We review the status of bouncing cosmologies as alternatives to cosmological inflation for providing a description of the very early universe, and a source for the cosmological perturbations which are observed today. We focus on the motivation for considering bouncing cosmologies, the origin of fluctuations in these models, and the challenges which various implementations face. I. MOTIVATIONThe inflationary scenario [1] is the current paradigm of early universe cosmology. Inflation solves several problems of Standard Big Bang cosmology, and it gives rise to a causal theory of structure formation [2] (see also [3]) which made a number of predictions for cosmological observations which were subsequently successfully verified. In spite of the phenomenological success, inflation faces a number of conceptual challenges (see e.g. [4] for a review of these problems) which motivate the exploration of alternative early universe scenarios. Before mentioning some of these challenges we must begin with a lightning review of inflationary Universe cosmology.According to the inflationary scenario, the universe underwent a period of almost exponential expansion at some very early time. As a consequence, the horizon expanded exponentially and became larger than our past light cone -both evaluated at the time of recombination -provided that the period of accelerated expansion was sufficiently long. During this period, spatial curvature was also diluted. Any wavelength of fluctuation was stretched quasi-exponentially during the period of inflation so that the wavelengths corresponding to scales which are being observed today in cosmological experiments were smaller than the Hubble radius H −1 (t) at the beginning of inflation, where H(t) is the expansion rate of space. The space-time geometry of inflationary cosmology is sketched in Fig. 1. In this figure, the vertical axis is time t, with t = t i denoting the beginning of the inflationary phase, and t = t R the end; the horizontal axis represents physical spatial distance. The Hubble radius is almost constant between t i and t R , and increases linearly before t i and after t R . The horizon is shown as the dashed curve which equals the Hubble radius at the beginning of the period of inflation but increases exponentially until t R . The curve labeled λ indicates the physical wavelength of a cosmological fluctuation mode. [5,6] for reviews of the theory of cosmological perturbations). One finds that the induced spectrum of fluctuations is approximately scaleinvariant and that the observed amplitude of fluctuations is achieved if the Hubble expansion rate during the period of inflation was of the order H ∼ 10 13 GeV, which corresponds to an energy density during the inflationary period which is of the order η ∼ 10 16 GeV, the scale of particle physics "Grand Unification". With this value of H, it turns out that the period of accelerated expansion has to last for at least 50 e-foldings in order for inflation to be able to solve the horizon and flatness problems.One key challenge fo...

Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The PLANCK data shows an unmistakably red, quasi scaleinvariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application level, as exemplified by the possible presence of shear. We provide a pedagogical introduction to these problems and also assess the fitness of different proposals with respect to the data. For example, many models predict a slightly blue spectrum and must be fine-tuned to generate a red spectral index; as a side effect, large non-Gaussianities often result.We highlight several promising attempts to violate the NEC without introducing dangerous instabilities at the classical and/or quantum level. If primordial gravitational waves are observed, certain bouncing cosmologies, such as the cyclic scenario, are in trouble, while others remain valid. We conclude that, while most bouncing cosmologies are far from providing an alternative to the inflationary paradigm, a handful of interesting proposals have surfaced, which warrant further research. The constraints and lessons learned as laid out in this review might guide future research.

The equation of state relating the tension T and the energy per unit length U of a cosmic strin gis investigated in the simplest nontrivial case, namely, that of a field theory with invariance, in four dimensions, which is interpretable as the zero-charge-coupling-constant limit of the more general superconducting string models that have been previously investigated. This limit has the advantage of giving vacuum vortex defects that are strictly local so that the quantities such as U and T that are relevant for the macroscopic description can be computed without ambiguity.In the case of "electricn states (with timelike current) for which no comparable previous calculations exist, it is shown there is a critical frequency w c beyond which the vortex becomes unstable due to "charge" carrier emission. In the case of "magnetic" states (with spacelike current), the present analysis provides more precise results than those of previous investigations, whose predictions are broadly confirmed for typical moderate models in which the tension T remains comparable to the energy density U though not for extreme models, in which serious discrepancies are revealed. PACS number(s): 98.80.Cq, 11.17.t~ I N T R O D U C T I O NT h e purpose of this work is t o derive the macroscopic quantities characterizing t h e dynamics of a currentcarrying cosmic-string model of a charge-uncoupled or neutral kind whose complexity is intermediate between t h a t of t h e original nonconducting kind proposed by Kibble [l] and t h a t of t h e charge-coupled current-carrying kind proposed by Witten [2]. T h e most significantly new feature of this work is a first quantitative investigation of "electric" states, meaning those for which the current is timelike whereas previous numerical results (confirmed in moderate situations by t h e more precise numerical method used here) were restricted t o "magnetic" states, meaning those for which the current is spacelike. One of t h e reasons why only a very few authors [3,4] have paid much attention t o "electricn-type states was the consideration t h a t t h e corresponding electromagnetic fields would tend t o b e screened. However, more recent discussions [5] have made t h e point t h a t the most important effects of currents in cosmic strings are mechanical rather t h a n electromagnetic a n d as such can b e studied even in the neutral (&coupled) limit t o which the present work is restricted.Early discussions of t h e potential astrophysical significance of strings of t h e latter kind concentrated on spectacular effects (such as the formation of cosmological voids [6]) t h a t might have been expected as a consequence of electromagnetic radiation resulting from the charge coupling of t h e currents. However it later became apparent t h a t t h e most important effects of currents in cosmic strings are of a purely mechanical nature, a n d can b e analyzed as a first approximation in terms of cosmicstring models of t h e simpler kind considered here, which are t o b e interpreted as corresponding t o t...