Modified Gravity and Cosmology

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

Non-Gaussianity from inflation: theory and observations

The cosmic microwave background (CMB) is the radiation left over from the Big Bang Recent analysis of the fluctuations in this radiation has given us valuable insights into our Universe and its parameters Examining the theory of CMB and recent developments, this textbook starts with a brief introduction to modern cosmology and its main successes, followed by a thorough derivation of cosmological perturbation theory It then explores the generation of initial fluctuations by inflation The Boltzmann equation governs the evolution of CMB anisotropies and polarization is derived using the total angular momentum method Cosmological parameter estimation and the lensing of CMB fluctuations and spectral distortions are also discussed This textbook is the first to contain a full derivation of the theory of CMB anisotropies and polarization Ideal for graduate students and researchers in this field, it includes end-of-chapter exercises, and solutions to selected exercises are provided

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The Cosmic Microwave Background

The effective evolution of an inhomogeneous universe model in any theory of gravitation may be described in terms of spatially averaged variables. In Einstein’s theory, restricting attention to scalar variables, this evolution can be modeled by solutions of a set of Friedmann equations for an effective volume scale factor, with matter and backreaction source terms. The latter can be represented by an effective scalar field (“morphon field”) modeling Dark Energy. The present work provides an overview over the Dark Energy debate in connection with the impact of inhomogeneities, and formulates strategies for a comprehensive quantitative evaluation of backreaction effects both in theoretical and observational cosmology. We recall the basic steps of a description of backreaction effects in relativistic cosmology that lead to refurnishing the standard cosmological equations, but also lay down a number of challenges and unresolved issues in connection with their observational interpretation. The present status of this subject is intermediate: we have a good qualitative understanding of backreaction effects pointing to a global instability of the standard model of cosmology; exact solutions and perturbative results modeling this instability lie in the right sector to explain Dark Energy from inhomogeneities. It is fair to say that, even if backreaction effects turn out to be less important than anticipated by some researchers, the concordance high-precision cosmology, the architecture of current N-body simulations, as well as standard perturbative approaches may all fall short in correctly describing the Late Universe.

Dark Energy from structure: a status report

A definition of perturbations of space-times in general relativity is proposed. The definition leads in a natural way to a concept of gauge invariance, and to an extension of a lemma of Sachs (i964). Coupled equations governing linearized perturbations of certain tetrad components of scalar, electromagnetic, and gravitational fields are derived by the use of Geroch, Held & Penrose's (I 973) version of the tetrad formalism of Newman & Penrose (i 962). It is shown that these perturbations are gauge invariant if and only if the unperturbed space-time is vacuum of algebraic type {22} or, equivalently, if and only if the perturbation equations decouple. Finally the maximal subclass of type {22} space-times for which the decoupled perturbation equations can be solved by separation of variables is found. This class comprises all the nonaccelerating type {22} space-times, including that of Kerr, thus elucidating earlier results of Bardeen & Press

M. Walker

Papers

Perturbations of space--times in general relativity