399 research outputs found

    An introduction to inflation after Planck: from theory to observations

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    These lecture notes have been written for a short introductory course on the status of inflation after Planck and BICEP2, given at the Xth Modave School of Mathematical Physics. The first objective is to give an overview of the theory of inflation: motivations, homogeneous scalar field dynamics, slow-roll approximation, linear theory of cosmological perturbations, classification of single field potentials and their observable predictions. This includes a pedagogical derivation of the primordial scalar and tensor power spectra for any effective single field potential. The second goal is to present the most recent results of Planck and BICEP2 and to discuss their implications for inflation. Bayesian statistical methods are introduced as a tool for model analysis and comparison. Based on the recent work of J. Martin et al., the best inflationary models after Planck and BICEP2 are presented. Finally a series of open questions and issues related to inflation are mentioned and briefly discussed.Comment: 39 pages, 9 figures, to be published in the proceedings of the Xth Modave School in Mathematical Physics. Important parts of those lecture notes draw from chapters 1 and 2 of the author's PhD thesis, arXiv:1109.557

    Disentangling causal webs in the brain using functional Magnetic Resonance Imaging: A review of current approaches

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    In the past two decades, functional Magnetic Resonance Imaging has been used to relate neuronal network activity to cognitive processing and behaviour. Recently this approach has been augmented by algorithms that allow us to infer causal links between component populations of neuronal networks. Multiple inference procedures have been proposed to approach this research question but so far, each method has limitations when it comes to establishing whole-brain connectivity patterns. In this work, we discuss eight ways to infer causality in fMRI research: Bayesian Nets, Dynamical Causal Modelling, Granger Causality, Likelihood Ratios, LiNGAM, Patel's Tau, Structural Equation Modelling, and Transfer Entropy. We finish with formulating some recommendations for the future directions in this area

    Non-Gaussianity from Inflation: Theory and Observations

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    This is a review of models of inflation and of their predictions for the primordial non-Gaussianity in the density perturbations which are thought to be at the origin of structures in the Universe. Non-Gaussianity emerges as a key observable to discriminate among competing scenarios for the generation of cosmological perturbations and is one of the primary targets of present and future Cosmic Microwave Background satellite missions. We give a detailed presentation of the state-of-the-art of the subject of non-Gaussianity, both from the theoretical and the observational point of view, and provide all the tools necessary to compute at second order in perturbation theory the level of non-Gaussianity in any model of cosmological perturbations. We discuss the new wave of models of inflation, which are firmly rooted in modern particle physics theory and predict a significant amount of non-Gaussianity. The review is addressed to both astrophysicists and particle physicists and contains useful tables which summarize the theoretical and observational results regarding non-Gaussianity.Comment: LaTeX file: 218 pages, 19 figures. Replaced to match the accepted version in Physics Reports. A high-resolution version of Fig. 2 can be downloaded from: http://www.pd.infn.it/~liguori/Non_Gaussianity

    Inflation Dynamics and Reheating

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    We review the theory of inflation with single and multiple fields paying particular attention to the dynamics of adiabatic and entropy/isocurvature perturbations which provide the primary means of testing inflationary models. We review the theory and phenomenology of reheating and preheating after inflation providing a unified discussion of both the gravitational and nongravitational features of multi-field inflation. In addition we cover inflation in theories with extra dimensions and models such as the curvaton scenario and modulated reheating which provide alternative ways of generating large-scale density perturbations. Finally we discuss the interesting observational implications that can result from adiabatic-isocurvature correlations and non-Gaussianity.Comment: 51 pages, latex, 16 figures, version to appear in Reviews of Modern Physic

    Gravitational waves from inflation

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    The production of a stochastic background of gravitational waves is a fundamental prediction of any cosmological inflationary model. The features of such a signal encode unique information about the physics of the Early Universe and beyond, thus representing an exciting, powerful window on the origin and evolution of the Universe. We review the main mechanisms of gravitational-wave production, ranging from quantum fluctuations of the gravitational field to other mechanisms that can take place during or after inflation. These include e.g. gravitational waves generated as a consequence of extra particle production during inflation, or during the (p)reheating phase. Gravitational waves produced in inflation scenarios based on modified gravity theories and second-order gravitational waves are also considered. For each analyzed case, the expected power-spectrum is given. We discuss the discriminating power among different models, associated with the validity/violation of the standard consistency relation between tensor-to-scalar ratio rr and tensor spectral index nTn_{\rm T}. In light of the prospects for (directly/indirectly) detecting primordial gravitational waves, we give the expected present-day gravitational radiation spectral energy-density, highlighting the main characteristics imprinted by the cosmic thermal history, and we outline the signatures left by gravitational waves on the Cosmic Microwave Background and some imprints in the Large-Scale Structure of the Universe. Finally, current bounds and prospects of detection for inflationary gravitational waves are summarized.Comment: 85 pages, 4 tables, 9 figures; table 2 added, references added; matches published versio
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