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COSMOLOGICAL *MODELS* OF MODIFIED GRAVITY

, 2013

"... The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld models in which multiple brane ..."

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The recent discovery of dark energy has prompted an investigation of ways in which the accelerated expansion of the universe can be realized. In this dissertation, we present two separate projects related to dark energy. The first project analyzes a class of braneworld

*models*in which multiple###
Nuclear Physics B *Proceedings* Supplement – preprint (2014) 1–42 Nuclear Physics B *Proceedings* Supplement Universal Aspects of QCD-like TheoriesI

"... In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe th ..."

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the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the

*2*+ 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin*models*can be exploited.### Akademisk avhandling för teknisk doktorsexamen vid

, 1994

"... mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group ..."

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mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond to integer n-sequences and the nodes in the path generate all n! permutations. The extra node has a more complicated action, adding a certain quantity to some of the numbers.

### 0 QUANTITATIVE UNIFORM IN TIME CHAOS PROPAGATION FOR BOLTZMANN COLLISION PROCESSES

, 2010

"... ar ..."

### Contents

, 1994

"... We study the generalizations of the well-known Lieb-Thirring inequality for the mag-netic Schrodinger operator with nonconstant magnetic eld. Our main result is the natu-rally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic elds (in ..."

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We study the generalizations of the well-known Lieb-Thirring inequality for the mag-netic Schrodinger operator with nonconstant magnetic eld. Our main result is the natu-rally expected magnetic Lieb-Thirring estimate on the moments of the negative eigenvalues for a certain class of magnetic elds (including even some unbounded ones). We develop a localization technique in path space of the stochastic Feynman-Kac representation of the heat kernel which eectively estimates the oscillatory eect due to the magnetic phase

### 1Local Identification of Overcomplete Dictionaries

"... This paper presents the first theoretical results showing that stable identification of overcomplete µ-coherent dictionaries Φ ∈ Rd×K is locally possible from training signals with sparsity levels S up to the order O(µ−2) and signal to noise ratios up to O( d). In particular the dictionary is recove ..."

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This paper presents the first theoretical results showing that stable identification of overcomplete µ-coherent dictionaries Φ ∈ Rd×K is locally possible from training signals with sparsity levels S up to the order O(µ−

*2*) and signal to noise ratios up to O( d). In particular the dictionary###
Minimum Variance Estimation of a Sparse Vector Within the Linear Gaussian *Model*: An

"... Abstract — We consider minimum variance estimation within the sparse linear Gaussian model (SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a characterizat ..."

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*Abstract*— We consider minimum variance estimation within the sparse linear Gaussian

*model*(SLGM). A sparse vector is to be estimated from a linearly transformed version embedded in Gaussian noise. Our analysis is based on the theory of reproducing kernel Hilbert spaces (RKHS). After a

### An Infinite Set of Ward Identities for Adiabatic Modes in Cosmology

"... We show that the correlation functions of any single-field cosmological model with constant growing-modes are constrained by an infinite number of novel consistency relations, which relate N + 1-point correlation functions with a soft-momentum scalar or tensor mode to a symmetry transformation on N- ..."

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are new. As a

*check*, we verify directly that the n =*2*identity is satisfied by known correlation functions in slow-roll inflation. ar X iv### Contents

"... We examine the late time behavior of the Bunch-Davies wavefunction for interacting light fields in a de Sitter background. We use perturbative techniques developed in the framework of AdS/CFT, and analytically continue to compute tree and loop level contributions to the Bunch-Davies wavefunction. We ..."

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-Graham expansion of classical asymptotically de Sitter solutions is used to show that the wavefunction contains no logarithmic growth in the pure graviton sector at tree level. Finally, assuming a holographic relation between the wavefunction and the partition function of a conformal field theory, we

*interpret*