Weak Gravitational Lensing in Fourth Order Gravity

For a general class of analytic $f(R,R_{\alpha\beta}R^{\alpha\beta},R_{\alpha\beta\gamma\delta}R^{\alpha\beta\gamma\delta})$ we discuss the gravitational lensing in the Newtonian Limit of theory. From the properties of Gauss Bonnet invariant it is successful to consider only two curvature invariants between the Ricci and Riemann tensor. Then we analyze the dynamics of photon embedded in a gravitational field of a generic $f(R,R_{\alpha\beta}R^{\alpha\beta})$-Gravity. The metric is time independent and spherically symmetric. The metric potentials are Schwarzschild-like, but there are two additional Yukawa terms linked to derivatives of $f$ with respect to two curvature invariants. Considering the case of a point-like lens, and after of a generic matter distribution of lens, we study the deflection angle and the images angular position. Though the additional Yukawa terms in the gravitational potential modifies dynamics with respect to General Relativity, the geodesic trajectory of photon is unaffected by the modification in the action by only $f(R)$. While we find different results (deflection angle smaller than one of General Relativity) only thank to introduction of a generic function of Ricci tensor square. Finally we can affirm the lensing phenomena for all $f(R)$-Gravities are equal to the ones known from General Relativity. We conclude the paper showing and comparing the deflection angle and image positions for $f(R,R_{\alpha\beta}R^{\alpha\beta})$-Gravity with respect to ones of General Relativity.Comment: 11 pages, 5 figure

Conformal Transformations and Weak Field Limit of Scalar-Tensor Gravity

The weak field limit of scalar tensor theories of gravity is discussed in view of conformal transformations. Specifically, we consider how physical quantities, like gravitational potentials derived in the Newtonian approximation for the same scalar-tensor theory, behave in the Jordan and in the Einstein frame. The approach allows to discriminate features that are invariant under conformal transformations and gives contributions in the debate of selecting the true physical frame. As a particular example, the case of $f(R)$ gravity is considered.Comment: 11 pages, preliminary versio

Astrophysical constraints on extended gravity models

We investigate the propagation of gravitational waves in the context of fourth order gravity nonminimally coupled to a massive scalar field. Using the damping of the orbital period of coalescing stellar binary systems, we impose constraints on the free parameters of extended gravity models. In particular, we find that the variation of the orbital period is a function of three mass scales which depend on the free parameters of the model under consideration; we can constrain these mass scales from current observational data.Comment: 22 pages; minor changes to match published versio

TAX SUBSIDIES AND THE PROVISION OF HEALTH INSURANCE IN SMALL FIRMS

This paper examines the effects of tax subsidies to employer provided health insurance on the distribution of insurance across firms of different sizes. I present a simple model which shows that the tax subsidies may increase the provision of insurance in smaller firms and hence help equalize the distribution of health benefits across firms. I then test this hypothesis using data in both the United States and Canada. My findings indicate that the subsidies reduce the disparity in coverage levels between large and small firms and promote insurance through the workplace instead of on the private market. These findings imply that the tax subsidies may be distorting the labor market by allowing a number of small firms to offer health insurance.

Galaxy rotation curves in f(R,ϕ)f(R,\phi)-gravity

We investigate the possibility to explain theoretically the galaxy rotation curves by a gravitational potential in total absence of dark matter. To this aim an analytic fourth-order theory of gravity, nonminimally coupled with a massive scalar field is considered. Specifically, the interaction term is given by an analytic function $f(R,\phi)$ where $R$ is the Ricci scalar and $\phi$ is the scalar field. The gravitational potential is generated by a point-like source and compared with the so called Sanders's potential that can be exactly reproduced in this case. This result means that the problem of dark matter in spiral galaxies could be fully addressed by revising general relativity at galactic scales and requiring further gravitational degrees of freedom instead of new material components that have not been found out up to now.Comment: 17 pages, 6 figures. To appear in Phys. Rev.

Open Cell Conducting Foams for High Synchrotron Radiation Beam Liners

The possible use of open-cell conductive foams in high synchrotron radiation particle accelerator beam liners is considered. Available materials and modeling tools are reviewed, potential pros and cons are discussed, and preliminary conclusions are drawn.Comment: 21 pages, 5 figures, 3 tables, 51 references, submitted to PR-STA