On the properties of the transition matrix in bouncing cosmologies

We elaborate further on the evolution properties of cosmological fluctuations through a bounce. We show this evolution to be describable either by ``transmission'' and ``reflection'' coefficients or by an effective unitary S-matrix. We also show that they behave in a time reversal invariant way. Therefore, earlier results are now interpreted in a different perspective and put on a firmer basis.Comment: 4 pages, 1 figure, to appear in PR

Assisted Contraction

We consider the dynamics of a contracting universe ruled by two minimally coupled scalar fields with general exponential potentials. This model describes string-inspired scenarios in the Einstein frame. Both background and perturbations can be solved analytically in this model. Curvature perturbations are generated with a scale invariant spectrum only for a dust-like collapse, as happens for a single field model with an exponential potential. We find the conditions for which a scale invariant spectrum for isocurvature perturbation is generated.Comment: 13 pages, 3 figures, revised version, conclusions unchange

Particle Physics Models of Inflation and the Cosmological Density Perturbation

This is a review of particle-theory models of inflation, and of their predictions for the primordial density perturbation that is thought to be the origin of structure in the Universe. It contains mini-reviews of the relevant observational cosmology, of elementary field theory and of supersymmetry, that may be of interest in their own right. The spectral index $n(k)$, specifying the scale-dependence of the spectrum of the curvature perturbation, will be a powerful discriminator between models, when it is measured by Planck with accuracy $\Delta n\sim 0.01$. The usual formula for $n$ is derived, as well as its less familiar extension to the case of a multi-component inflaton; in both cases the key ingredient is the separate evolution of causally disconnected regions of the Universe. Primordial gravitational waves will be an even more powerful discriminator if they are observed, since most models of inflation predict that they are completely negligible. We treat in detail the new wave of models, which are firmly rooted in modern particle theory and have supersymmetry as a crucial ingredient. The review is addressed to both astrophysicists and particle physicists, and each section is fairly homogeneous regarding the assumed background knowledge.Comment: 156 pages, after final proof corrections and addition

Identification of perturbation modes and controversies in ekpyrotic perturbations

If the linear perturbation theory is valid through the bounce, the surviving fluctuations from the ekpyrotic scenario (cyclic one as well) should have very blue spectra with suppressed amplitude for the scalar-type structure. We derive the same (and consistent) result using the curvature perturbation in the uniform-field (comoving) gauge and in the zero-shear gauge. Previously, Khoury et al. interpreted results from the latter gauge condition incorrectly and claimed the scale-invariant spectrum, thus generating controversy in the literature. We also correct similar errors in the literature based on wrong mode identification and joining condition. No joining condition is needed for the derivation.Comment: 5 pages, substantially revised, match with PLB versio

Quantum Fields in a Big Crunch/Big Bang Spacetime

We consider quantum field theory on a spacetime representing the Big Crunch/Big Bang transition postulated in the ekpyrotic or cyclic cosmologies. We show via several independent methods that an essentially unique matching rule holds connecting the incoming state, in which a single extra dimension shrinks to zero, to the outgoing state in which it re-expands at the same rate. For free fields in our construction there is no particle production from the incoming adiabatic vacuum. When interactions are included the total particle production for fixed external momentum is finite at tree level. We discuss a formal correspondence between our construction and quantum field theory on de Sitter spacetime.Comment: 30 pages, RevTex file, five postscript figure file

Zonal Modes of Cosmic Microwave Background Temperature Maps

All-sky maps of the cosmic microwave background temperature fluctuations are usually represented by a spherical harmonic decomposition involving modes labelled by their degree l and order m (where -l < m < +l). The zonal modes (i.e those with m = 0) are of particular interest because they vary only with galactic latitude; any anomalous behaviour in them might therefore be an indication of erroneous foreground substraction. We perform a simple statistical analysis of the modes with low l for sky maps derived via different cleaning procedures from the Wilkinson Microwave Anisotropy Probe (WMAP) and show that the zonal modes provide a useful diagnostic of possible systematics.Comment: 5 pages, 4 tables, 2 figures, accepted for publication in MNRA

The scalar bi-spectrum during preheating in single field inflationary models

In single field inflationary models, preheating refers to the phase that immediately follows inflation, but precedes the epoch of reheating. During this phase, the inflaton typically oscillates at the bottom of its potential and gradually transfers its energy to radiation. At the same time, the amplitude of the fields coupled to the inflaton may undergo parametric resonance and, as a consequence, explosive particle production can take place. A priori, these phenomena could lead to an amplification of the super-Hubble scale curvature perturbations which, in turn, would modify the standard inflationary predictions. However, remarkably, it has been shown that, although the Mukhanov-Sasaki variable does undergo narrow parametric instability during preheating, the amplitude of the corresponding super-Hubble curvature perturbations remain constant. Therefore, in single field models, metric preheating does not affect the power spectrum of the large scale perturbations. In this article, we investigate the corresponding effect on the scalar bi-spectrum. Using the Maldacena's formalism, we analytically show that, for modes of cosmological interest, the contributions to the scalar bi-spectrum as the curvature perturbations evolve on super-Hubble scales during preheating is completely negligible. Specifically, we illustrate that, certain terms in the third order action governing the curvature perturbations which may naively be expected to contribute significantly are exactly canceled by other contributions to the bi-spectrum. We corroborate selected analytical results by numerical investigations. We conclude with a brief discussion of the results we have obtained.Comment: v1: 15 pages, 4 figures; v2: 15 pages, 4 figures, discussion and references added, to appear in Phys. Rev.

Design of a Cyclic Multiverse

Recently, it has been noticed that the amplification of the amplitude of curvature perturbation cycle by cycle can lead to a cyclic multiverse scenario, in which the number of universes increases cycle by cycle. However, this amplification will also inevitably induce either the ultimate end of corresponding cycle, or the resulting spectrum of perturbations inside corresponding universe is not scale invariant, which baffles the existence of observable universes. In this paper, we propose a design of a cyclic multiverse, in which the observable universe can emerges naturally. The significance of a long period of dark energy before the turnaround of each cycle for this implementing is shown.Comment: 6 pages, 3 eps figures, v2: 1 eps figure added and some arguments added, to published in PL

The Primordial Perturbation Spectrum from Various Expanding and Contracting Phases

In this paper, focusing on the case of single scalar field, we discuss various expanding and contracting phases generating primordial perturbations, and study the relation between the primordial perturbation spectrum from these phases and the parameter w of state equation in details. Furthermore, we offer an interesting classification for the primordial perturbation spectrum from various phases, which may have important implications for building an early universe scenario embedded in possible high energy theories.Comment: 5 pages, 3 eps figure

Parametric amplification of metric fluctuations through a bouncing phase

We clarify the properties of the behavior of classical cosmological perturbations when the Universe experiences a bounce. This is done in the simplest possible case for which gravity is described by general relativity and the matter content has a single component, namely a scalar field in a closed geometry. We show in particular that the spectrum of scalar perturbations can be affected by the bounce in a way that may depend on the wave number, even in the large scale limit. This may have important implications for string motivated models of the early Universe.Comment: 17 pages, 12 figures, LaTeX-ReVTeX format, version to match Phys. Rev.