How Material Heterogeneity Creates Rough Fractures

Fractures are a critical process in how materials wear, weaken, and fail whose unpredictable behavior can have dire consequences. While the behavior of smooth cracks in ideal materials is well understood, it is assumed that for real, heterogeneous systems, fracture propagation is complex, generating rough fracture surfaces that are highly sensitive to specific details of the medium. Here we show how fracture roughness and material heterogeneity are inextricably connected via a simple framework. Studying hydraulic fractures in brittle hydrogels that have been supplemented with microbeads or glycerol to create controlled material heterogeneity, we show that the morphology of the crack surface depends solely on one parameter: the probability to perturb the front above a critical size to produce a step-like instability. This probability scales linearly with the number density, and as heterogeneity size to the $5/2$ power. The ensuing behavior is universal and is captured by the 1D ballistic propagation and annihilation of steps along the singular fracture front

Challenges for Superstring Cosmology

We consider whether current notions about superstring theory below the Planck scale are compatible with cosmology. We find that the anticipated form for the dilaton interaction creates a serious roadblock for inflation and makes it unlikely that the universe ever reaches a state with zero cosmological constant and time-independent gravitational constant.Comment: 14 pages, 2 figures available as eps files on reques

Strong Brane Gravity and the Radion at Low Energies

For the 2-brane Randall-Sundrum model, we calculate the bulk geometry for strong gravity, in the low matter density regime, for slowly varying matter sources. This is relevant for astrophysical or cosmological applications. The warped compactification means the radion can not be written as a homogeneous mode in the orbifold coordinate, and we introduce it by extending the coordinate patch approach of the linear theory to the non-linear case. The negative tension brane is taken to be in vacuum. For conformally invariant matter on the positive tension brane, we solve the bulk geometry as a derivative expansion, formally summing the `Kaluza-Klein' contributions to all orders. For general matter we compute the Einstein equations to leading order, finding a scalar-tensor theory with $\omega(\Psi) \propto \Psi / (1 - \Psi)$, and geometrically interpret the radion. We comment that this radion scalar may become large in the context of strong gravity with low density matter. Equations of state allowing $(\rho - 3 P)$ to be negative, can exhibit behavior where the matter decreases the distance between the 2 branes, which we illustrate numerically for static star solutions using an incompressible fluid. For increasing stellar density, the branes become close before the upper mass limit, but after violation of the dominant energy condition. This raises the interesting question of whether astrophysically reasonable matter, and initial data, could cause branes to collide at low energy, such as in dynamical collapse.Comment: 24 pages, 3 figure

Seeking Evolution of Dark Energy

We study how observationally to distinguish between a cosmological constant (CC) and an evolving dark energy with equation of state $\omega(Z)$. We focus on the value of redshift Z* at which the cosmic late time acceleration begins and $\ddot{a}(Z^{*}) = 0$. Four $\omega(Z)$ are studied, including the well-known CPL model and a new model that has advantages when describing the entire expansion era. If dark energy is represented by a CC model with $\omega \equiv -1$, the present ranges for $\Omega_{\Lambda}(t_0)$ and $\Omega_m(t_0)$ imply that Z* = 0.743 with 4% error. We discuss the possible implications of a model independent measurement of Z* with better accuracy.Comment: 9 pages, LaTeX, 5 figure

Extended Inflation from Strings

We study the possibility of extended inflation in the effective theory of gravity from strings compactified to four dimensions and find that it strongly depends on the mechanism of supersymmetry breaking. We consider a general class of string--inspired models which are good candidates for successful extended inflation. In particular, the $\omega$--problem of ordinary extended inflation is automatically solved by the production of only very small bubbles until the end of inflation. We find that the inflaton field could belong either to the untwisted or to the twisted massless sectors of the string spectrum, depending on the supersymmetry breaking superpotential.Comment: 18p

High frequency oscillations of Newton's constant induced by inflation

We examine the possibility that an epoch of inflationary expansion induces high-frequency oscillations of Newton's constant, $G$. The effect occurs because inflation can shift the expectation value of a non-minimally coupled, Brans-Dicke-like field away from the minimum of its effective potential. At some time after inflation ends, the field begins to oscillate, resulting in periodic variations in $G$. We find conditions for which the oscillation energy would be sufficient to close the universe, consistent with all known constraints from cosmology and local tests of general relativity.Comment: 30 pages, Penn Preprint UPR-0628T, Wash. U. Preprint WUGRAV 94-10 Four figures available by ftp (read comment at head of file

A time varying speed of light as a solution to cosmological puzzles

We consider the cosmological implications of light travelling faster in the early Universe. We propose a prescription for deriving corrections to the cosmological evolution equations while the speed of light $c$ is changing. We then show how the horizon, flatness, and cosmological constant problems may be solved. We also study cosmological perturbations in this scenario and show how one may solve the homogeneity and isotropy problems. As it stands, our scenario appears to most easily produce extreme homogeneity, requiring structure to be produced in the Standard Big Bang epoch. Producing significant perturbations during the earlier epoch would require a rather careful design of the function $c(t)$. The large entropy inside the horizon nowadays can also be accounted for in this scenario.Comment: To be published in Physical Review D. Note added referring to John Moffat's early work on VSL theorie

Quintessence, the Gravitational Constant, and Gravity

Dynamical vacuum energy or quintessence, a slowly varying and spatially inhomogeneous component of the energy density with negative pressure, is currently consistent with the observational data. One potential difficulty with the idea of quintessence is that couplings to ordinary matter should be strongly suppressed so as not to lead to observable time variations of the constants of nature. We further explore the possibility of an explicit coupling between the quintessence field and the curvature. Since such a scalar field gives rise to another gravity force of long range (\simg H^{-1}_0), the solar system experiments put a constraint on the non-minimal coupling: |\xi| \siml 10^{-2}.Comment: 9 pages, a version to be published in Phys.Rev.

Cosmic Acceleration in Brans-Dicke Cosmology

We consider Brans-Dicke theory with a self-interacting potential in Einstein conformal frame. We show that an accelerating expansion is possible in a spatially flat universe for large values of the Brans-Dicke parameter consistent with local gravity experiments.Comment: 10 Pages, 3 figures, To appear in General Relativity and Gravitatio

General Relativity as an Attractor in Scalar-Tensor Stochastic Inflation

Quantum fluctuations of scalar fields during inflation could determine the very large-scale structure of the universe. In the case of general scalar-tensor gravity theories these fluctuations lead to the diffusion of fundamental constants like the Planck mass and the effective Brans--Dicke parameter, $\omega$. In the particular case of Brans--Dicke gravity, where $\omega$ is constant, this leads to runaway solutions with infinitely large values of the Planck mass. However, in a theory with variable $\omega$ we find stationary probability distributions with a finite value of the Planck mass peaked at exponentially large values of $\omega$ after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.Comment: LaTeX (with RevTex) 11 pages, 2 uuencoded figures appended, also available on WWW via http://star.maps.susx.ac.uk/index.htm