Phantom dark energy from non-local infrared modifications of General Relativity

We discuss the cosmological consequences of a model based on a non-local infrared modification of Einstein equations. We find that the model generates a dynamical dark energy that can account for the presently observed value of $\Omega_{\rm DE}$, without introducing a cosmological constant. Tuning a free mass parameter $m$ to a value $m\simeq 0.67 H_0$ we reproduce the observed value $\Omega_{\rm DE}\simeq 0.68$. This leaves us with no free parameter and we then get a pure prediction for the EOS parameter of dark energy. Writing $w_{\rm DE}(a)=w_0+(1-a) w_a$, we find $w_0\simeq-1.04$ and $w_a\simeq -0.02$, consistent with the Planck data, and on the phantom side. We also argue that non-local equations of the type that we propose must be understood as purely classical effective equations, such as those derived in semiclassical gravity for the in-in matrix elements of the metric. As such, any apparent ghost instability in such equations only affects the classical dynamics, but there is no propagating degree of freedom associated to the ghost, and no issue of ghost-induced quantum vacuum decay.Comment: 7 pages, 2 figures; v3: the version accepted in Phys Rev. D. Title changed in journa

Spherically symmetric static solutions in a non-local infrared modification of General Relativity

We discuss static spherically symmetric solutions in a recently proposed non-local infrared modification of Einstein equations induced by a term $m^2g_{\mu\nu}\Box^{-1} R$, where $m$ is a mass scale. We find that, contrary to what happens in usual theories of massive gravity, in this non-local theory there is no vDVZ discontinuity and classical non-linearities do not become large below a Vainshtein radius parametrically larger than the Schwarzschild radius $r_S$. Rather on the contrary, in the regime $r\ll m^{-1}$ the corrections to the metric generated by a static body in GR are of the form $1+{\cal O}(m^2r^2)$ and become smaller and smaller toward smaller values of $r$. The modification to the GR solutions only show up at $r > m^{-1}$. For $m={\cal O}(H_0)$, as required for having interesting cosmological consequences, the non-local theory therefore recovers all successes of GR at the solar system and lab scales.Comment: 29 pages, 5 figures. v2: expanded discussion of conceptual aspects. The version to appear in JHE

The Halo Mass Function from Excursion Set Theory with a Non-Gaussian Trispectrum

A sizeable level of non-Gaussianity in the primordial cosmological perturbations may be induced by a large trispectrum, i.e. by a large connected four-point correlation function. We compute the effect of a primordial non-Gaussian trispectrum on the halo mass function, within excursion set theory. We use the formalism that we have developed in a previous series of papers and which allows us to take into account the fact that, in the presence of non-Gaussianity, the stochastic evolution of the smoothed density field, as a function of the smoothing scale, is non-markovian. In the large mass limit, the leading-order term that we find agrees with the leading-order term of the results found in the literature using a more heuristic Press-Schecther (PS)-type approach. Our approach however also allows us to evaluate consistently the subleading terms, which depend not only on the four-point cumulant but also on derivatives of the four-point correlator, and which cannot be obtained within non-Gaussian extensions of PS theory. We perform explicitly the computation up to next-to-leading order.Comment: LaTeX file, 15 page