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Register a new userMixmaster Horava-Witten Cosmology
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Authors
Mariusz P. Dabrowski
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We discuss various superstring effective actions and, in particular, their common sector which leads to the so-called pre-big-bang cosmology (cosmology in a weak coupling limit of heterotic superstring). Then, we review the main ideas of the Horava-Witten theory which is a strong coupling limit of heterotic superstring theory. Using the conformal relationship between these two theories we present Kasner asymptotic solutions of Bianchi type IX geometries within these theories and make predictions about possible emergence of chaos. Finally, we present a possible method of generating Horava-Witten cosmological solutions out of the well-known general relativistic pre-big-bang solutions.
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Bianchi type I and type IX (Mixmaster) geometries are investigated within the framework of Hov{r}ava-Witten cosmology. We consider the models for which the fifth coordinate is a $S^1/Z_2$ orbifold while the four coordinates are such that the 3-space is homogeneous and has geometry of Bianchi type I or IX while the rest six dimensions have already been compactified on a Calabi-Yau space. In particular, we study Kasner-type solutions of the Bianchi I field equations and discuss Kasner asymptotics of Bianchi IX field equations. We are able to recover the isotropic 3-space solutions found by Lukas {it et al}. Finally, we discuss if such Bianchi IX configuration can result in chaotic behaviour of these Hov{r}ava-Witten cosmologies.
We consider scalar perturbations in the time-dependent Hou{r}ava-Witten Model in order to probe its stability. We show that during the non-singular epoque the model evolves without instabilities until it encounters the curvature singularity where a big crunch is supposed to occur. We compute the frequencies of the scalar field oscillation during the stable period and show how the oscillations can be used to prove the presence of such a singularity.
We consider the branch of the projectable Horava-Lifshitz model which exhibits ghost instabilities in the low energy limit. It turns out that, due to the Lorentz violating structure of the model and to the presence of a finite strong coupling scale, the vacuum decay rate into photons is tiny in a wide range of phenomenologically acceptable parameters. The strong coupling scale, understood as a cutoff on ghosts spatial momenta, can be raised up to $Lambda sim 10$ TeV. At lower momenta, the projectable Horava-Lifshitz gravity is equivalent to General Relativity supplemented by a fluid with a small positive sound speed squared ($10^{-42}lesssim$) $c^2_s lesssim 10^{-20}$, that could be a promising candidate for the Dark Matter. Despite these advantages, the unavoidable presence of the strong coupling obscures the implementation of the original Horavas proposal on quantum gravity. Apart from the Horava-Lifshitz model, conclusions of the present work hold also for the mimetic matter scenario, where the analogue of the projectability condition is achieved by a non-invertible conformal transformation of the metric.
We consider cosmological models with a scalar field with equation of state $wge 1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1$. We generalize the results to theories where the scalar field couples to p-forms and show that there exists a finite value of $w$, depending on the p-forms, such that chaotic oscillations are suppressed. We show that $Z_2$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.
We consider the electrostatic field of a point charge coupled to Horava-Lifshitz gravity and find an exact solution describing the space with a surplus (or deficit) solid angle. Although, theoretically in general relativity, a surplus angle is hardly to be obtained in the presence of ordinary matter with positive energy distribution, it seems natural in Horava-Lifshitz gravity. We present the sudden disappearance and reappearance of a star image as an astrophysical effect of a surplus angle. We also consider matter configurations of all possible power law behaviors coupled to Horava-Lifshitz gravity and obtain a series of exact solutions.
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