We study the cosmological consequences of a recently proposed nonlocal modification of general relativity, obtained by adding a term m 2 R 2 −2 R to the Einstein-Hilbert action. The model has the same number of parameters as ΛCDM, with m replacing Ω Λ , and is very predictive. At the background level, after fixing m so as to reproduce the observed value of Ω M , we get a pure prediction for the equation of state of dark energy as a function of redshift, w DE (z), with w DE (0) in the range [−1.165, −1.135] as Ω M varies over the broad range Ω M ∈ [0.20, 0.36]. We find that the cosmological perturbations are well-behaved, and the model fully fixes the dark energy perturbations as a function of redshift z and wavenumber k. The nonlocal model provides a good fit to supernova data and predicts deviations from General Relativity in structure formation and in weak lensing at the level of 3-4%, therefore consistent with existing data but readily detectable by future surveys. For the logarithmic growth factor we obtain γ 0.53, to be compared with γ 0.55 in ΛCDM. For the Newtonian potential on subhorizon scales our results are well fitted by Ψ(a; k) = [1 + µ s a s ]Ψ GR (a; k) with a scale-independent µ s 0.09 and s 2, while the anisotropic stress is negligibly small.

We investigate brane inflation driven by two stacks of mobile branes in a throat. The stack closest to the bottom of the throat annihilates first with antibranes, resulting in particle production and a change of the equation of state parameter w. We calculate analytically some observable signatures of the collision; related decays are common in multi-field inflation, providing the motivation for this case study. The discontinuity in w enters the matching conditions relating perturbations in the remaining degree of freedom before and after the collision, affecting the power-spectrum of curvature perturbations. We find an oscillatory modulation of the power-spectrum for scales within the horizon at the time of the collision, and a slightly redder spectrum on super-horizon scales. We comment on implications for staggered inflation.

A generalization to the theory of massive gravity is presented which includes three dynamical metrics. It is shown that at the linear level, the theory predicts a massless spin-2 field which is decoupled from the other two gravitons, which are massive and interacting. In this regime, the matter should naturally couple to massless gravitons which introduce a preferred metric that is the average of the primary metrics. The cosmological solution of the theory shows the de Sitter behavior with a function of mass as its cosmological constant. Surprisingly, it lacks any nontrivial solution when one of the metrics is taken to be Minkowskian and seems to enhance the predictions which suggest that there is no homogeneous, isotropic, and flat solution for the standard massive cosmology.

We study linear perturbations around time dependent spherically symmetric solutions in the Λ3 massive gravity theory, which self-accelerate in the vacuum. We find that the dynamics of the scalar perturbations depend on the choice of the fiducial metric for the background solutions. For particular choice of fiducial metric there is a symmetry enhancement, leaving no propagating scalar degrees of freedom at linear order in perturbations. In contrast, any other choice propagates a single scalar mode. We find that the Hamiltonian of this scalar mode is unbounded from below for all self-accelerating solutions, signalling an instability.