Cosmological attractors in massive gravity

We study Lorentz-violating models of massive gravity which preserve rotations and are invariant under time-dependent shifts of the spatial coordinates. In the linear approximation the Newtonian potential in these models has an extra confining term proportional to the distance from the source. We argue that during cosmological expansion the Universe may be driven to an attractor point with larger symmetry which includes particular simultaneous dilatations of time and space coordinates. The confining term in the potential vanishes as one approaches the attractor. In the vicinity of the attractor the extra contribution is present in the Friedmann equation which, in a certain range of parameters, gives rise to the cosmic acceleration.

Figure 1

Limits on the gravitational wave signal in the frequency/relative graviton abundance plane. Light shaded region is excluded by the observations of binary pulsars [23]. Dark shaded region is excluded by the timing of the millisecond pulsars [29]. Dashed lines show the expected sensitivity of the Australian pulsar timing array and LISA. Frequencies higher than that marked by the solid line correspond to graviton masses large enough to allow for gravitons to cluster in galaxies. Note that if all of the galactic dark matter is comprised of massive gravitons then the gravitational wave signal corresponds to graviton abundance ${\Omega }_g\sim {10}^5$.