The Pioneer anomaly and the holographic scenario

In this paper we discuss the recently obtained relation between the Verlinde's holographic model and the first phenomenological Modified Newtonian dynamics. This gives also a promising possible explanation to the Pioneer anomaly.Comment: 5 pages, Accepted for publication in Astrophysics & Space Scienc

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

N-body simulations in modified Newtonian dynamics

We describe some results obtained with N-MODY, a code for N-body simulations of collisionless stellar systems in modified Newtonian dynamics (MOND). We found that a few fundamental dynamical processes are profoundly different in MOND and in Newtonian gravity with dark matter. In particular, violent relaxation, phase mixing and galaxy merging take significantly longer in MOND than in Newtonian gravity, while dynamical friction is more effective in a MOND system than in an equivalent Newtonian system with dark matter.Comment: 4 pages, no figures. To appear in EAS Publication Series (Proceedings of Symposium 7 of the JENAM 2008, Vienna

Probing Brownstein-Moffat Gravity via Numerical Simulations

In the standard scenario of the Newtonian gravity, a late-type galaxy (i.e., a spiral galaxy) is well described by a disk and a bulge embedded in a halo mainly composed by dark matter. In Brownstein-Moffat gravity, there is a claim that late-type galaxy systems would not need to have halos, avoiding as a result the dark matter problem, i.e., a modified gravity (non-Newtonian) would account for the galactic structure with no need of dark matter. In the present paper, we probe this claim via numerical simulations. Instead of using a "static galaxy," where the centrifugal equilibrium is usually adopted, we probe the Brownstein-Moffat gravity dynamically via numerical $N$-body simulations.Comment: 33 pages and 14 figures - To appear in The Astrophysical Journa

Gravitational anomalies signaling the breakdown of classical gravity

Recent observations for three types of astrophysical systems severely challenge the GR plus dark matter scenario, showing a phenomenology which is what modified gravity theories predict. Stellar kinematics in the outskirts of globular clusters show the appearance of MOND type dynamics on crossing the $a_{0}$ threshold. Analysis shows a ``Tully-Fisher'' relation in these systems, a scaling of dispersion velocities with the fourth root of their masses. Secondly, an anomaly has been found at the unexpected scales of wide binaries in the solar neighbourhood. Binary orbital velocities cease to fall along Keplerian expectations, and settle at a constant value, exactly on crossing the $a_{0}$ threshold. Finally, the inferred infall velocity of the bullet cluster is inconsistent with the standard cosmological scenario, where much smaller limit encounter velocities appear. This stems from the escape velocity limit present in standard gravity; the ``bullet'' should not hit the ``target'' at more than the escape velocity of the joint system, as it very clearly did. These results are consistent with extended gravity, but would require rather contrived explanations under GR, each. Thus, observations now put us in a situation where modifications to gravity at low acceleration scales cease to be a matter of choice, to now become inevitable.Comment: 10 pages, 5 figures, Astrophysics and Space Science Proceedings 38, 4

Propagation of gravitational waves in multimetric gravity

We discuss the propagation of gravitational waves in a recently discussed class of theories containing N >= 2 metric tensors and a corresponding number of standard model copies. Using the formalism of gauge-invariant linear perturbation theory we show that all gravitational waves propagate at the speed of light. We then employ the Newman-Penrose formalism to show that two to six polarizations of gravitational waves may exist, depending on the parameters entering the equations of motion. This corresponds to E(2) representations N_2, N_3, III_5 and II_6. We finally apply our general discussion to a recently presented concrete multimetric gravity model and show that it is of class N_2, i.e., it allows only two tensor polarizations, as it is the case for general relativity. Our results provide the theoretical background for tests of multimetric gravity theories using the upcoming gravitational wave experiments.Comment: 21 pages, no figures, journal versio

Massive particles in acoustic space-times emergent inertia and passive gravity

I show that massive-particle dynamics can be simulated by a weak, spherical, external perturbation on a potential flow in an ideal fluid. The effective Lagrangian is of the form mc^2L(U^2/c^2), where U is the velocity of the particle relative to the fluid and c the speed of sound. This can serve as a model for emergent relativistic inertia a la Mach's principle with m playing the role of inertial mass, and also of analog gravity where it is also the passive gravitational mass. m depends on the particle type and intrinsic structure, while L is universal: For D dimensional particles L is proportional to the hypergeometric function F(1,1/2;D/2;U^2/c^2). Particles fall in the same way in the analog gravitational field independent of their internal structure, thus satisfying the weak equivalence principle. For D less or equal 5 they all have a relativistic limit with the acquired energy and momentum diverging as U approaches c. For D less or equal 7 the null geodesics of the standard acoustic metric solve our equation of motion. Interestingly, for D=4 the dynamics is very nearly Lorentzian. The particles can be said to follow the geodesics of a generalized acoustic metric of a Finslerian type that shares the null geodesics with the standard acoustic metric. In vortex geometries, the ergosphere is automatically the static limit. As in the real world, in ``black hole'' geometries circular orbits do not exist below a certain radius that occurs outside the horizon. There is a natural definition of antiparticles; and I describe a mock particle vacuum in whose context one can discuss, e.g., particle Hawking radiation near event horizons.Comment: 15 page: version published in Physical Review

Mapping the galactic gravitational potential with peculiar acceleration

It has been suggested recently that the change in cosmological redshift (the Sandage test of expansion) could be observed in the next generation of large telescopes and ultra-stable spectrographs. In a recent paper we estimated the change of peculiar velocity, i.e. the peculiar acceleration, in nearby galaxies and clusters and shown it to be of the same order of magnitude as the typical cosmological signal. Mapping the acceleration field allows for a reconstruction of the galactic gravitational potential without assuming virialization. In this paper we focus on the peculiar acceleration in our own Galaxy, modeled as a Kuzmin disc and a dark matter spherical halo. We estimate the peculiar acceleration for all known Galactic globular clusters and find some cases with an expected velocity shift in excess of 20 cm/sec for observations fifteen years apart, well above the typical cosmological acceleration. We then compare the predicted signal for a MOND (modified Newtonian dynamics) model in which the spherical dark matter halo is absent. We find that the signal pattern is qualitatively different, showing that the peculiar acceleration field could be employed to test competing theories of gravity. However the difference seems too small to be detectable in the near future.Comment: 11 pages, 10 figures, 3 tables, minor changes, accepted for publication by MNRA

Virial mass in DGP brane cosmology

We study the virial mass discrepancy in the context of a DPG brane-world scenario and show that such a framework can offer viable explanations to account for the mass discrepancy problem. This is done by defining a geometrical mass $\mathcal{N}$ that we prove to be proportional to the virial mass. Estimating $\mathcal{N}$ using observational data, we show that it behaves linearly with $r$ and has a value of the order of $M_{200}$, pointing to a possible resolution of the virial mass discrepancy. We also obtain the radial velocity dispersion of galaxy clusters and show that it is compatible with the radial velocity dispersion profile of such clusters. This velocity dispersion profile can be used to differentiate various models predicting the virial mass.Comment: 12 pages, 1 figure, to appear in CQ

Organizing the innovation process : complementarities in innovation networking

This paper contributes to the developing literature on complementarities in organizational design. We test for the existence of complementarities in the use of external networking between stages of the innovation process in a sample of UK and German manufacturing plants. Our evidence suggests some differences between the UK and Germany in terms of the optimal combination of innovation activities in which to implement external networking. Broadly, there is more evidence of complementarities in the case of Germany, with the exception of the product engineering stage. By contrast, the UK exhibits generally strong evidence of substitutability in external networking in different stages, except between the identification of new products and product design and development stages. These findings suggest that previous studies indicating strong complementarity between internal and external knowledge sources have provided only part of the picture of the strategic dilemmas facing firms