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We introduce the wedge diagram, an intuitive way to illustrate how cosmological models with a classical (non-singular) bounce generically resolve fundamental problems in cosmology. These include the well-known horizon, flatness, and inhomogeneity problems; the small tensor-to-scalar ratio observed in the cosmic microwave background; the low entropy at the beginning of a hot, expanding phase; and the avoidance of quantum runaway. The same diagrammatic approach can be used to compare with other cosmological scenarios.
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Although the inflationary paradigm is the most widely accepted explanation for the current cosmological observations, it does not necessarily correspond to what actually happened in the early stages of our Universe. To decide on this issue, two paths can be followed: first, all the possible predictions it makes must be derived thoroughly and compared with available data, and second, all imaginable alternatives must be ruled out. Leaving the first task to all other contributors of this volume, we concentrate here on the second option, focusing on the bouncing alternatives and their consequences.
In this paper we present four simple expressions for the relativistic first and second order fractional density perturbations for $Lambda$CDM cosmologies in different gauges: the Poisson, uniform curvature, total matter and synchronous gauges. A distinctive feature of our approach is the use of a canonical set of quadratic differential expressions involving an arbitrary spatial function, the so-called comoving curvature perturbation, to describe the spatial dependence, which enables us to unify, simplify and extend previous seemingly disparate results. The simple structure of the expressions makes the evolution of the density perturbations completely transparent and clearly displays the effect of the cosmological constant on the dynamics, namely that it stabilizes the perturbations. We expect that the results will be useful in applications, for example, studying the effects of primordial non-Gaussianity on the large scale structure of the universe.
A new approach to vacuum decay in quantum field theory, based on a simple variational formulation in field space using a tunneling potential, is ideally suited to study the effects of gravity on such decays. The method allows to prove in new and simple ways many results, among others, that gravitational corrections tend to make Minkowski or Anti de Sitter false vacua more stable semiclassically or that higher barriers increase vacuum lifetime. The approach also offers a very clean picture of gravitational quenching of vacuum decay and its parametric dependence on the features of a potential and allows to study the BPS domain-walls between vacua in critical cases. Special attention is devoted to supersymmetric potentials and to the discussion of near-critical vacuum decays, for which it is shown how the new method can be usefully applied beyond the thin-wall approximation.
Bouncing models have been proposed by many authors as a completion, or even as an alternative to inflation for the description of the very early and dense Universe. However, most bouncing models contain a contracting phase from a very large and rarefied state, where dark energy might have had an important role as it has today in accelerating our large Universe. In that case, its presence can modify the initial conditions and evolution of cosmological perturbations, changing the known results already obtained in the literature concerning their amplitude and spectrum. In this paper, we assume the simplest and most appealing candidate for dark energy, the cosmological constant, and evaluate its influence on the evolution of cosmological perturbations during the contracting phase of a bouncing model, which also contains a scalar field with a potential allowing background solutions with pressure and energy density satisfying p = w*rho, w being a constant. An initial adiabatic vacuum state can be set at the end of domination by the cosmological constant, and an almost scale invariant spectrum of perturbations is obtained for w~0, which is the usual result for bouncing models. However, the presence of the cosmological constant induces oscillations and a running towards a tiny red-tilted spectrum for long wavelength perturbations.
In this paper we compute the CMB bispectrum for bouncing models motivated by Loop Quantum Cosmology. Despite the fact that the primordial bispectrum of these models is decaying exponentially above a large pivot scale, we find that the cumulative signal-to-noise ratio of the bispectrum induced in the CMB from scales $ell < 30$ is larger than $10$ in all cases of interest and therefore can, in principle, be detected in the Planck data.
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