesis that the Universe is the inside of an hypersphere in 4 dimensions, where our 3-dimensional world consists of hypersurfaces at different radii. Based on this assumption it is possible to show that…
By way of a complete integration of the Friedmann equations, in terms of observables, it is shown that for the cosmological constant $\Lambda > 0$ there exist non-flat FLRW models for which the total density parameter $\Omega$ remains $\sim…
We study a possibility of the fate of universe, in which there is neither the rip singularity, which results in the disintegration of bound systems, nor the endless expansion, instead the universe will be quasi static. We discuss the…
What is the shape of the Universe? Is it curved or flat, finite or infinite ? Is space "wrapped around" to create ghost images of faraway cosmic sources? We review how tessellations allow to build multiply-connected 3D Riemannian spaces…
We describe the non-minimal Standard Model, consisting of minimalistic extensions of the Standard Model, which for all we know is the theory of the universe, able to describe all of the universe from the beginning of time. Extensions…
Is the universe finite or infinite, and what shape does it have? These fundamental questions, of which relatively little is known, are typically studied within the context of the standard model of cosmology where the universe is assumed to…
Matter with an equation of state $p=-\rho/3$ may arise in certain scalar field theories, and the energy density of this matter decreases as $a^{-2}$ with the scale factor $a$ of the Universe. In this case, the Universe could be closed but…
The evidence for a Big Bang origin of the Universe is truly compelling, though its cause remains a complete mystery. As the cosmic spacetime is revealed to us with ever improving detail, however, we are beginning to refine the range of its…