Cosmological Imprint of an Energy Component with General Equation of State

We examine the possibility that a significant component of the energy density of the universe has an equation-of-state different from that of matter, radiation or cosmological constant ($\Lambda$). An example is a cosmic scalar field evolving in a potential, but our treatment is more general. Including this component alters cosmic evolution in a way that fits current observations well. Unlike $\Lambda$, it evolves dynamically and develops fluctuations, leaving a distinctive imprint on the microwave background anisotropy and mass power spectrum.Comment: revised version, with added references, to appear in Phys. Rev. Lett. (4 pages Latex, 2 postscript figures

Kasner and Mixmaster behavior in universes with equation of state w \ge 1

We consider cosmological models with a scalar field with equation of state $w\ge 1$ that contract towards a big crunch singularity, as in recent cyclic and ekpyrotic scenarios. We show that chaotic mixmaster oscillations due to anisotropy and curvature are suppressed, and the contraction is described by a homogeneous and isotropic Friedmann equation if $w>1$. We generalize the results to theories where the scalar field couples to p-forms and show that there exists a finite value of $w$, depending on the p-forms, such that chaotic oscillations are suppressed. We show that $Z_2$ orbifold compactification also contributes to suppressing chaotic behavior. In particular, chaos is avoided in contracting heterotic M-theory models if $w>1$ at the crunch.Comment: 25 pages, 2 figures, minor changes, references adde

Optical Absorption Characteristics of Silicon Nanowires for Photovoltaic Applications

Solar cells have generated a lot of interest as a potential source of clean renewable energy for the future. However a big bottleneck in wide scale deployment of these energy sources remain the low efficiency of these conversion devices. Recently the use of nanostructures and the strategy of quantum confinement have been as a general approach towards better charge carrier generation and capture. In this article we have presented calculations on the optical characteristics of nanowires made out of Silicon. Our calculations show these nanowires form excellent optoelectronic materials and may yield efficient photovoltaic devices

Formal Verification of Neural Network Controlled Autonomous Systems

In this paper, we consider the problem of formally verifying the safety of an autonomous robot equipped with a Neural Network (NN) controller that processes LiDAR images to produce control actions. Given a workspace that is characterized by a set of polytopic obstacles, our objective is to compute the set of safe initial conditions such that a robot trajectory starting from these initial conditions is guaranteed to avoid the obstacles. Our approach is to construct a finite state abstraction of the system and use standard reachability analysis over the finite state abstraction to compute the set of the safe initial states. The first technical problem in computing the finite state abstraction is to mathematically model the imaging function that maps the robot position to the LiDAR image. To that end, we introduce the notion of imaging-adapted sets as partitions of the workspace in which the imaging function is guaranteed to be affine. We develop a polynomial-time algorithm to partition the workspace into imaging-adapted sets along with computing the corresponding affine imaging functions. Given this workspace partitioning, a discrete-time linear dynamics of the robot, and a pre-trained NN controller with Rectified Linear Unit (ReLU) nonlinearity, the second technical challenge is to analyze the behavior of the neural network. To that end, we utilize a Satisfiability Modulo Convex (SMC) encoding to enumerate all the possible segments of different ReLUs. SMC solvers then use a Boolean satisfiability solver and a convex programming solver and decompose the problem into smaller subproblems. To accelerate this process, we develop a pre-processing algorithm that could rapidly prune the space feasible ReLU segments. Finally, we demonstrate the efficiency of the proposed algorithms using numerical simulations with increasing complexity of the neural network controller

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

Quantum Cosmology for the General Bianchi Type II, VI(Class A) and VII(Class A) vacuum geometries

The canonical quantization of the most general minisuperspace actions --i.e. with all six scale factor as well as the lapse function and the shift vector present-- describing the vacuum type II, VI and VII geometries, is considered. The reduction to the corresponding physical degrees of freedom is achieved through the usage of the linear constraints as well as the quantum version of the entire set of classical integrals of motion.Comment: 23 pages, LaTeX2e, No figure

A note on wavemap-tensor cosmologies

We examine theories of gravity which include finitely many coupled scalar fields with arbitrary couplings to the curvature (wavemaps). We show that the most general scalar-tensor $\sigma$-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a novel way due to the combined effect of arbitrary curvature couplings and wavemap self-interactions. A new interpretation of the conformal equivalence theorem proved for such `wavemap-tensor' theories through brane-bulk dynamics is also discussed.Comment: 8 pages, LaTeX, to appear in the Proceedings of the 2nd Hellenic Cosmology Workshop, National Observatory of Athens, April 21-22, 2001, (Kluwer 2001

Two dimensional QCD and abelian bosonization

A bosonized action, that reproduces the structure of the 't Hooft equation for $QCD_2$ in the large-$N$ limit, up to regularization dependent terms, is derived.Comment: paper revised, several signs and coefficients corrected. A comment on regularization dependence and several references adde

Quintessence and cosmic acceleration

A cosmological model with perfect fluid and self-interacting quintessence field is considered in the framework of the spatially flat Friedmann-Robertson-Walker (FRW) geometry. By assuming that all physical quantities depend on the volume scale factor of the Universe, the general solution of the gravitational field equations can be expressed in an exact parametric form. The quintessence field is a free parameter. With an appropriate choice of the scalar field a class of exact solutions is obtained, with an exponential type scalar field potential fixed via the gravitational field equations. The general physical behavior of the model is consistent with the recent cosmological scenario favored by supernova Type Ia observations, indicating an accelerated expansion of the Universe.Comment: 6 pages, 3 figures, to appear in Int. J. Mod. Phys.

Matter density perturbations in interacting quintessence models

Models with dark energy decaying into dark matter have been proposed to solve the coincidence problem in cosmology. We study the effect of such coupling in the matter power spectrum. Due to the interaction, the growth of matter density perturbations during the radiation dominated regime is slower compared to non-interacting models with the same ratio of dark matter to dark energy today. This effect introduces a damping on the power spectrum at small scales proportional to the strength of the interaction and similar to the effect generated by ultrarelativistic neutrinos. The interaction also shifts matter--radiation equality to larger scales. We compare the matter power spectrum of interacting quintessence models with the measurments of 2dFGRS. We particularize our study to models that during radiation domination have a constant dark matter to dark energy ratio.Comment: 11 pages, 4 figures, accepted for publication in Phys. Rev.