In this paper we pursue a new technique to search for evidence of a finite Universe, making use of a spherical mexican-hat wavelet decomposition of the microwave background fluctuations. Using the information provided by the wavelet coefficients at several scales we test whether compact orientable flat topologies are consistent with the COBE-DMR data. We consider topological sizes ranging from ...

We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

Topological defects, in particular cosmic strings, give rise to an interesting mechanism for generating the primordial perturbations in the early Universe which are required to explain the present structure. An overview of the cosmic string model will be given, focusing on the predictions of the theory for the large-scale structure of the Universe and for cosmic microwave background anisotropies.

The notion of soft topological space which is defined over an initial universe with a fixed set of parameters was introduced by Shabir and Naz. In this paper, the concept of soft continuous mapping between two soft topological spaces is first proposed. Then the main properties of soft continuous mappings are studied. Finally, the notion of soft connectedness of soft topological spaces is propos...

We clarify the relation between 2-form Einstein gravity and its topological version. The physical space of the topological version is contained in that of the Einstein gravity. Moreover a new vector field is introduced into 2-form Einstein gravity to restore the large symmetry of its topological version. The wave function of the universe is obtained for each model. † Talk given at the Workshop ...

Topological Defects like magnetic monopoles, cosmic strings, domain walls, etc., could have formed during symmetry breaking phase transitions in the early universe. We give an overview of the implications of topological defects for cosmology, with particular emphasis on their possible role as sources of the extremely high energy cosmic rays detected in several recent cosmic ray experiments; the...

Multi–connected Universe models with space idenfication scales smaller than the size of the observable universe produce topological images in the catalogs of cosmic sources. In this review, we present the recent developments for the search of the topology of the universe focusing on three dimensional methods. We present the crystallographic method, we give a new lower bound on the size of local...

This talk will explore the evolution of topological defects in an open universe. The rapid expansion of the universe in an open model slows defects and suppresses the generation of CBR fluctuations at large angular scale as does the altered relationship between angle and length in an open universe. Defect models, when normalized to COBE in an open universe, predict a galaxy power spectrum consi...

We study the nonequilibrium dynamics leading to the formation of topological defects in a symmetry-breaking phase transition of a quantum scalar field with λΦ4 self-interaction in a spatially flat, radiation-dominated FriedmannRobertson Walker Universe. The quantum field is initially in a finitetemperature symmetry-restored state and the phase transition develops as the Universe expands and coo...