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

The neuropilin 1 cytoplasmic domain is required for VEGF-A-dependent arteriogenesis.

Neuropilin 1 (NRP1) plays an important but ill-defined role in VEGF-A signaling and vascular morphogenesis. We show that mice with a knockin mutation that ablates the NRP1 cytoplasmic tail (Nrp1(cyto)) have normal angiogenesis but impaired developmental and adult arteriogenesis. The arteriogenic defect was traced to the absence of a PDZ-dependent interaction between NRP1 and VEGF receptor 2 (VEGFR2) complex and synectin, which delayed trafficking of endocytosed VEGFR2 from Rab5+ to EAA1+ endosomes. This led to increased PTPN1 (PTP1b)-mediated dephosphorylation of VEGFR2 at Y(1175), the site involved in activating ERK signaling. The Nrp1(cyto) mutation also impaired endothelial tubulogenesis in vitro, which could be rescued by expressing full-length NRP1 or constitutively active ERK. These results demonstrate that the NRP1 cytoplasmic domain promotes VEGFR2 trafficking in a PDZ-dependent manner to regulate arteriogenic ERK signaling and establish a role for NRP1 in VEGF-A signaling during vascular morphogenesis

On the Past Asymptotic Dynamics of Non-minimally Coupled Dark Energy

We apply dynamical systems techniques to investigate cosmological models inspired in scalar-tensor theories written in the Einstein frame. We prove that if the potential and the coupling function are sufficiently smooth functions, the scalar field almost always diverges into the past. The dynamics of two important invariant sets is investigated in some detail. By assuming some regularity conditions for the potential and for the coupling function, it is constructed a dynamical system well suited to investigate the dynamics where the scalar field diverges, i.e. near the initial singularity. The critical points therein are investigated and the cosmological solutions associated to them are characterized. We find that our system admits scaling solutions. Some examples are taken from the bibliography to illustrate the major results. Also we present asymptotic expansions for the cosmological solutions near the initial space-time singularity, which extend in a way previous results of other researchers.Comment: 38 pages, 2 figures, accepted for publication in CQ

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

Modified gravity with R-matter couplings and (non-)geodesic motion

We consider alternative theories of gravity with a direct coupling between matter and the Ricci scalar We study the relation between these theories and ordinary scalar-tensor gravity, or scalar-tensor theories which include non-standard couplings between the scalar and matter. We then analyze the motion of matter in such theories, its implications for the Equivalence Principle, and the recent claim that they can alleviate the dark matter problem in galaxies.Comment: typos corrected, minor changes, version published in CQ

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

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

Breakdown of the initial value formulation of scalar-tensor gravity and its physical meaning

We revisit singularities of two distinct kinds in the Cauchy problem of general scalar-tensor theories of gravity (previously discussed in the literature), and of metric and Palatini f(R) gravity, in both their Jordan and Einstein frame representations. Examples and toy models are used to shed light onto the problem and it is shown that, contrary to common lore, the two conformal frames are equivalent with respect to the initial value problem.Comment: 14 pages, LaTex, to appear in Phys. Rev.

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

Gibbons-Hawking Boundary Terms and Junction Conditions for Higher-Order Brane Gravity Models

We derive the most general junction conditions for the fourth-order brane gravity constructed of arbitrary functions of curvature invariants. We reduce these fourth-order theories to second order theories at the expense of introducing new scalar and tensor fields - the scalaron and the tensoron. In order to obtain junction conditions we apply the method of generalized Gibbons-Hawking boundary terms which are appended to the appropriate actions. After assuming the continuity of the scalaron and the tensoron on the brane, we recover junction conditions for such general brane universe models previously obtained by different methods. The derived junction conditions can serve studying the cosmological implications of the higher-order brane gravity models.Comment: REVTEX4, 6 pages, no figures, version to match a JCAP accepted pape