The Force of Gravity from a Lagrangian containing Inverse Powers of the Ricci Scalar

We determine the gravitational response to a diffuse source, in a locally de Sitter background, of a class of theories which modify the Einstein-Hilbert action by adding a term proportional to an inverse power of the Ricci scalar. We find a linearly growing force which is not phenomenologically acceptable.Comment: 10 pages, LaTeX 2 epsilon, no figures. Minor conceptual change

The Axial Anomaly in D=3+1 Light-Cone QED

We consider $(3+1)$-dimensional, Dirac electrons of arbitrary mass, propagating in the presence of electric and magnetic fields which are both parallel to the $x^3$ axis. The magnetic field is constant in space and time whereas the electric field depends arbitrarily upon the light-cone time parameter $x^+ = (x^0 + x^3)/\sqrt{2}$. We present an explicit solution to the Heisenberg equations for the electron field operator in this background. The electric field results in the creation of electron-positron pairs. We compute the expectation values of the vector and axial vector currents in the presence of a state which is free vacuum at $x^+ = 0$. Both current conservation and the standard result for the axial vector anomaly are verified for the first time ever in $(3+1)$-dimensional light-cone QED. An interesting feature of our operator solution is the fact that it depends in an essential way upon operators from the characteristic at $x^- = -L$, in addition to the usual dependence upon operators at $x^+ = 0$. This dependence survives even in the limit of infinite $L$. Ignoring the $x^-$ operators leads to a progressive loss of unitarity, to the violation of current conservation, to the loss of renormalizability, and to an incorrect result for the axial vector anomaly.Comment: 31 pages, LaTeX 2 epsilon, no figures, some typoes corrected for publicatio

Gravitational waves and lensing of the metric theory proposed by Sobouti

We investigate in detail two physical properties of the metric f(R) theory developed by Sobouti (2007). We first look for the possibility of producing gravitational waves that travel at the speed of light. We then check the possibility of producing extra bending in the lenses produced by the theory. We do this by using standard weak field approximations to the gravitational field equations that appear in Sobouti's theory. We show in this article that the metric theory of gravitation proposed by Sobouti (2007) predicts the existence of gravitational waves travelling at the speed of light in vacuum. In fact, this is proved in general terms for all metric theories of gravity which can be expressed as powers of Ricci's scalar. We also show that an extra additional lensing as compared to the one predicted by standard general relativity is produced. These two points are generally considered to be of crucial importance in the development of relativistic theories of gravity that could provide an alternative description to the dark matter paradigm.Comment: 10 pages, 2 figures. Added a comment on the recent article by Saffari (arXiv:0704.3345v1) and small typos as well as general comments in the introuduction and conclusio

Comparing scalar-tensor gravity and f(R)-gravity in the Newtonian limit

Recently, a strong debate has been pursued about the Newtonian limit (i.e. small velocity and weak field) of fourth order gravity models. According to some authors, the Newtonian limit of $f(R)$-gravity is equivalent to the one of Brans-Dicke gravity with $\omega_{BD} = 0$, so that the PPN parameters of these models turn out to be ill defined. In this paper, we carefully discuss this point considering that fourth order gravity models are dynamically equivalent to the O'Hanlon Lagrangian. This is a special case of scalar-tensor gravity characterized only by self-interaction potential and that, in the Newtonian limit, this implies a non-standard behavior that cannot be compared with the usual PPN limit of General Relativity. The result turns out to be completely different from the one of Brans-Dicke theory and in particular suggests that it is misleading to consider the PPN parameters of this theory with $\omega_{BD} = 0$ in order to characterize the homologous quantities of $f(R)$-gravity. Finally the solutions at Newtonian level, obtained in the Jordan frame for a $f(R)$-gravity, reinterpreted as a scalar-tensor theory, are linked to those in the Einstein frame.Comment: 9 page

Possible Enhancement of High Frequency Gravitational Waves

We study the tensor perturbations in a class of non-local, purely gravitational models which naturally end inflation in a distinctive phase of oscillations with slight and short violations of the weak energy condition. We find the usual generic form for the tensor power spectrum. The presence of the oscillatory phase leads to an enhancement of gravitational waves with frequencies somewhat less than 10^{10} Hz.Comment: 27 pages, 11 figures, LaTeX.2

A Note on Energy-Momentum Conservation in Palatini Formulation of L(R) Gravity

By establishing that Palatini formulation of $L(R)$ gravity is equivalent to $\omega=-3/2$ Brans-Dicke theory, we show that energy-momentum tensor is covariantly conserved in this type of modified gravity theory.Comment: 7 page

Modified gravity without dark matter

On an empirical level, the most successful alternative to dark matter in bound gravitational systems is the modified Newtonian dynamics, or MOND, proposed by Milgrom. Here I discuss the attempts to formulate MOND as a modification of General Relativity. I begin with a summary of the phenomenological successes of MOND and then discuss the various covariant theories that have been proposed as a basis for the idea. I show why these proposals have led inevitably to a multi-field theory. I describe in some detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and discuss its successes and shortcomings. This lecture is primarily pedagogical and directed to those with some, but not a deep, background in General RelativityComment: 28 pages, 10 figures, lecture given at Third Aegean Summer School, The Invisible Universe: Dark Matter and Dark Energy, minor errors corrected, references update

R2R^2 corrections to the cosmological dynamics of inflation in the Palatini formulation

We investigate the corrections to the inflationary cosmological dynamics due to a $R^2$ term in the Palatini formulation which may arise as quantum corrections to the effective Lagrangian in early universe. We found that the standard Friedmann equation will not be changed when the scalar field is in the potential energy dominated era. However, in the kinetic energy dominated era, the standard Friedmann equation will be modified and in the case of closed and flat universe, the Modified Friedmann equation will automatically require that the initial kinetic energy density of the scalar field must be in sub-Planckian scale.Comment: 11 pages, no figures. Accepted by Class.Quant.Grav.v2:References adde

Matter loops corrected modified gravity in Palatini formulation

Recently, corrections to the standard Einstein-Hilbert action are proposed to explain the current cosmic acceleration in stead of introducing dark energy. In the Palatini formulation of those modified gravity models, there is an important observation due to Arkani-Hamed: matter loops will give rise to a correction to the modified gravity action proportional to the Ricci scalar of the metric. In the presence of such term, we show that the current forms of modified gravity models in Palatini formulation, specifically, the 1/R gravity and $\ln R$ gravity, will have phantoms. Then we study the possible instabilities due to the presence of phantom fields. We show that the strong instability in the metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales for the phantom fields may be long enough for the theories to make sense as effective field theory . On the other hand, if we change the sign of the modification terms to eliminate the phantoms, some other inconsistencies will arise for the various versions of the modified gravity models. Finally, we comment on the universal property of the Palatini formulation of the matter loops corrected modified gravity models and its implications.Comment: 11 pages, 1 figures, References adde