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.

Brane-World Gravity

We present a simple mechanism for obtaining large-field inflation, and hence a gravitational wave signature, from string theory compactified on twisted tori. For nil manifolds, we obtain a leading inflationary potential proportional to ${\ensuremath{\phi}}^{2/3}$ in terms of the canonically normalized field $\ensuremath{\phi}$, yielding predictions for the tilt of the power spectrum and the tensor-to-scalar ratio, ${n}_{s}\ensuremath{\approx}0.98$ and $r\ensuremath{\approx}0.04$ with 60 e-foldings of inflation; we note also the possibility of a variant with a candidate inflaton potential proportional to ${\ensuremath{\phi}}^{2/5}$. The basic mechanism involved in extending the field range---monodromy in $D$-branes as they move in circles on the manifold---arises in a more general class of compactifications, though our methods for controlling the corrections to the slow-roll parameters require additional symmetries.

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Monodromy in the CMB: Gravity Waves and String Inflation

This is a pedagogical review on primordial non-Gaussianities from inflation models. We introduce formalisms and techniques that are used to compute such quantities. We review different mechanisms which can generate observable large non-Gaussianities during inflation, and distinctive signatures they leave on the non-Gaussian profiles. They are potentially powerful probes to the dynamics of inflation. We also provide a non-technical and qualitative summary of the main results and underlying physics.

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Primordial Non-Gaussianities from Inflation Models

A Critical Review of Classical Bouncing Cosmologies

We study cosmological perturbations in general inflation models with multiple scalar fields and arbitrary kinetic terms, with special emphasis on the multifield extension of Dirac-Born-Infeld (DBI) inflation. We compute the second-order action governing the dynamics of linear perturbations in the most general case. Specializing to DBI inflation, we show that the adiabatic and entropy modes propagate with a common effective sound speed and are thus amplified at sound horizon crossing. In the small sound speed limit, we find that the amplitude of the entropy modes is much higher than that of the adiabatic modes. We also derive, in the general case, the third-order action which is useful for studying primordial non-Gaussianities generated during inflation. In the DBI case, we compute the dominant contributions to non-Gaussianities, which depend on both the adiabatic and entropy modes.

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Primordial perturbations and non-Gaussianities in DBI and general multifield inflation

We present a brief review of recent advances in string cosmology Starting with the Dilaton-Moduli Cosmology (known also as the Pre Big Bang), we go on to include the effects of axion fields and address the thorny issue of the Graceful Exit in String Cosmology This is followed by a review of density perturbations arising in string cosmology and we finish with a brief introduction to the impact moving five branes can have on the Dilaton-Moduli cosmological solutions

Edmund J Copeland

Papers

String Cosmology