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Register a new userEvolution to a smooth universe in an ekpyrotic contracting phase with w > 1
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A period of slow contraction with equation of state w > 1, known as an ekpyrotic phase, has been shown to flatten and smooth the universe if it begins the phase with small perturbations. In this paper, we explore how robust and powerful the ekpyrotic smoothing mechanism is by beginning with highly inhomogeneous and anisotropic initial conditions and numerically solving for the subsequent evolution of the universe. Our studies, based on a universe with gravity plus a scalar field with a negative exponential potential, show that some regions become homogeneous and isotropic while others exhibit inhomogeneous and anisotropic behavior in which the scalar field behaves like a fluid with w=1. We find that the ekpyrotic smoothing mechanism is robust in the sense that the ratio of the proper volume of the smooth to non-smooth region grows exponentially fast along time slices of constant mean curvature.
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We consider the four-dimensional effective field theory which has been used in previous studies of perturbations in the Ekpyrotic Universe, and discuss the spectrum of cosmological fluctuations induced on large scales by quantum fluctuations of the bulk brane. By matching cosmological fluctuations on a constant energy density hypersurface we show that the growing mode during the very slow collapsing pre-impact phase couples only to the decaying mode in the expanding post-impact phase, and that hence no scale-invariant spectrum of adiabatic fluctuations is generated. Note that our conclusions may not apply to improved toy models for the Ekpyrotic scenario.
We assume that the early universe is homogeneous, anisotropic, and is dominated by the mutually BPS 2255 intersecting branes of M theory. The spatial directions are all taken to be toroidal. Using analytical and numerical methods, we study the evolution of such an universe. We find that, asymptotically, three spatial directions expand to infinity and the remaining spatial directions reach stabilised values. Any stabilised values can be obtained by a fine tuning of initial brane densities. We give a physical description of the stabilisation mechanism. Also, from the perspective of four dimensional spacetime, the effective four dimensional Newtons constant G_4 is now time varying. Its time dependence will follow from explicit solutions. We find in the present case that, asymptotically, G_4 exhibits characteristic log periodic oscillations.
In Pre-Big-Bang and in Ekpyrotic Cosmology, perturbations on cosmological scales today are generated from quantum vacuum fluctuations during a phase when the Universe is contracting (viewed in the Einstein frame). The backgrounds studied to date do not yield a scale invariant spectrum of adiabatic fluctuations. Here, we present a new contracting background model (neither of Pre-Big-Bang nor of the Ekpyrotic form) involving a single scalar field coupled to gravity in which a scale-invariant spectrum of curvature fluctuations and gravitational waves results. The equation of state of this scalar field corresponds to cold matter. We demonstrate that if this contracting phase can be matched via a nonsingular bounce to an expanding Friedmann cosmology, the scale-invariance of the curvature fluctuations is maintained. We also find new background solutions for Pre-Big-Bang and for Ekpyrotic cosmology, which involve two scalar fields with exponential potentials with background values which are evolving in time. We comment on the difficulty of obtaining a scale-invariant spectrum of adiabatic fluctuations with background solutions which have been studied in the past.
The Ekpyrotic scenario assumes that our visible Universe is a boundary brane in a five-dimensional bulk and that the hot Big Bang occurs when a nearly supersymmetric five-brane travelling along the fifth dimension collides with our visible brane. We show that the generation of isocurvature perturbations is a generic prediction of the Ekpyrotic Universe. This is due to the interactions in the kinetic terms between the brane modulus parametrizing the position of the five-brane in the bulk and the dilaton and volume moduli. We show how to separate explicitly the adiabatic and isorcuvature modes by performing a rotation in field space. Our results indicate that adiabatic and isocurvature pertubations might be cross-correlated and that curvature perturbations might be entirely seeded by isocurvature perturbations.
In a recent paper arXiv:0910.2230, Khoury and Steinhardt proposed a way to generate adiabatic cosmological perturbations with a nearly flat spectrum in a contracting Universe. To produce these perturbations they used a regime in which the equation of state exponentially rapidly changed during a short time interval. Leaving aside the singularity problem and the difficult question about the possibility to transmit these perturbations from a contracting Universe to the expanding phase, we will show that the methods used in arXiv:0910.2230 are inapplicable for the description of the cosmological evolution and of the process of generation of perturbations in this scenario.
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