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[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] 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] 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
[en] In single-field models of inflation the effect of a long mode with momentum q reduces to a diffeomorphism at zeroth and first order in q. This gives the well-known consistency relations for the n-point functions. At order q2 the long mode has a physical effect on the short ones, since it induces curvature, and we expect that this effect is the same as being in a curved FRW universe. In this paper we verify this intuition in various examples of the three-point function, whose behaviour at order q2 can be written in terms of the power spectrum in a curved universe. This gives a simple alternative understanding of the level of non-Gaussianity in single-field models. Non-Gaussianity is always parametrically enhanced when modes freeze at a physical scale kph, f shorter than H: fNL ∼ (kph, f/H)2
[en] Many cosmologists (myself included) have advocated volume weighting for the cosmological measure problem, weighting spatial hypersurfaces by their volume. However, this often leads to the Boltzmann brain problem, that almost all observations would be by momentary Boltzmann brains that arise very briefly as quantum fluctuations in the late universe when it has expanded to a huge size, so that our observations (too ordered for Boltzmann brains) would be highly atypical and unlikely. Here it is suggested that volume weighting may be a mistake. Volume averaging is advocated as an alternative. One consequence may be a loss of the argument that eternal inflation gives a nonzero probability that our universe now has infinite volume
[en] The new standard cosmology, based on the theory of inflation, has very impressive observational support. I review some outstanding problems of the new cosmology and the global view of the universe - the multiverse - that it suggests. I focus in particular on prospects for further observational tests of inflation and of the multiverse.