We construct a fully covariant theory of massive gravity which does not require the introduction of an external reference metric, and overcomes the usual problems of massive gravity theories (fatal ghosts instabilities, acausality and/or vDVZ discontinuity). The equations of motion of the theory are non-local, but respect causality. The starting point is the quadratic action proposed in the context of the degravitation idea. We show that it is possible to extended it to a fully non-linear covariant theory. This theory describes the five degrees of freedom of a massive graviton plus a scalar ghost. However, contrary to generic non-linear extensions of Fierz-Pauli massive gravity, the ghost has the same mass m as the massive graviton, independently of the background, and smoothly goes into a non-radiative degree of freedom for m → 0. As a consequence, for m ∼ H 0 the vacuum instability induced by the ghost is irrelevant even over cosmological time-scales. We finally show that an extension of the model degravitates a vacuum energy density of order M 4 Pl down to a value of order M 2 Pl m 2 , which for m = O(H 0 ) is of order of the observed value of the vacuum energy density.

We study the cosmological dynamics of a recently proposed infrared modification of the Einstein equations, based on the introduction of a nonlocal term constructed with m2gμν□-1R, where m is a mass parameter. The theory generates automatically a dynamical dark energy component, that can reproduce the observed value of the dark energy density without introducing a cosmological constant. Fixing m so to reproduce the observed value ΩDE≃0.68, and writing wDE(a)= w0+(1-a)wa, the model provides a neat prediction for the equation of state parameters of dark energy, w0≃-1.042 and wa≃-0.020, and more generally provides a pure prediction for wDE as a function of redshift. We show that, because of some freedom in the definition of □-1, one can extend the construction so to define a more general family of nonlocal models. However, in a first approximation this turns out to be equivalent to adding an explicit cosmological constant term on top of the dynamical dark energy component. This leads to an extended model with two parameters, ΩΛ and m. Even in this extension the EOS parameter w0 is always on the phantom side, in the range -1.33 ≲w0≤-1, and there is a prediction for the relation between w0 and wa

Recent work has shown that non-local modifications of the Einstein equations can have interesting cosmological consequences and can provide a dynamical origin for dark energy, consistent with existing data. At first sight these theories are plagued by ghosts. We show that these apparent ghost-like instabilities do not describe actual propagating degrees of freedom, and there is no issue of ghost-induced quantum vacuum decay

We present the gauge-invariant formalism of cosmological weak lensing, accounting for all the relativistic effects due to the scalar, vector, and tensor perturbations at the linear order. While the light propagation is fully described by the geodesic equation, the relation of the photon wavevector to the physical quantities requires the specification of the frames, where they are defined. By constructing the local tetrad bases at the observer and the source positions, we clarify the relation of the weak lensing observables such as the convergence, the shear, and the rotation to the physical size and shape defined in the source rest-frame and the observed angle and redshift measured in the observer restframe. Compared to the standard lensing formalism, additional relativistic effects contribute to all the lensing observables. We explicitly verify the gauge-invariance of the lensing observables and compare our results to previous work. In particular, we demonstrate that even in the presence of the vector and tensor perturbations, the physical rotation of the lensing observables vanishes at the linear order, while the tetrad basis rotates along the light propagation compared to a FRW coordinate. Though the latter is often used as a probe of primordial gravitational waves, the rotation of the tetrad basis is indeed not a physical observable. We further clarify its relation to the E-B decomposition in weak lensing. Our formalism provides a transparent and comprehensive perspective of cosmological weak lensing.1

We examine a cosmological model with a dark energy density of the form ρDE(t)=ρX(t)+ρZ(t)ρDE(t)=ρX(t)+ρZ(t), where ρXρX is the component that accelerates the Hubble expansion at late times and ρZ(t)ρZ(t) is an extra contribution proportional to H2(t)H2(t). This form of ρZ(t)ρZ(t) follows from the recent proposal that the contribution of zero-point fluctuations of quantum fields to the total energy density should be computed by subtracting the Minkowski-space result from that computed in the FRW space–time. We discuss theoretical arguments that support this subtraction. By definition, this eliminates the quartic divergence in the vacuum energy density responsible for the cosmological constant problem. We show that the remaining quadratic divergence can be reabsorbed into a redefinition of Newtonʼs constant only under the assumption that ∇μ〈0|Tμν|0〉=0∇μ〈0|Tμν|0〉=0, i.e. that the energy–momentum tensor of vacuum fluctuations is conserved in isolation. However in the presence of an ultra-light scalar field X with mX