Adventures in Friedmann Cosmology: An Educationally Detailed Expansion of the Cosmological Friedmann Equations

The general relativistic cosmological Friedmann equations which describe how the scale factor of the universe evolves are expanded explicitly to include energy forms not usually seen. The evolution of the universe as predicted by the Friedmann equations when dominated by a single, isotropic, stable, static, perfect-fluid energy form is discussed for different values of its gravitational pressure to density ratio $w$. These energy forms include phantom energy ($w<-1$), cosmological constant ($w=-1$), domain walls ($w = -2/3$), cosmic strings ($w = -1/3$), normal matter ($w = 0$), radiation and relativistic matter ($w = 1/3$), and a previously little-discussed form of energy called "ultralight" ($w>1/3$). A brief history and possible futures of Friedmann universes dominated by a single energy form are discussed.Comment: 32 pages, 4 tables; modified version accepted for publication in the American Journal of Physic

Shock waves and Birkhoff's theorem in Lovelock gravity

Spherically symmetric shock waves are shown to exist in Lovelock gravity. They amount to a change of branch of the spherically symmetric solutions across a null hypersurface. The implications of their existence for the status of Birkhoff's theorem in the theory is discussed.Comment: 9 pages, no figures, clarifying changes made in the text of section III and references adde

A simple proof of Birkhoff's theorem for cosmological constant

We provide a simple, unified proof of Birkhoff's theorem for the vacuum and cosmological constant case, emphasizing its local nature. We discuss its implications for the maximal analytic extensions of Schwarzschild, Schwarzschild(-anti)-de Sitter and Nariai spacetimes. In particular, we note that the maximal analytic extensions of extremal and over-extremal Schwarzschild-de Sitter spacetimes exhibit no static region. Hence the common belief that Birkhoff's theorem implies staticity is false for the case of positive cosmological constant. Instead, the correct point of view is that generalized Birkhoff's theorems are local uniqueness theorems whose corollary is that locally spherically symmetric solutions of Einstein's equations exhibit an additional local killing vector field.Comment: 10 pages, 5 figures References added; typo in eqn. 12 fixe

A two-mass expanding exact space-time solution

In order to understand how locally static configurations around gravitationally bound bodies can be embedded in an expanding universe, we investigate the solutions of general relativity describing a space-time whose spatial sections have the topology of a 3-sphere with two identical masses at the poles. We show that Israel junction conditions imply that two spherically symmetric static regions around the masses cannot be glued together. If one is interested in an exterior solution, this prevents the geometry around the masses to be of the Schwarzschild type and leads to the introduction of a cosmological constant. The study of the extension of the Kottler space-time shows that there exists a non-static solution consisting of two static regions surrounding the masses that match a Kantowski-Sachs expanding region on the cosmological horizon. The comparison with a Swiss-Cheese construction is also discussed.Comment: 15 pages, 5 figures. Replaced to match the published versio

The Tensor-Vector-Scalar theory and its cosmology

Over the last few decades, astronomers and cosmologists have accumulated vast amounts of data clearly demonstrating that our current theories of fundamental particles and of gravity are inadequate to explain the observed discrepancy between the dynamics and the distribution of the visible matter in the Universe. The Modified Newtonian Dynamics (MOND) proposal aims at solving the problem by postulating that Newton's second law of motion is modified for accelerations smaller than ~10^{-10}m/s^2. This simple amendment, has had tremendous success in explaining galactic rotation curves. However, being non-relativistic, it cannot make firm predictions for cosmology. A relativistic theory called Tensor-Vector-Scalar (TeVeS) has been proposed by Bekenstein building on earlier work of Sanders which has a MOND limit for non-relativistic systems. In this article I give a short introduction to TeVeS theory and focus on its predictions for cosmology as well as some non-cosmological studies.Comment: 44 pages, topical review for Classical and Quantum Gravit

Birkhoff's Theorem in f(T) Gravity up to the Perturbative Order

f(T) gravity, a generally modified teleparallel gravity, has become very popular in recent times as it is able to reproduce the unification of inflation and late-time acceleration without the need of a dark energy component or an inflation field. In this present work, we investigate specifically the range of validity of Birkhoff's theorem with the general tetrad field via perturbative approach. At zero order, Birkhoff's theorem is valid and the solution is the well known Schwarzschild-(A)dS metric. Then considering the special case of the diagonal tetrad field, we present a new spherically symmetric solution in the frame of f(T) gravity up to the perturbative order. The results with the diagonal tetrad field satisfy the physical equivalence between the Jordan and the so-called Einstein frames, which are realized via conformal transformation, at least up to the first perturbative order.Comment: 8 pages, no figure. Final version, accepted for publication in EPJ

Age-Related Attenuation of Dominant Hand Superiority

The decline of motor performance of the human hand-arm system with age is well-documented. While dominant hand performance is superior to that of the non-dominant hand in young individuals, little is known of possible age-related changes in hand dominance. We investigated age-related alterations of hand dominance in 20 to 90 year old subjects. All subjects were unambiguously right-handed according to the Edinburgh Handedness Inventory. In Experiment 1, motor performance for aiming, postural tremor, precision of arm-hand movement, speed of arm-hand movement, and wrist-finger speed tasks were tested. In Experiment 2, accelerometer-sensors were used to obtain objective records of hand use in everyday activities

Granulocyte-Colony Stimulating Factor (G-CSF) in Stroke Patients with Concomitant Vascular Disease—A Randomized Controlled Trial

G-CSF has been shown in animal models of stroke to promote functional and structural regeneration of the central nervous system. It thus might present a therapy to promote recovery in the chronic stage after stroke.Here, we assessed the safety and tolerability of G-CSF in chronic stroke patients with concomitant vascular disease, and explored efficacy data. 41 patients were studied in a double-blind, randomized approach to either receive 10 days of G-CSF (10 µg/kg body weight/day), or placebo. Main inclusion criteria were an ischemic infarct >4 months prior to inclusion, and white matter hyperintensities on MRI. Primary endpoint was number of adverse events. We also explored changes in hand motor function for activities of daily living, motor and verbal learning, and finger tapping speed, over the course of the study.Adverse events (AEs) were more frequent in the G-CSF group, but were generally graded mild or moderate and from the known side-effect spectrum of G-CSF. Leukocyte count rose after day 2 of G-CSF dosing, reached a maximum on day 8 (mean 42/nl), and returned to baseline 1 week after treatment cessation. No significant effect of treatment was detected for the primary efficacy endpoint, the test of hand motor function.These results demonstrate the feasibility, safety and reasonable tolerability of subcutaneous G-CSF in chronic stroke patients. This study thus provides the basis to explore the efficacy of G-CSF in improving chronic stroke-related deficits.ClinicalTrials.gov NCT00298597

Robotic neurorehabilitation: a computational motor learning perspective

Conventional neurorehabilitation appears to have little impact on impairment over and above that of spontaneous biological recovery. Robotic neurorehabilitation has the potential for a greater impact on impairment due to easy deployment, its applicability across of a wide range of motor impairment, its high measurement reliability, and the capacity to deliver high dosage and high intensity training protocols