A Model-Independent Approach to Dark Energy Cosmologies: Current and Future Constraints

The effective anisotropic stress eta = − Phi/Psi is a key variable in the characterisation of the physical origin of the dark energy. It is however important to use a fully model-independent approach when measuring eta to avoid introducing a theoretical bias into the results. We forecast the precision with which future large surveys can determine eta in a way that only relies on directly observable quantities, using the joint combination of Galaxy Clustering, Weak Lensing and Supernovae probes. Among the results, we find that a future large scale survey can constrain eta to within 10% if k-independent, and to within 60% if it is restricted to follow the Horndeski model. In order to find current constraints on eta data for the growth rate f sigma_8 coming from Redshift Space Distortion measurements, observations of the Hubble expansion H(z), and a constraint for the quantity P2 defined as the expectation value of the ratio between galaxy-galaxy and galaxy-velocity cross correlations, have been used. We find a value at z = 0.32 of eta = 0.646 +/- 0.678, in agreement with the predicted value for the LCDM model. Finally, we produce a cosmological exclusion plot for modified gravity in analogy with the exclusion plots produced in laboratory experiments

Topological mass generation and 2−2-forms

In this work we revisit the topological mass generation of 2-forms and establish a connection to the unique derivative coupling arising in the quartic Lagrangian of the systematic construction of massive $2-$form interactions, relating in this way BF theories to Galileon-like theories of 2-forms. In terms of a massless $1-$form $A$ and a massless $2-$form $B$, the topological term manifests itself as the interaction $B\wedge F$, where $F = {\rm d} A$ is the field strength of the $1-$form. Such an interaction leads to a mechanism of generation of mass, usually referred to as "topological generation of mass" in which the single degree of freedom propagated by the $2-$form is absorbed by the $1-$form, generating a massive mode for the $1-$form. Using the systematical construction in terms of the Levi-Civita tensor, it was shown that, apart from the quadratic and quartic Lagrangians, Galileon-like derivative self-interactions for the massive 2-form do not exist. A unique quartic Lagrangian $\epsilon^{\mu\nu\rho\sigma}\epsilon^{\alpha\beta\gamma}_{\;\;\;\;\;\;\sigma}\partial_{\mu}B_{\alpha\rho}\partial_{\nu}B_{\beta\gamma}$ arises in this construction in a way that it corresponds to a total derivative on its own but ceases to be so once an overall general function is introduced. We show that it exactly corresponds to the same interaction of topological mass generation. Based on the decoupling limit analysis of the interactions, we bring out supporting arguments for the uniqueness of such a topological mass term and absence of the Galileon-like interactions. Finally, we discuss some preliminary applications in cosmology.Comment: 14 pages, 3 figures, journal versio