[en] 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 the 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. Among the bouncing alternatives we have: the exotic hydrodynamical fluids that violate the null-energy condition, the minimally coupled scalar fields theories, and the conformal galileons

[en] The inflationary paradigm is now part of the standard cosmological model as a description of its primordial phase. While its original motivation was to solve the standard problems of the hot big bang model, it was soon understood that it offers a natural theory for the origin of the large-scale structure of the universe. Most models rely on a slow-rolling scalar field and enjoy very generic predictions. Besides, all the matter of the universe is produced by the decay of the inflaton field at the end of inflation during a phase of reheating. These predictions can be (and are) tested from their imprint of the large-scale structure and in particular the cosmic microwave background. Inflation stands as a window in physics where both general relativity and quantum field theory are at work and which can be observationally studied. It connects cosmology with high-energy physics. Today most models are constructed within extensions of the standard model, such as supersymmetry or string theory. Inflation also disrupts our vision of the universe, in particular with the ideas of chaotic inflation and eternal inflation that tend to promote the image of a very inhomogeneous universe with fractal structure on a large scale. This idea is also at the heart of further speculations, such as the multi-verse. This introduction summarizes the connections between inflation and the hot big bang model and details the basics of its dynamics and predictions. (author)

[en] Linde in J. Cosmol. Astropart. Phys. 01 (2007) 022 shows that some (though not all) versions of the global (volume-weighted) description avoid the 'Boltzmann brain' problem raised by Page [Phys. Rev. D 78, 063535 (2008)] if the universe does not have a decay time less than 20 Gyr. Here I give an apparently natural version of the volume-weighted description in which the problem persists, highlighting the ambiguity of taking the ratios of infinite volumes that appear to arise from eternal inflation.

[en] The paper deals with Warm Inflationary scenario in FLRW with torsion both from theoretical and observational point of view. In the background of flat FLRW model the Hubble parameter is found to be proportional to the torsion function and warm inflation is examined both in weak and strong dissipation regimes for the power law choice of potential using slow-roll approximation with quasi-stable criteria for radiation. The slow-roll parameters, no.of e-folds, scalar spectral index, and tensor-to-scalar ratio are determined in the present model for mainly three choices of the dissipation coefficient $\mathrm{\Gamma <!--\; ??\; -->}$ using the Planck data set. Finally, we focus on single-field chaotic quartic potential with the above choices of the dissipation coefficient to confront the warm inflation observational predictions directly with the latest observational data set.

[en] This article reviews the properties and limitations associated with the existence of particle, visual, and event horizons in cosmology in general and in inflationary universes in particular, carefully distinguishing them from 'Hubble horizons'. It explores to what extent one might be able to probe conditions beyond the visual horizon (which is close in size to the present Hubble radius), thereby showing that visual horizons place major limits on what are observationally testable aspects of a multi-verse, if such exists. Indeed these limits largely prevent us from observationally proving a multi-verse either does or does not exist. We emphasize that event horizons play no role at all in observational cosmology, even in the multi-verse context, despite some claims to the contrary in the literature. (authors)

[en] I will discuss the formation of domain walls through the phase transition that ends inflation and their statistics and evolution. This document is composed of the slides of the presentation. (author)

[en] In this work we analyze how the spectrum of primordial scalar perturbations is modified, within the emergent universe scenario, when a particular version of the Continuous Spontaneous Localization (CSL) model is incorporated as the generating mechanism of initial perturbations, providing also an explanation to the quantum-to-classical transition of such perturbations. On the other hand, a phase of super-inflation, prior to slow-roll inflation, is a characteristic feature of the emergent universe hypothesis. In recent works, it was shown that the super-inflation phase could generically induce a suppression of the temperature anisotropies of the CMB at large angular scales. We study here under what conditions the CSL maintains or modifies these characteristics of the emergent universe and their compatibility with the CMB observations.

[en] We show that the constraints which follow from the Trans-Planckian Censorship Conjecture for inflationary cosmology can be strengthened if the pre-inflationary period the universe was dominated by radiation. The resulting upper bound on the energy scale of inflation is $\mathrm{\eta <!--\; ??\; -->}\sim <!--\; ???\; -->{10}^4\mathrm{G}\mathrm{e}\mathrm{V}$, close to the scale accessible to accelerator experiments.

[en] The possibility of inflation taking place in closed universe which admits the creation of matter is discussed. (orig.)

[en] In recent literature on eternal inflation, a number of measures have been introduced which attempt to assign probabilities to different pocket universes by counting the number of each type of pocket according to a specific procedure. We give an overview of the existing measures, pointing out some interesting connections and generic predictions. For example, pairs of vacua that undergo fast transitions between themselves will be strongly favored. The resultant implications for making predictions in a generic potential landscape are discussed. We also raise a number of issues concerning the types of transitions that observers in eternal inflation are able to experience