Fate of Large-Scale Structure in Modified Gravity After GW170817 and GRB170817A.

The coincident detection of gravitational waves (GW) and a gamma-ray burst from a merger of neutron stars has placed an extremely stringent bound on the speed of GWs. We showed previously that the presence of gravitational slip (η) in cosmology is intimately tied to modifications of GW propagation. This new constraint implies that the only remaining viable source of gravitational slip is a conformal coupling to gravity in scalar-tensor theories, while viable vector-tensor theories cannot now generate gravitational slip at all. We discuss structure formation in the remaining viable models, demonstrating that (i) the dark-matter growth rate must now be at least as fast as in general relativity (GR), with the possible exception of that beyond the Horndeski model, and (ii) if there is any scale dependence at all in the slip parameter, it is such that it takes the GR value at large scales. We show a consistency relation that must be violated if gravity is modified.

Anisotropic stress as a signature of nonstandard propagation of gravitational waves.

We make precise the heretofore ambiguous statement that anisotropic stress is a sign of a modification of gravity. We show that in cosmological solutions of very general classes of models extending gravity-all scalar-tensor theories (Horndeski), Einstein-aether models, and bimetric massive gravity-a direct correspondence exists between perfect fluids apparently carrying anisotropic stress and a modification in the propagation of gravitational waves. Since the anisotropic stress can be measured in a model-independent manner, a comparison of the behavior of gravitational waves from cosmological sources with large-scale-structure formation could, in principle, lead to new constraints on the theory of gravity.

Cosmic variance and the measurement of the local Hubble parameter.

There is an approximately 9% discrepancy, corresponding to 2.4 σ, between two independent constraints on the expansion rate of the Universe: one indirectly arising from the cosmic microwave background and baryon acoustic oscillations and one more directly obtained from local measurements of the relation between redshifts and distances to sources. We argue that by taking into account the local gravitational potential at the position of the observer this tension--strengthened by the recent Planck results--is partially relieved and the concordance of the Standard Model of cosmology increased. We estimate that measurements of the local Hubble constant are subject to a cosmic variance of about 2.4% (limiting the local sample to redshifts z > 0.010) or 1.3% (limiting it to z > 0.023), a more significant correction than that taken into account already. Nonetheless, we show that one would need a very rare fluctuation to fully explain the offset in the Hubble rates. If this tension is further strengthened, a cosmology beyond the Standard Model may prove necessary.