# Theories Beyond the Standard Model

01 Jan 2018-pp 39-57

TL;DR: In this paper, it was shown that neutrinos or antineutrinos are degenerate and neutrons shift less neutrons through β-equilibrium, and the plausible ranges of the degeneracy parameter and the baryon-to-photon ratio were derived.

Abstract: Many alternative models are proposed, though remarkable agreement is obtained on the primordial abundance of standard BBN. As an approach to nonstandard models, first we investigate a possibility that neutrinos or antineutrinos are degenerate. An excess density of neutrinos speeds up the expansion of the universe, leaving more neutrons at the onset of nucleosynthesis. In addition, degenerate electron-neutrinos shift less neutrons through β-equilibrium. Performing χ2 analysis for the calculated and observed abundances of 4He and D, we determine the plausible ranges of the degeneracy parameter and the baryon-to-photon ratio. Next, we explore BBN under the brane-world cosmology. The Friedmann-like equation is derived in the five-dimensional universe. It is found that more 4He is produced than in standard BBN because of rapid expansion due to the interaction energy on the brane. Finally, we examine thermal evolution in the early universe including a decaying cosmological term which is treated as a source of the gravitational field.

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TL;DR: In this paper, the weak scale is generated from the Planck scale through an exponential hierarchy, but this exponential arises not from gauge interactions but from the background metric, which is a slice of spacetime.

Abstract: We propose a new higher-dimensional mechanism for solving the hierarchy problem. The weak scale is generated from the Planck scale through an exponential hierarchy. However, this exponential arises not from gauge interactions but from the background metric (which is a slice of ${\mathrm{AdS}}_{5}$ spacetime). We demonstrate a simple explicit example of this mechanism with two 3-branes, one of which contains the standard model fields. The phenomenology of these models is new and dramatic. None of the current constraints on theories with very large extra dimensions apply.

9,088 citations

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TL;DR: In this paper, a single 3-brane embedded in five dimensions was shown to reproduce four-dimensional Newtonian and general relativistic gravity to more than adequate precision, even without a gap in the Kaluza-Klein spectrum.

Abstract: Conventional wisdom states that Newton's force law implies only four noncompact dimensions. We demonstrate that this is not necessarily true in the presence of a nonfactorizable background geometry. The specific example we study is a single 3-brane embedded in five dimensions. We show that even without a gap in the Kaluza-Klein spectrum, four-dimensional Newtonian and general relativistic gravity is reproduced to more than adequate precision.

6,936 citations

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10 Sep 2007

TL;DR: This new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded, and adopts an object-oriented style particularly suited to scientific applications.

Abstract: Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit www.nr.com or www.cambridge.org/us/numericalrecipes for more details. New key features: 2 new chapters, 25 new sections, 25% longer than Second Edition Thorough upgrades throughout the text Over 100 completely new routines and upgrades of many more. New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector MachinesNew Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions An expanded treatment of ODEs with completely new routines Plus comprehensive coverage of linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory And much, much more! Visit the authors' web site for information about electronic subscriptions www.nr.com/aboutNR3book.html

4,130 citations

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01 Jan 1972

TL;DR: In this paper, the General Theory of Relativity and Feneral Relativity are discussed, as well as applications of feneral relativity in cosmology and cosmology.

Abstract: Preface. Notation. Copyright Acknowledgements. Part One Preliminaries. Part Two the General Theory of Relativity. Part Three Applications of Feneral Relativity. Part Four Formal Developments. Part Five Cosmology. Appendix. Some Useful Numbers. Index.

4,056 citations

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TL;DR: In this article, the authors discuss the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional braneworlds based on the Randall-Sundrum models.

Abstract: The observable universe could be a 1 + 3-surface (the “brane”) embedded in a 1 + 3 + d-dimensional spacetime (the “bulk”), with Standard Model particles and fields trapped on the brane while gravity is free to access the bulk. At least one of the d extra spatial dimensions could be very large relative to the Planck scale, which lowers the fundamental gravity scale, possibly even down to the electroweak (∼ TeV) level. This revolutionary picture arises in the framework of recent developments in M theory. The 1 + 10-dimensional M theory encompasses the known 1 + 9-dimensional superstring theories, and is widely considered to be a promising potential route to quantum gravity. General relativity cannot describe gravity at high enough energies and must be replaced by a quantum gravity theory, picking up significant corrections as the fundamental energy scale is approached. At low energies, gravity is localized at the brane and general relativity is recovered, but at high energies gravity “leaks” into the bulk, behaving in a truly higher-dimensional way. This introduces significant changes to gravitational dynamics and perturbations, with interesting and potentially testable implications for high-energy astrophysics, black holes, and cosmology. Brane-world models offer a phenomenological way to test some of the novel predictions and corrections to general relativity that are implied by M theory. This review discusses the geometry, dynamics and perturbations of simple brane-world models for cosmology and astrophysics, mainly focusing on warped 5-dimensional brane-worlds based on the Randall-Sundrum models.

1,140 citations