Density Perturbations in the Ekpyrotic Scenario

We study the generation of density perturbations in the ekpyrotic scenario for the early universe, including gravitational backreaction. We expose interesting subtleties that apply to both inflationary and ekpyrotic models. Our analysis includes a detailed proposal of how the perturbations generated in a contracting phase may be matched across a `bounce' to those in an expanding hot big bang phase. For the physical conditions relevant to the ekpyrotic scenario, we re-obtain our earlier result of a nearly scale-invariant spectrum of energy density perturbations. We find that the perturbation amplitude is typically small, as desired to match observation.Comment: 36 pages, compressed and RevTex file, one postscript figure file. Minor typographical and numerical errors corrected, discussion added. This version to appear in Physical Review

Nonlinear Interferometry via Fock State Projection

We use a photon-number resolving detector to monitor the photon number distribution of the output of an interferometer, as a function of phase delay. As inputs we use coherent states with mean photon number up to seven. The postselection of a specific Fock (photon-number) state effectively induces high-order optical non-linearities. Following a scheme by Bentley and Boyd [S.J. Bentley and R.W. Boyd, Optics Express 12, 5735 (2004)] we explore this effect to demonstrate interference patterns a factor of five smaller than the Rayleigh limit.Comment: 4 pages, 5 figure

Non-Gaussian signatures of Tachyacoustic Cosmology

I investigate non-Gaussian signatures in the context of tachyacoustic cosmology, that is, a noninflationary model with superluminal speed of sound. I calculate the full non-Gaussian amplitude $\mathcal{A}$, its size $f_{\rm NL}$, and corresponding shapes for a red-tilted spectrum of primordial scalar perturbations. Specifically, for cuscuton-like models I show that $f_{\rm NL}\sim {\cal O}(1)$, and the shape of its non-Gaussian amplitude peaks for both equilateral and local configurations, the latter being dominant. These results, albeit similar, are quantitatively distinct from the corresponding ones obtained by Magueijo {\it{et. al}} in the context of superluminal bimetric models.Comment: Some comments and references added. Matches the version published in JCA

The four fixed points of scale invariant single field cosmological models

We introduce a new set of flow parameters to describe the time dependence of the equation of state and the speed of sound in single field cosmological models. A scale invariant power spectrum is produced if these flow parameters satisfy specific dynamical equations. We analyze the flow of these parameters and find four types of fixed points that encompass all known single field models. Moreover, near each fixed point we uncover new models where the scale invariance of the power spectrum relies on having simultaneously time varying speed of sound and equation of state. We describe several distinctive new models and discuss constraints from strong coupling and superluminality.Comment: 24 pages, 6 figure

Vector Bundle Moduli and Small Instanton Transitions

We give the general presciption for calculating the moduli of irreducible, stable SU(n) holomorphic vector bundles with positive spectral covers over elliptically fibered Calabi-Yau threefolds. Explicit results are presented for Hirzebruch base surfaces B=F_r. The transition moduli that are produced by chirality changing small instanton phase transitions are defined and specifically enumerated. The origin of these moduli, as the deformations of the spectral cover restricted to the ``lift'' of the horizontal curve of the M5-brane, is discussed. We present an alternative description of the transition moduli as the sections of rank n holomorphic vector bundles over the M5-brane curve and give explicit examples. Vector bundle moduli appear as gauge singlet scalar fields in the effective low-energy actions of heterotic superstrings and heterotic M-theory.Comment: 52 pages, LATEX, corrected typo

String production at the level of effective field theory

Pair creation of strings in time-dependent backgrounds is studied from an effective field theory viewpoint, and some possible cosmological applications are discussed. Simple estimates suggest that excited strings may have played a significant role in preheating, if the string tension as measured in four-dimensional Einstein frame falls a couple of orders of magnitude below the four-dimensional Planck scale.Comment: 20 pages, latex2e. v2: a reference adde

Vector Bundle Moduli Superpotentials in Heterotic Superstrings and M-Theory

The non-perturbative superpotential generated by a heterotic superstring wrapped once around a genus-zero holomorphic curve is proportional to the Pfaffian involving the determinant of a Dirac operator on this curve. We show that the space of zero modes of this Dirac operator is the kernel of a linear mapping that is dependent on the associated vector bundle moduli. By explicitly computing the determinant of this map, one can deduce whether or not the dimension of the space of zero modes vanishes. It is shown that this information is sufficient to completely determine the Pfaffian and, hence, the non-perturbative superpotential as explicit holomorphic functions of the vector bundle moduli. This method is illustrated by a number of non-trivial examples.Comment: 81 pages, LaTeX, corrected typo