Recently a remarkable relation has been demonstrated between the observed radial acceleration in disk galaxies and the acceleration predicted on the basis of baryonic matter alone. Here we study this relation within the framework of the modified gravity model MOND. The field equations of MOND automatically imply the radial acceleration relation (RAR) for spherically symmetric galaxies, but for disk galaxies deviations from the relation are expected. Here we investigate whether these deviations are of sufficient magnitude to bring MOND into conflict with the observed relation. In the quasilinear formulation of MOND, to calculate the gravitational field of a given distribution of matter, an intermediate step is to calculate the 'pristine field', which is a simple nonlinear function of the Newtonian field corresponding to the same distribution of matter. Hence, to the extent that the quasilinear gravitational field is approximately equal to the pristine field, the RAR will be satisfied. We show that the difference between the quasilinear and pristine fields obeys the equations of magnetostatics; the curl of the pristine field serves as the source for the difference in the two fields, much as currents serve as sources for the magnetic field. Using the magnetostatic analogy we numerically study the difference between the pristine and quasilinear fields for simple model galaxies with a Gaussian profile. Our principal finding is that the difference between the fields is small compared to the observational uncertainties and that quasilinear MOND is therefore compatible with the observed RAR.

Vacuum radiation has been the subject of theoretical study in both cosmology and condensed matter physics for many decades. Recently there has been impressive progress in experimental realizations as well. Here we study vacuum radiation when a field mode is driven both parametrically and by a classical source. We find that in the Heisenberg picture the field operators of the mode undergo a Bogolyubov transformation combined with a displacement; in the Schrödinger picture the oscillator evolves from the vacuum to a squeezed coherent state. Whereas the Bogolyubov transformation is the same as would be obtained if only the parametric drive were applied the displacement is determined by both the parametric drive and the force. If the force is applied well after the parametric drive then the displacement is the same as would be obtained by the action of the force alone and it is essentially independent of t f , the time lag between the application of the force and the parametric drive. If the force is applied well before the parametric drive the displacement is found to oscillate as a function of t f . This behavior can be understood in terms of quantum interference. A rich variety of behavior is observed for intermediate values of t f . The oscillations can turn off smoothly or grow dramatically and decrease depending on strength of the parametric drive and force and the durations for which they are applied. The displacement depends only on the Fourier component of the force at a single resonant fre-

This paper provides a pedagogical introduction to the physics of extra dimensions by examining the behavior of scalar fields in three landmark models: the ADD, Randall-Sundrum and DGP spacetimes. Results of this analysis provide qualitative insights into the corresponding behavior of gravitational fields and elementary particles in each of these models. In these "brane world" models the familiar four dimensional spacetime of everyday experience is called the brane and is a slice through a higher dimensional spacetime called the bulk. The particles and fields of the standard model are assumed to be confined to the brane while gravitational fields are assumed to propagate in the bulk. For all three spacetimes we calculate the spectrum of propagating scalar wave modes and the scalar field produced by a static point source located on the brane. For the ADD and Randall-Sundrum models, at large distances the field looks like that of a point source in four spacetime dimensions, but at short distances it crosses over to a form appropriate to the higher dimensional spacetime. For the DGP model the field has the higher dimensional form at long distances rather than short. The behavior of these scalar fields, derived using only undergraduate level mathematics, closely mirror the results that one would obtain by performing the far more difficult task of analyzing the behavior of gravitational fields in these spacetimes.

The symmetron model is a scalar-tensor theory of gravity with a screening mechanism that suppresses the effect of the symmetron field at high densities characteristic of the solar system and laboratory scales but allows it to act with gravitational strength at low density on the cosmological scale. We elucidate the screening mechanism by showing that in the quasi-static Newtonian limit there are precise analogies between symmetron gravity and electrostatics for both strong and weak screening. For strong screening we find that large dense bodies behave in a manner analogous to perfect conductors in electrostatics. Based on this analogy we find that the symmetron field exhibits a lightning rod effect wherein the field gradients are enhanced near the ends of pointed or elongated objects. An ellipsoid placed in a uniform symmetron gradient is shown to experience a torque. By symmetry there is no gravitational torque in this case. Hence this effect unmasks the symmetron and might serve as the basis for future laboratory experiments. The symmetron force between a point mass and a large dense body includes a component corresponding to the interaction of the point mass with its image in the larger body. None of these effects have counterparts in the Newtonian limit of Einstein gravity. We discuss the similarities between symmetron gravity and the chameleon model as well as the differences between the two.