A comment on "The Cauchy problem of f(R)- gravity", Class. Quantum Grav., 24, 5667 (2007), arXiv:0709.4414

A critical comment on [N. Lanahan--Tremblay and V. Faraoni, 2007, {\it Class. Quantum Grav.}, {\bf 24}, 5667, arXiv:0709.4414] is given discussing the well-formulation of the Chauchy problem for $f(R)$-gravity in metric-affine theories.Comment: 3 page

ERK1/2-Akt1 Crosstalk Regulates Arteriogenesis in Mice and Zebrafish

Arterial morphogenesis is an important and poorly understood process. In particular, the signaling events controlling arterial formation have not been established. We evaluated whether alterations in the balance between ERK1/2 and PI3K signaling pathways could stimulate arterial formation in the setting of defective arterial morphogenesis in mice and zebrafish. Increased ERK1/2 activity in mouse ECs with reduced VEGF responsiveness was achieved in vitro and in vivo by downregulating PI3K activity, suppressing Akt1 but not Akt2 expression, or introducing a constitutively active ERK1/2 construct. Such restoration of ERK1/2 activation was sufficient to restore impaired arterial development and branching morphogenesis in synectin-deficient mice and synectin-knockdown zebrafish. The same approach effectively stimulated arterial growth in adult mice, restoring arteriogenesis in mice lacking synectin and in atherosclerotic mice lacking both LDL-R and ApoB48. We therefore conclude that PI3K-ERK1/2 crosstalk plays a key role in the regulation of arterial growth and that the augmentation of ERK signaling via suppression of the PI3K signaling pathway can effectively stimulate arteriogenesis

Two approaches to testing general relativity in the strong-field regime

Observations of compact objects in the electromagnetic spectrum and the detection of gravitational waves from them can lead to quantitative tests of the theory of general relativity in the strong-field regime following two very different approaches. In the first approach, the general relativistic field equations are modified at a fundamental level and the magnitudes of the potential deviations are constrained by comparison with observations. In the second approach, the exterior spacetimes of compact objects are parametrized in a phenomenological way, the various parameters are measured observationally, and the results are finally compared against the general relativistic predictions. In this article, I discuss the current status of both approaches, focusing on the lessons learned from a large number of recent investigations.Comment: To appear in the proceedings of the conference New Developments in Gravit

Constraint propagation equations of the 3+1 decomposition of f(R) gravity

Theories of gravity other than general relativity (GR) can explain the observed cosmic acceleration without a cosmological constant. One such class of theories of gravity is f(R). Metric f(R) theories have been proven to be equivalent to Brans-Dicke (BD) scalar-tensor gravity without a kinetic term. Using this equivalence and a 3+1 decomposition of the theory it has been shown that metric f(R) gravity admits a well-posed initial value problem. However, it has not been proven that the 3+1 evolution equations of metric f(R) gravity preserve the (hamiltonian and momentum) constraints. In this paper we show that this is indeed the case. In addition, we show that the mathematical form of the constraint propagation equations in BD-equilavent f(R) gravity and in f(R) gravity in both the Jordan and Einstein frames, is exactly the same as in the standard ADM 3+1 decomposition of GR. Finally, we point out that current numerical relativity codes can incorporate the 3+1 evolution equations of metric f(R) gravity by modifying the stress-energy tensor and adding an additional scalar field evolution equation. We hope that this work will serve as a starting point for relativists to develop fully dynamical codes for valid f(R) models.Comment: 25 pages, matches published version in CQG, references update

A new approach to cosmological perturbations in f(R) models

We propose an analytic procedure that allows to determine quantitatively the deviation in the behavior of cosmological perturbations between a given f(R) modified gravity model and a LCDM reference model. Our method allows to study structure formation in these models from the largest scales, of the order of the Hubble horizon, down to scales deeply inside the Hubble radius, without employing the so-called "quasi-static" approximation. Although we restrict our analysis here to linear perturbations, our technique is completely general and can be extended to any perturbative order.Comment: 21 pages, 2 figures; Revised version according to reviewer's suggestions; Typos corrected; Added Reference

The Cauchy problem of f(R) gravity

The initial value problem of metric and Palatini f(R)gravity is studied by using the dynamical equivalence between these theories and Brans-Dicke gravity. The Cauchy problem is well-formulated for metric f(R)gravity in the presence of matter and well-posed in vacuo. For Palatini f(R)gravity, instead, the Cauchy problem is not well-formulated.Comment: 16 latex pages, to appear in Class. Quantum Grav; typographical errors corrected, new references adde

f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Scalar field mass in generalized gravity

The notions of mass and range of a Brans-Dicke-like scalar field in scalar-tensor and f(R) gravity are subject to an ambiguity that hides a potential trap. We spell out this ambiguity and identify a physically meaningful and practical definition for these quantities. This is relevant when giving a mass to this scalar in order to circumvent experimental limits on the PPN parameters coming from Solar System experiments.Comment: 11 pages, no figures, to appear in Class. Quantum Grav. References adde