Cosmological fluctuation growth in bimetric MOND

I look at the growth of weak density inhomogeneities of nonrelativistic matter, in bimetric-MOND (BIMOND) cosmology. I concentrate on matter-twin-matter-symmetric versions of BIMOND, and assume that, on average, the universe is symmetrically populated in the two sectors. MOND effects are absent in an exactly symmetric universe, apart from the appearance of a cosmological constant, Lambda~(a0/c)^2. MOND effects-local and cosmological-do enter when density inhomogeneities that differ in the two sectors appear and develop. MOND later takes its standard form in systems that are islands dominated by pure matter. I derive the nonrelativistic equations governing small-scale fluctuation growth. The equations split into two uncoupled systems, one for the sum, the other for the difference, of the fluctuations in the two sectors. The former is governed strictly by Newtonian dynamics. The latter is governed by MOND dynamics, which entails stronger gravity, and nonlinearity even for the smallest of perturbations. These cause the difference to grow faster than the sum, conducing to matter-twin-matter segregation. The nonlinearity also causes interaction between nested perturbations on different scales. Because matter and twin matter (TM) repel each other in the MOND regime, matter inhomogeneities grow not only by their own self gravity, but also through shepherding by flanking TM overdensitie. The relative importance of gravity and pressure in the MOND system depends also on the strength of the perturbation. The development of structure in the universe, in either sector, thus depends crucially on two initial fluctuation spectra: that of matter alone and that of the matter-TM difference. I also discuss the back reaction on cosmology of BIMOND effects that appear as "phantom matter" resulting from inhomogeneity differences between the two sectors.Comment: 14 pages. Some clarifications added. Version published in Phys. Rev.

Non-linear conformally invariant generalization of the Poisson equation to D>2 dimensions

I propound a non-linear generalization of the Poisson equation describing a "medium" in D dimensions with a "dielectric constant" proportional to the field strength to the power D-2. It is the only conformally invariant scalar theory that is second order, and in which the scalar $phi$ couples to the sources $\rho$ via a $\phi\rho$ contact term. The symmetry is used to generate solutions for the field for some non-trivial configurations (e.g. for two oppositely charged points). Systems comprising N point charges afford further application of the symmetry. For these I derive e.g. exact expressions for the following quantities: the general two-point-charge force; the energy function and the forces in any three-body configuration with zero total charge; the few-body force for some special configurations; the virial theorem for an arbitrary, bound, many-particle system relating the time-average kinetic energy to the particle charges. Possible connections with an underlying conformal quantum field theory are mentioned.Comment: Revtex, 16 pages. To be published in Phys. Rev.

Distinguishing Between CDM and MOND: Predictions for the Microwave Background

Two hypothesized solutions of the mass discrepancy problem are cold dark matter (CDM) and modified Newtonian dynamics (MOND). The virtues and vices of these very different hypotheses are largely disjoint, making the process of distinguishing between them very dependent on how we weigh disparate lines of evidence. One clear difference is the nature of the principal mass constituent of the universe (CDM or baryons). This difference in the baryon fraction ($f_b \approx 0.1$ vs. 1) should leave a distinctive signature in the spectrum of fluctuations in the cosmic microwave background. Here I discuss some of the signatures which should be detectable in the near future. The most promising appears to be the ratio of the amplitudes of the first two peaks relative to the intervening trough.Comment: 8 pages, 1 figure, AASTeX. Accepted for publication in ApJ Letter

Near-optimal asymmetric binary matrix partitions

We study the asymmetric binary matrix partition problem that was recently introduced by Alon et al. (WINE 2013) to model the impact of asymmetric information on the revenue of the seller in take-it-or-leave-it sales. Instances of the problem consist of an $n \times m$ binary matrix $A$ and a probability distribution over its columns. A partition scheme $B=(B_1,...,B_n)$ consists of a partition $B_i$ for each row $i$ of $A$. The partition $B_i$ acts as a smoothing operator on row $i$ that distributes the expected value of each partition subset proportionally to all its entries. Given a scheme $B$ that induces a smooth matrix $A^B$, the partition value is the expected maximum column entry of $A^B$. The objective is to find a partition scheme such that the resulting partition value is maximized. We present a $9/10$-approximation algorithm for the case where the probability distribution is uniform and a $(1-1/e)$-approximation algorithm for non-uniform distributions, significantly improving results of Alon et al. Although our first algorithm is combinatorial (and very simple), the analysis is based on linear programming and duality arguments. In our second result we exploit a nice relation of the problem to submodular welfare maximization.Comment: 17 page

Development of a Flame Resistant Silicone Rubber

Flame resistant silicone rubber using aluminum silicates and aromatic bromide

The modified dynamics (MOND) predicts an absolute maximum to the acceleration produced by `dark halos'

We have recently discovered that the modified dynamics (MOND) implies some universal upper bound on the acceleration that can be contributed by a `dark halo'--assumed in a Newtonian analysis to account for the effects of MOND. Not surprisingly, the limit is of the order of the acceleration constant of the theory. This can be contrasted directly with the results of structure-formation simulations. The new limit is substantial and different from earlier MOND acceleration limits (discussed in connection with the MOND explanation of the Freeman law for galaxy disks, and the Fish law for ellipticals): It pertains to the `halo', and not to the observed galaxy; it is absolute, and independent of further physical assumptions on the nature of the galactic system; and it applies at all radii, whereas the other limits apply only to the mean acceleration in the system.Comment: Latex, five pages, final version to be published in Astrophys. J. Let

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

The Bright Side of Dark Matter

We show that it is not possible in the absence of dark matter to construct a four-dimensional metric that explains galactic observations. In particular, by working with an effective potential it is shown that a metric which is constructed to fit flat rotation curves in spiral galaxies leads to the wrong sign for the bending of light i.e. repulsion instead of attraction. Hence, without dark matter the motion of particles on galactic scales cannot be explained in terms of geodesic motion on a four- dimensional metric. This reveals a new bright side to dark matter: it is indispensable if we wish to retain the cherished equivalence principle.Comment: 7 pages, latex, no figures. Received an honorable mention in the 1999 Gravity research Foundation Essay Competition. Submitted to Phys. Rev. Let

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

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