Cosmological attractors in massive gravity

TL;DR

This work investigates Lorentz-violating massive gravity with residual rotational invariance and time-dependent spatial shifts, focusing on cosmological dynamics and linearized perturbations. The authors show that cosmology generically drives the theory toward an attractor with enhanced dilatation symmetry, at which the Newtonian potential loses its linear confining term and the Friedmann equation acquires additional dark-energy-like contributions while graviton masses remain finite. The tensor sector remains two massive spin-2 modes, the vector sector has no propagating degrees of freedom, and the scalar sector yields a controlled modification to gravity with a ghost-condensate-like mode that can be set to zero in the linear regime. They argue the model is UV-stable near Minkowski, exhibits no Boulware-Deser instability, and offers distinctive phenomenology for dark matter and cosmic acceleration, with rich implications for cosmology and future tests.

Abstract

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.

Figures (1)

• 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 pulsars). Dark shaded region is excluded by the timing of the millisecond pulsars timing. 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 $\Omega_g\sim 10^5$.