Systems on universe spaces

The paper studies the class of analytic input/state/output systems for which the vector fields and the observation functions are only partially defined. The state space of the system is a universe space — a newly defined concept. As an example, quotient systems and observability are studied in detail. Observability is defined in a new way, consistent with the universe approach.     

Metric affine geometry on the universe of lines

We prove that in dimensions 4 metric affine geometry over infinite fields is interpretable in terms of orthogonality of its lines, and thus it can be formalized as a theory of such an orthogonality.     

The chaotic universe

In this paper we suggest a formulation that would bear out the spirit of Prigogine's “Order Out of Chaos” and Wheeler's “Law Without Law”. In it a typical elementary particle length, namely the pion Compton wavelength arises from the random motion of the N particles in the universe of dimension R. It is then argued in the light of recent work that this is the origin of the laws of physics and leads to a cosmology consistent with observation.     

The scaled universe II

In an earlier paper we had pointed out that quantum mechanical type effects are seen at different scales in the macrouniverse also. In this paper we obtain a rationale for this, which lies in the picture of bound material systems, spanning a Compton wavelength type extent, separated by much larger and relatively much less dense distances.     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

Static universe and cosmic field

Summary It is found that in the presence of the cosmic field, which singles out a time-like direction, a static closed homogeneous isotropic universe of the Einstein type is possible, provided matter is present. On the other hand, a universe of the de Sitter type is not permitted by the field equations. A Bruno Finzi nel suo 70^mo compleanno Entrata in Redazione il 4 febbraio 1970.     

Induced gravity and universe creation on the domain wall in five-dimensional space-time

We present a model with a strong fermion self-interaction and an induced gravitational interaction in five-dimensional space-time. In the strong-coupling regime, this model develops a spontaneous breaking of translational invariance, which results in localizing light particles on the (3+1)-dimensional domain wall embedded in the anti-de Sitter five-dimensional space-time. We obtain the corresponding low-energy effective action and investigate kink-type vacuum solutions in a quasiflat Riemannian metric. We discuss the physics of light particles in 3+1 dimensions and establish the fundamental relations between the induced gravitational constant and both the curvature in the five-dimensional anti-de Sitter space-time and the Newton gravitational constant of our universe. Dedicated to Yu. V. Novozhilov on his 80th birthday __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 4–22, July, 2006.     

Cosmological natural selection and the purpose of the universe

The cosmological natural selection (CNS) hypothesis holds that the fundamental constants of nature have been fine‐tuned by an evolutionary process in which universes produce daughter universes via the formation of black holes. Here, we formulate the CNS hypothesis using standard mathematical tools of evolutionary biology. Specifically, we capture the dynamics of CNS using Price's equation, and we capture the adaptive purpose of the universe using an optimization program. We establish mathematical correspondences between the dynamics and optimization formalisms, confirming that CNS acts according to a formal design objective, with successive generations of universes appearing designed to produce black holes. © 2013 Wiley Periodicals, Inc. Complexity 18: 48–56, 2013     

How much sweetness is there in the universe?

We continue investigations of forcing notions with strong ccc properties introducing new methods of building sweet forcing notions. We also show that quotients of topologically sweet forcing notions over Cohen reals are topologically sweet while the quotients over random reals do not have to be such. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physical characters of KLS time-periodic universe

In this paper we consider the physical characters of the new time-periodic solution of the vacuum Einstein’s field equations which was constructed by Kong, Liu and Shen. By the analysis of the Penrose diagram associated with this solution, we find that this solution is very different from the other solutions.     

Mathematical modeling of the distribution of galaxies in the universe

On the base of a random walk model with the transition probability given as a three-dimensional spherically symmetric stable law, a structural function is derived for the distribution of galaxies in the Universe which satisfactorily describes the scaling properties (fractality) of the distribution at small distances as well as the violation of scaling at large distances, in accordance with the data in the CfA catalogue. Proceedings of the XVII Seminar on Stability Problems for Stochastic Models, Kazan, Russia, 1995, Part III.