[en] This spontaneous workshop (SW) brings together specialists on recent insights in particle physics, astrophysics and cosmology. The aim is to stimulate debates on common topics in views of providing the scientific community with innovating ideas. The main topics are gravity, dark matter and cosmological models. This document is made of the slides of the presentations.

[en] We review the different frameworks in which Galileon scalar fields have been seen to emerge such as in DGP, New Massive Gravity and Ghost-free Massive Gravity and emphasize their relation with the Lovelock invariant in brane-world models. The existence of a non-renormalization theorem for Galileon scalar fields makes them especially attractive candidates for inflation as well as for late-time acceleration. In particular, we review the self-accelerating and de-gravitating branches of solutions present in Galileon models when arising from Massive Gravity and discuss their phenomenology. (author)

[en] It is generic for the bulk fields sourced by branes having codimension two and higher to diverge at the brane position, much as does the Coulomb potential at the position of its source charge. This complicates finding the relation between brane properties and the bulk geometries they source. (These complications do not arise for codimension-1 sources, such as in RS geometries, because of the special properties unique to codimension one.) Understanding these relations is a prerequisite for phenomenological applications involving higher-codimension branes. Using codimension-2 branes in extra-dimensional scalar-tensor theories as an example, we identify the classical matching conditions that relate the near-brane asymptotic behaviour of bulk fields to the low-energy effective actions describing how space-filling codimension-2 branes interact with the surrounding extra-dimensional bulk. We do so by carefully regulating the near-brane divergences, and show how these may be renormalized in a general way. Among the interesting consequences is a constraint relating the on-brane curvature to its action, for maximally symmetric brane geometries. It represents the codimension-2 generalization of the well-known modification of the Friedmann equation for codimension-1 branes. We argue that its interpretation within an effective field theory framework in this case is as a relation 4πU₂ ≅ κ²(T₂')² between the codimension-2 brane tension, T₂(φ), and its contribution to the low-energy on-brane effective potential, U₂(φ). This relation implies that any dynamics that minimizes a brane contribution to the on-brane curvature automatically also minimizes its couplings to the extra-dimensional scalar.

[en] We explore the cosmological solutions of a recently proposed extension of general relativity with a Lorentz-invariant mass term. We show that the same constraint that removes the Boulware-Deser ghost in this theory also prohibits the existence of homogeneous and isotropic cosmological solutions. Nevertheless, within domains of the size of inverse graviton mass we find approximately homogeneous and isotropic solutions that can well describe the past and present of the Universe. At energy densities above a certain crossover value, these solutions approximate the standard Friedmann-Robertson-Walker evolution with great accuracy. As the Universe evolves and density drops below the crossover value the inhomogeneities become more and more pronounced. In the low-density regime each domain of the size of the inverse graviton mass has essentially non-Friedmann-Robertson-Walker cosmology. This scenario imposes an upper bound on the graviton mass, which we roughly estimate to be an order of magnitude below the present-day value of the Hubble parameter. The bound becomes especially restrictive if one utilizes an exact self-accelerated solution that this theory offers. Although the above are robust predictions of massive gravity with an explicit mass term, we point out that if the mass parameter emerges from some additional scalar field condensation, the constraint no longer forbids the homogeneous and isotropic cosmologies. In the latter case, there will exist an extra light scalar field at cosmological scales, which is screened by the Vainshtein mechanism at shorter distances.