John D. Barrow a,1 , Antˆnio B. Batista b,2 , J´ lio C. Fabris b,3 , o u Mahouton J.S. Houndjo c,4 and Giuseppe Dito d,e,5 , DAMTP, Centre for Mathematical Sciences, University of Cambridge, UK Departamento de F´ ısica, Universidade Federal do Esp´ ırito Santo, ES, Brazil c Instituto de F´ ısica, Universidade Federal da Bahia, Ba, Brazil d Instituto deMatem´tica, Universidade Federal da Bahia, Ba, Brazil a e Institut de Math´matiques de Bourgogne, Universit´ de Bourgogne, Dijon, e e France
arXiv:1201.1138v1 [gr-qc] 5 Jan 2012
General relativity allows a variety of future singularities to occur in the evolution of the universe. At these future singularities, the universe will end in a singular state after a ﬁnite proper time andgeometrical invariants of the space time will diverge. One question that naturally arises with respect to these cosmological scenarios is the following: can quantum eﬀects lead to the avoidance of these future singularities? We analyze this problem considering massless and conformally coupled scalar ﬁelds in an isotropic and homogeneous background leading to future singularities. It is shown thatnear strong, big rip-type singularities, with violation of the energy conditions, the quantum eﬀects are very important, while near some milder classes of singularity like the sudden singularity, which preserve the energy conditions, quantum eﬀects are irrelevant. PACS number: 98.80-k
It is general believed that today the Universe is in a stage of accelerated expansion. Theprimary evidence for this accelerated phase of cosmic evolution came from the use of the supernova type Ia as standard candles to measure distances in the universe. Supernova are very bright objects that can be seen to great distances. Presently, measurements of supernova type Ia up to z ∼ 1.8
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are available. The fact that these very distant supernova appear dimmer than would be expected in a pure matter-dominated universe led to the conclusion that the universe is accelerating. Much speculation has arisen as to the source of this acceleration and even its reality has been questioned. But, the fact that the spectrum ofanisotropy of the cosmic microwave background radiation indicates that the spatial section of the geometry of the universe must be almost ﬂat, while the observations of the virialized system (galaxies, clusters of galaxies, etc.) indicate a low density of the universe, implies indirectly the acceleration of the universe. In fact, in order to complete the cosmic energy budget and have ﬂat spatialsections, it is necessary to include a component that does not agglomerate locally, but remains as a smooth component of universe. To have this feature, this component must have negative pressure, and consequently it must dominate the matter content of the universe asymptotically, driving the accelerated expansion in the later phases of the cosmic evolution. In brief, to explain the acceleration ofthe universe, an exotic component in the cosmic budget exhibiting negative pressure is needed. This exotic component is named dark energy. We must remember that observations require also a second non-baryonic component, called dark matter, with zero pressure, necessary to explain conveniently the formation of structures in the universe and the dynamics of local, virialized system, like galaxies andclusters of galaxies. However, while there exists a lot of reasonable candidates to represent dark matter (neutralinos, axions, sterile neutrinos, primordial black holes etc – for a review, see reference ), it is not clear what kind of ﬂuid or ﬁeld would constitute dark energy. The ﬁrst natural candidate to be evoked has been the cosmological constant, seen as a phenomenological manifestation...