On the Generation of a Scale-Invariant Spectrum of Adiabatic Fluctuations in Cosmological Models with a Contracting Phase

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.Comment: 8 pages, revised version without the section on perturbations, matching the version published on Phys. Rev. D. For cosmological perturbations in the two field model see astro-ph/021127

Classical Stabilization of Homogeneous Extra Dimensions

If spacetime possesses extra dimensions of size and curvature radii much larger than the Planck or string scales, the dynamics of these extra dimensions should be governed by classical general relativity. We argue that in general relativity, it is highly nontrivial to obtain solutions where the extra dimensions are static and are dynamically stable to small perturbations. We also illustrate that intuition on equilibrium and stability built up from non-gravitational physics can be highly misleading. For all static, homogeneous solutions satisfying the null energy condition, we show that the Ricci curvature of space must be nonnegative in all directions. Much of our analysis focuses on a class of spacetime models where space consists of a product of homogeneous and isotropic geometries. A dimensional reduction of these models is performed, and their stability to perturbations that preserve the spatial symmetries is analyzed. We conclude that the only physically realistic examples of classically stabilized large extra dimensions are those in which the extra-dimensional manifold is positively curved.Comment: 25 pages; minor changes, improved reference

The Trans-Planckian Problem of Inflationary Cosmology

In most current models of inflation based on a weakly self-coupled scalar matter field minimally coupled to gravity, the period of inflation lasts so long that, at the beginning of the inflationary period, the physical wavelengths of comoving scales which correspond to the present large-scale structure of the Universe were smaller than the Planck length. Thus, the usual computations of the spectrum of fluctuations in these models involve extrapolating low energy physics (both in the matter and gravitational sector) into regions where this physics is not applicable. In this paper we demonstrate that the usual predictions of inflation for the spectrum of cosmological fluctuations do indeed depend on the hidden assumptions about super-Planck scale physics. We introduce a class of modified dispersion relations to mimic possible effects of super-Planck scale physics, and show that in some cases important deviations from the usual predictions of inflation are obtained. Some implications of this result for the unification of fundamental physics and early Universe cosmology are discussed.Comment: 16 pages, 2 figures. One important correction in the Corley/Jacobson case with b_m>0 and some misprints corrected. Version published in PR

On the Construction of Nonsingular Pre-Big-Bang and Ekpyrotic Cosmologies and the Resulting Density Perturbations

We consider the construction of nonsingular Pre-Big-Bang and Ekpyrotic type cosmological models realized by the addition to the action of specific higher-order terms stemming from quantum corrections. We study models involving general relativity coupled to a single scalar field with a potential motivated by the Ekpyrotic scenario. We find that the inclusion of the string loop and quantum correction terms in the string frame makes it possible to obtain solutions of the variational equations which are nonsingular and bouncing in the Einstein frame, even when a negative exponential potential is present, as is the case in the Ekpyrotic scenario. We analyze the spectra of perturbations produced during the bouncing phase and find that the spectrum of curvature fluctuations in the model proposed originally to implement the Ekpyrotic scenario has a large blue tilt ($n_R= 3$). Except for instabilities introduced on small scales, the result agrees with what is obtained by imposing continuity of the induced metric and of the extrinsic curvature across a constant scalar field (up to $k^2$ corrections equal to the constant energy density) matching surface between the contracting and the expanding Einstein Universes. We also discuss nonsingular cosmological solutions obtained when a Gauss-Bonnet term with a coefficient suitably dependent on the scalar matter field is added to the action in the Einstein frame with a potential for the scalar field present.Comment: 29 pages, 9 figures, accepted for publication in Physical Review D, reference added, discussion section expande

Inflation and Brane Gases

We investigate a new way of realizing a period of cosmological inflation in the context of brane gas cosmology. It is argued that a gas of co-dimension one branes, out of thermal equilibrium with the rest of the matter, has an equation of state which can - after stabilization of the dilaton - lead to power-law inflation of the bulk. The most promising implementation of this mechanism might be in Type IIB superstring theory, with inflation of the three large spatial dimensions triggered by ``stabilized embedded 2-branes''. Possible applications and problems with this proposal are discussed.Comment: 7 pages, uses REVTeX, version to appear in Phys. Rev.

Holographic studies of quasi-topological gravity

Quasi-topological gravity is a new gravitational theory including curvature-cubed interactions and for which exact black hole solutions were constructed. In a holographic framework, classical quasi-topological gravity can be thought to be dual to the large $N_c$ limit of some non-supersymmetric but conformal gauge theory. We establish various elements of the AdS/CFT dictionary for this duality. This allows us to infer physical constraints on the couplings in the gravitational theory. Further we use holography to investigate hydrodynamic aspects of the dual gauge theory. In particular, we find that the minimum value of the shear-viscosity-to-entropy-density ratio for this model is $\eta/s \simeq 0.4140/(4\pi)$.Comment: 45 pages, 6 figures. v2: References adde

Lee Strasberg's Method

Lee Strasberg (1901–1982) is a divisive figure whose method of acting is often misunderstood. Few people really know what it is or how it works, or what is its true relationship to the Stanislavski System. This is due to a number of misconceptions about the nature of his training with its emphasis on the development of the sensory imagination. This paper aims to challenge some of the myths about the Method, and to clarify Strasberg’s unique contribution to actor training