399 research outputs found
An introduction to inflation after Planck: from theory to observations
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
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
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
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
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 and tensor spectral
index . 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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