Dualidade de Fator de Escala e Cosmologias Pre-Big-Bang. - Lima, Andre Luiz Alves (2017)
This thesis is an investigation of cosmological models dual under an inversion of the scale factor in conformal time, in Einstein gravity. The Scale Factor Duality in conformal time (SFD) acts as a map between high and small energy, and between accelerated and decelerated evolutions of the universe. Used as a symmetry principle, the SFD selects models with two phases of acceleration of the scale factor, symmetric by reflection over the point when acceleration vanishes. We derive a class of such models, corresponding to a modified Chaplygin gas, which might be used as a toy model in more than one phenomenological regime, e.g. a hilltop inflationary phase or a quintessence model. In Einstein gravity, SFD is analogous to a well known duality in dilatonic gravity, in which the inversion of the scale factor in the string frame, along with an appropriate transformation of the dilaton, is a symmetry of the gravidilatonic equations for a restricted class of potentials. Although it is a symmetry of the Friedmann equations in the Einstein frame, dual solutions obtained with the SFD, for any potential, may be mapped to the string frame, providing transformations which relate small and large values of the (string-frame) scale factor. Gravidilatonic duality gives rise to the so-called Pre-Big-Bang Scenario of string cosmology. Analogously, a universe obtained by the SFD may be interpreted as being “before” the big-bang of its dual, in Einstein gravity. We concentrate in the analysis of such pre-big-bang universes which are eternally expanding (in contrast with bouncing models), and their final, accelerated phase plays the rˆole of an inflationary phase previous to the big-bang of the ensuing decelerated universe. This idea is reminiscent of a ‘Conformal Cyclic Cosmology’. The transition across the singularity requires a conformal identification; we address this issue by making use of the dS/CFT correspondence and the holographic renormalization group.