In a massive vector field theory, one can have cosmological expansion which depends on the spatial component, v, of the vector field. While the beyond-generalized-Proca theories were constructed to be ghost free on isotropric cosmological backgrounds, it is shown that the they remain free of the Ostrogradski ghost on anisotropic backgrounds. In the second-order generalized Proca theories, there are anisotropic solutions in which the ratio of anisotropic expansion to isotropic expansion remains nearly constant during the radiation-domination epoch (and v plays the role of dark energy), and then decreases during the matter-dominated epoch (approaching the isotropic de Sitter solution with v=0). In the higher-order generalized Proca, the only consistent anisotropic solutions are those with v=0, in which case the anisotropic expansion always fades away and these solutions quickly approximate isotropic de Sitter.

The Proca theory describes a massive vector field on a flat background with at most second order equations of motion. Generalized Proca theories describe massive vector fields on curved background with at most second-order derivative interactions (=> second order equations of motion). Recently, beyond generalized Proca theories have also been constructed, describing massive vector fields on curved backgrounds with higher-order derivative interactions, but which nonetheless maintain second order equations of motion due to the presence of a second-class Hamiltonian constraint. While the isotropic cosmologies of generalized Proca theories have been previously studied, this is one of the first investigations into the new beyond-generalized-Proca theories and the role played by anisotropies.

This letter suggests that while the growth of structure predicted by LCDM is typically higher than the values from redshift measurements, if one assumed a graviton mass m = 9.8 x 10 ^-33 eV one obtains better agreement with data. This is in the context of the Minimal Theory of Massive Gravity, which explicitly breaks Lorentz invariance at large scales, and on the so-called `normal branch', in which the fiducial metric is related to the physical metric by an overall scaling. (In this branch there is no consistent nonlinear completion to dRGT gravity, and therefore it is possible to have stable FRW solutions).

Recent observations (e.g. from LIGO) are placing ever tighter upper bounds on any potential graviton mass, as they seem well-described by standard cosmology (GR with massless gravitons). It is, however, constructive to also look for measurements which actually favour a nonzero mass, and to check whether it is possible to achieve an agreement with observation which is as good as, or even better than, standard cosmology. This letter points out one particular measurement which may prefer a small nonzero graviton mass, and in future it will be interesting to see if this mass is also consistent with other data.

An NEC-violating cubic Galileon coupled to an NEC-respecting scalar field (with first derivative interactions) does not admit bouncing FRLW cosmologies or static spherically-symmetric Lorenztian wormholes. This represents an extension of recent no-go theorems (predicting the existence of ghosts and gradient instabilites) for pure Galileon theories.

While it has long been known that generalized Galileon theories are capable of NEC violation, two recent no-go theorems have argued that this cannot be used to create a Lorentzian wormhole or a bouncing Universe. These no-go theorems considered only a single Galileon field, and so it is natural to ask whether including other fields might allow one to evade the no-go theorems. Here, we see that the addition of a second scalar field does not change the result that wormholes or bounces are always accompanied by ghosts and gradients. instabilities.