Dark energy is often assumed to be composed by a single scalar field. The background cosmic expansion is not sufficient to determine whether this is true or not. We study multi-field scalar-tensor models with a general dark matter source and write th
e observable modified gravity parameters (effective gravitational constant and anisotropic stress) in the form of a ratio of polynomials in the Fourier wavenumber k of order 2N, where N is the number of scalar fields. By comparing these observables to real data it is in principle possible to determine the number of dark energy scalar fields coupled to gravity. We also show that there are no realistic non-trivial cases in which the order of the polynomials is reduced.
The number of Italian firms in function of the number of workers is well approximated by an inverse power law up to 15 workers but shows a clear downward deflection beyond this point, both when using old pre-1999 data and when using recent (2014) dat
a. This phenomenon could be associated with employent protection legislation which applies to companies with more than 15 workers (the Statuto dei Lavoratori). The deflection disappears for agriculture firms, for which the protection legislation applies already above 5 workers. In this note it is estimated that a correction of this deflection could bring an increase from 3.9 to 5.8% in new jobs in firms with a workforce between 5 to 25 workers.
Modified gravity theories predict in general a non standard equation for the propagation of gravitational waves. Here we discuss the impact of modified friction and speed of tensor modes on cosmic microwave polarization B modes. We show that the non
standard friction term, parametrized by $alpha_{M}$, is degenerate with the tensor-to-scalar ratio $r$, so that small values of $r$ can be compensated by negative constant values of $alpha_M$. We quantify this degeneracy and its dependence on the epoch at which $alpha_{M}$ is different from the standard, zero, value and on the speed of gravitational waves $c_{T}$. In the particular case of scalar-tensor theories, $alpha_{M}$ is constant and strongly constrained by background and scalar perturbations, $0le alpha_{M}< 0.01$ and the degeneracy with $r$ is removed. In more general cases however such tight bounds are weakened and the B modes can provide useful constraints on early-time modified gravity.
The aim of this paper is to answer the following two questions: (1) Given cosmological observations of the expansion history and linear perturbations in a range of redshifts and scales as precise as is required, which of the properties of dark energy
could actually be reconstructed without imposing any parameterization? (2) Are these observables sufficient to rule out not just a particular dark energy model, but the entire general class of viable models comprising a single scalar field? This paper bears both good and bad news. On one hand, we find that the goal of reconstructing dark energy models is fundamentally limited by the unobservability of the present values of the matter density Omega_m0, the perturbation normalization sigma_8 as well as the present matter power spectrum. On the other, we find that, under certain conditions, cosmological observations can nonetheless rule out the entire class of the most general single scalar-field models, i.e. those based on the Horndeski Lagrangian.
