Cosmological attractors and no-hair theorems.
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Date
1996
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Abstract
Interest in the attracting property of de Sitter space-time has grown during the 'inflationary
era' of cosmology. In this dissertation we discuss the more important attempts
to prove the so called 'cosmic no-hair conjecture' ie the proposition that all expanding
universes with a positive cosmological constant asymptotically approach de Sitter
space-time. After reviewing briefly the standard FRW cosmology and the success of the
inflationary scenario in resolving most of the problems of standard cosmology, we carefully
formulate the cosmic no-hair conjecture and discuss its limitations. We present a
proof of the cosmic no-hair theorem for homogeneous space-times in the context of general
relativity assuming a positive cosmological constant and discuss its generalisations.
Since, in inflationary cosmology, the universe does not have a true cosmological constant
but rather a vacuum energy density which behaves like a cosmological term, we take into
account the dynamical role of the inflaton field in the no-hair hypothesis and examine the
no-hair conjecture for the three main inflationary models, namely new inflation, chaotic
inflation and power-law inflation. A generalisation of a well-known result of Collins and
Hawking [21] in the presence of a scalar field matter source, regarding Bianchi models
which can approach isotropy is given. In the context of higher order gravity theories,
inflation emerges quite naturally without artificially imposing an inflaton field. The conformal
equivalence theorem relating the solution space of these theories to that of general
relativity is reviewed and the applicability of the no-hair theorems in the general framework
of f (R) theories is developed. We present our comments and conclusions about
the present status of the cosmic no-hair theorem and suggest possible paths of future
research in the field.
Description
Theses (M.Sc.)-University of Natal, 1996.
Keywords
Cosmology., Space and time., Big bang theory., General relativity (Physics), Cosmic background radiation., Theses--Mathematics.