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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…

Cosmology as an exact physical science is of new date, but it has long roots in the past. This essay is concerned with four important themes in the history of cosmological thought which, if taken together, offer a fairly comprehensive…

Starting from a short review of the "classical" space problem in the sense of the 19th century (Helmholtz -- Lie -- Klein) it is discussed how the challenges posed by special and general relativity to the classical analysis were taken up by…

While purely philosophical in the early times, and still very speculative at the beginning of the twentieth century, Cosmology has gradually entered into the realm of experimental science over the past eighty years. It has raised some…

The recognition that physical space (or space-time) is curved is a product of the general theory of relativity, such as dramatically shown by the 1919 solar eclipse measurements. However, the mathematical possibility of non-Euclidean…

What is the shape of the Universe? Is it finite or infinite ? Is space multi-connected to create ghost images of faraway cosmic sources? After a "dark age" period, the field of cosmic topology has now become one of the major concerns in…

In a previous work [1], it was speculated that the lack of homogeneity of the large-scale structure of the universe may be due to quantum fluctuations of space in the early universe. In [1], this was argued for a Friedmann-type universe for…

A fascinating and deep question about nature is what one would see if one could probe space and time at smaller and smaller distances. Already the 19th-century founders of modern geometry contemplated the possibility that a piece of empty…

In the period from about 1890 to 1915 an interdisciplinary and unifying research programme known as "cosmical physics" attracted much scientific and public attention. It typically included aspects of the earth sciences (such as magnetic…

The global shape (topology) of the Universe is not derivable from General Relativity but should be determined by observations. Here we propose a method for estimation of this shape using patterns of fundamental physical parameters, for…

``One could imagine that as a result of enormously extended astronomical experience, the entire universe consists of countless identical copies of our Milky Way, that the infinite space can be partitioned into cubes each containing an…

A new cosmological theory is proposed in the theoretical framework of modified gravity theories which is based on a tachyonic field non-minimally coupled with a specific topological invariant constructed with third order contractions of the…

In the last decade, the study of the overall shape of the universe, called Cosmic Topology, has become testable by astronomical observations, especially the data from the Cosmic Microwave Background (hereafter CMB) obtained by WMAP and…

This review aims to cover the central aspects of current research in cosmic topology from a topological and observational perspective. Beginning with an overview of the basic concepts of cosmology, it is observed that though a determinant…

Before the discovery of the expanding universe, one of the challenges faced in early relativistic cosmology was the determination of the finite and constant curvature radius of space-time by using astronomical observations. Great interest…

Understanding the nature of time remains a key unsolved problem in science. Newton in the Principia asserted an absolute universal time that {\it `flows equably'}. Hamilton then proposed a mathematical unification of space and time within…

In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of…

General relativity does not allow one to specify the topology of space, leaving the possibility that space is multiply rather than simply connected. We review the main mathematical properties of multiply connected spaces, and the different…

From antiquity the conceptual perception of space changed painfully and at a relatively slow pace. It went through mythological descriptions, religious beliefs, metaphysical worldviews and cosmological models with a mechanistic structure,…

In a paper presented a few years ago, De Lorenci et al. showed, in the context of canonical quantum cosmology, a model which allowed space topology changes (Phys. Rev. D 56, 3329 (1997)). The purpose of this present work is to go a step…