Alternative to particle dark matter

We propose an alternative to particle dark matter that borrows ingredients of modified Newtonian dynamics (MOND) while adding new key components. The first new feature is a dark matter fluid, in the form of a scalar field with small equation of state and sound speed. This component is critical in reproducing the success of cold dark matter for the expansion history and the growth of linear perturbations, but does not cluster significantly on nonlinear scales. Instead, the missing mass problem on nonlinear scales is addressed by a modification of the gravitational force law. The force law approximates MOND at large and intermediate accelerations, and therefore reproduces the empirical success of MOND at fitting galactic rotation curves. At ultralow accelerations, the force law reverts to an inverse-square law, albeit with a larger Newton’s constant. This latter regime is important in galaxy clusters and is consistent with their observed isothermal profiles, provided the characteristic acceleration scale of MOND is mildly varying with scale or mass, such that it is 12 times higher in clusters than in galaxies. We present an explicit relativistic theory in terms of two scalar fields. The first scalar field is governed by a Dirac-Born-Infeld action and behaves as a dark matter fluid on large scales. The second scalar field also has single-derivative interactions and mediates a fifth force that modifies gravity on nonlinear scales. Both scalars are coupled to matter via an effective metric that depends locally on the fields. The form of this effective metric implies the equality of the two scalar gravitational potentials, which ensures that lensing and dynamical mass estimates agree. Further work is needed in order to make both the acceleration scale of MOND and the fraction at which gravity reverts to an inverse-square law explicitly dynamical quantities, varying with scale or mass.

Figure 1

Rotations curves from 21 cm observations of LSB galaxy NGC-1560 [22] and HSB galaxy NGC-2903 [23], reproduced from [21]. The dotted and dashed lines are the Newtonian rotation curves from the stellar mass and the gas, respectively. The solid line is the MOND fits, with $a_0$ given by (5). The only free parameter in each case is the mass-to-light ratio $M/L$.

Figure 2

MOND and the Virgo cluster, reproduced from [27]. The data points are from ROSAT [32] and ASCA [33] observations. The solid lines are the MOND predictions, for different choices of initial temperature at 1 Mpc. The MOND predictions are inconsistent with the nearly isothermal profile.

Figure 3

Sketch of the MOND acceleration law (left) and our modification to the MOND law (right), outside a static, spherically symmetric source. Unlike the MOND case, our modified law reverts back to an inverse-square law at large distances, albeit $f$ times stronger than the standard Newtonian acceleration.

Figure 4

Temperature (left) and surface brightness (right) profiles for the Virgo cluster from the XMM-Newton satellite, reproduced from [113].

Figure 5

Density (left) and temperature (right) profiles for the REXCESS cluster sample, reproduced from [124].

Figure 6

Stacked tangential shear profile for LoCuSS clusters, reproduced from [127].

Figure 7

Mass discrepancy as a function of the Newtonian acceleration for a large sample of disc galaxies, reproduced from [128]. Each galaxy plotted has a velocity uncertainty of less than 5%. The mass-to-light ratio was obtained using the MOND fit, as detailed in [21].

Figure 8

Line-of-sight velocity dispersion as a function of characteristic radius for pressure-supported systems, reproduced from [21]. The stars are globular clusters, the circles are massive molecular clouds, the triangles are dwarf spheroidal satellites of the Milky Way, the dashes are compact elliptical galaxies, the crosses are massive elliptical galaxies, and the squares are galaxy clusters. The solid line corresponds to ${\sigma }^2/r=a_0^{\text{galaxies}}$. The dashed lines have slopes a factor of 5 larger or smaller than this relation. The dotted lines (added by the author) have slopes a factor of 10 larger or smaller.

Figure 9

Luminosity distance as a function of redshift for $\mathrm{\Lambda }\mathrm{CDM}$ with ${\mathrm{\Omega }}_{\mathrm{m}}=0.25$ (solid line) and DBI with $C=0.32$. The percentage difference is less than 5% over the entire redshift range.