Modern cosmology - astronomical, physical and logical approaches
by
Gyula Dávid
Department of Atomic Physics, Eötvös University, Budapest, Hungary

Cosmology is the physics of the Universe as a whole. General models of modern cosmology are based on astronomical observations, well founded physical theories and, to simplify the so obtained mathematical model, aesthetical-philosophical 'a priori' assumptions e.g. the so-called "cosmological principle". These theories and assumptions allow describing astronomically observed expansion of the Universe and building a two-parameter family of cosmological models, characterized by the so-called Einstein-Friedman-Robertson-Walker (EFRW) metrics of space-time. Certainly there are more exotic cosmological theories beyond this family (e. g. steady-state model, multiverse) but up to recent years there was no strict experimental evidence against or in favor of one or another theory.
In the last 15 years, there have been revolutionary new developments in observational and data processing methods of astronomy and cosmology. Different kinds of observations led to precise determination of cosmological parameters, which allowed selecting the right model from the EFRW family of theories which fits all experimental data. Today we know that the Universe is infinite in space, its three dimensional space-like slices have Euclidean geometry, the ^Slife^T of Universe began 13.7 billion years ago with the so-called Big Bang and will be infinite in the future and the expansion rate of the Universe has been accelerating recently. The Universe is infinite in time and space and it contains an infinite amount of matter. In two or three years the analysis of recent observational projects are going to give the cosmological parameters with accuracy of one percent. Cosmology of the following years differs from its earlier image: it will not be a scene of speculations or a whirling set of curious space-times but regular natural science based on facts and measured data.
In the present lecture we will sketch the astronomical and physical foundations of modern cosmology, describe the EFRW family of models and show the different scenarios for temporal development of the Universe using different cosmological parameters of theories. The new astronomical measurements and theoretical considerations will be briefly reviewed. Using these we will explain what the generally accepted models of the Universe are like and will derive the specific values of the parameters to select the ^Sright^T one from these models. The present status of the above-mentioned ^Scosmological principle^T will be discussed: today it is not only a simplifying assumption but an experimental fact of finite accuracy which works as a first approximation to describe the real distribution of matter. The second approximation of perturbation theory is not a simple correction: it is a positive and fruitful theory of fluctuations of matter and space-time, which led to the correct interpretation of observed fluctuations of the cosmic background radiation and led to fit successfully the cosmological parameters.
In such a consolidated epoch of a branch of science it is worthwhile to analyze critically the basic foundations and logical structure of the theories involved. In particular, one could search for the theoretical and logical properties which pick out the successful version of theory from the enormous set of unsuccessful ones. This question is very delicate in the case of the One and Only Universe we can observe, namely, we are not sure what it means to ask whether certain observed properties of the Universe are necessary or accidental (i.e. whether they are laws of science or just facts). The revolutionary 'phase transition' of experimental and theoretical cosmology motivates further work on the logical foundation of space-time theory, on which the present author is collaborating with the Németi-Andréka school.

Date received: July 19, 2005