Towards a gauge theory of frames

The equivalence principle postulates a frame. This implies globally special and locally general relativity. It is proposed here that spacetime emerges from the gauge potential of translations, whilst the Lorenz symmetry is gauged into the interactions of the particle sector. This is, though more intuitive, the opposite to the standard formulation of gravity, and seems to lead to conceptual and technical improvements of the theory.

Doubly-boosted vector cosmologies from disformal metrics

A systematic dynamical system approach is applied to study the cosmology of anisotropic Bianchi I universes in which a vector field is assumed to operate on a disformal frame. This study yields a number of new fixed points, among which anisotropic scaling solutions. Within the simplifying assumption of (nearly) constant-slope potentials these are either not stable attractors, do not describe accelerating expansion or else they feature too large anisotropies to be compatible with observations. Nonetheless, some solutions do have an appeal for cosmological applications in that isotropy is retained due to rapid oscillations of the vector field.

Novel aspects of C-theories in Cosmology

The field equations in FRW background for the so called C-theories are presented and investigated. In these theories the usual Ricci scalar is substituted with $f(mathcal{R})$ where $mathcal{R}$ is a Ricci scalar related to a conformally scaled metric $hat{g}_{mu u} = mathcal{C}(mathcal{R})g_{mu u}$, where the conformal factor itself depends on $mathcal{R}$. It is shown that homogeneous perturbations of this Ricci scalar around general relativity FRW background of a large class of these theories are either inconsistent or unstable.

Coupled three-form dark energy

Cosmology with a three-form field interacting with cold dark matter is considered. In particular, the mass of the dark matter particles is assumed to depend upon the amplitude of the three-form field invariant. In comparison to coupled scalar field quintessence, the new features include an effective pressure contribution to the field equations that manifests both in the background and perturbation level. The dynamics of the background is analyzed, and new scaling solutions are found. A simple example model leading to a de Sitter expansion without a potential is studied. The Newtonian limit of cosmological perturbations is derived, and it is deduced that the coupling can be very tightly constrained by the large-scale structure data. This is demonstrated with numerical solutions for a model with nontrivial coupling and a quadratic potential.

DBI Galileons in the Einstein Frame: Local Gravity and Cosmology

It is shown that a disformally coupled theory in which the gravitational sector has the Einstein-Hilbert form is equivalent to a quartic DBI Galileon Lagrangian, possessing non-linear higher derivative interactions, and hence allowing for the Vainshtein effect. This Einstein Frame description considerably simplifies the dynamical equations and highlights the role of the different terms. The study of highly dense, non-relativistic environments within this description unravels the existence of a disformal screening mechanism, while the study of static vacuum configurations reveals the existence of a Vainshtein radius, at which the asymptotic solution breaks down. Disformal couplings to matter also allow the construction of Dark Energy models, which behave differently than conformally coupled ones and introduce new effects on the growth of Large Scale Structure over cosmological scales, on which the scalar force is not screened. We consider a simple Disformally Coupled Dark Matter model in detail, in which standard model particles follow geodesics of the gravitational metric and only Dark Matter is affected by the disformal scalar field. This particular model is not compatible with observations in the linearly perturbed regime. Nonetheless, disformally coupled theories offer enough freedom to construct realistic cosmological scenarios, which can be distinguished from the standard model through characteristic signatures.

Screening Modifications of Gravity through Disformally Coupled Fields

It is shown that extensions to General Relativity, which introduce a strongly coupled scalar field, can be viable if the interaction has a non-conformal form. Such disformal coupling depends upon the gradients of the scalar field. Thus, if the field is locally static and smooth, the coupling becomes invisible in the solar system: this is the disformal screening mechanism. A cosmological model is considered where the disformal coupling triggers the onset of accelerated expansion after a scaling matter era, giving a good fit to a wide range of observational data. Moreover, the interaction leaves signatures in the formation of large-scale structure that can be used to probe such couplings.

The post-Newtonian limit in C-theories of gravitation

C-theory provides a unified framework to study metric, metric-affine and more general theories of gravity. In the vacuum weak-field limit of these theories, the parameterized post-Newtonian (PPN) parameters $beta$ and $gamma$ can differ from their general relativistic values. However, there are several classes of models featuring long-distance modifications of gravity but nevertheless passing the Solar system tests. Here it is shown how to compute the PPN parameters in C-theories and also in nonminimally coupled curvature theories, correcting previous results in the literature for the latter.

Disformal quintessence

A canonic scalar field minimally coupled to a disformal metric generated by the field itself is considered. Causality and stability conditions are derived for such a field. Cosmological effects are studied and it is shown that the disformal modification could viably trigger an acceleration after a scaling matter era, thus possibly alleviating the coincidence problem.

Newtonian limit of nonlocal cosmology

We study the consequences of the $f(R/Box)$ gravity models for the Solar system and the large scale structure of the universe. The spherically symmetric solutions can be used to obtain bounds on the constant and the linear parts of the correction terms. The evolution of cosmological matter structures is shown to be governed by an effective time dependent Newtons constant. We also analyze the propagation of the perturbation modes. Tensor and vector modes are only slightly modified, but two new scalar degrees of freedom are present. Their causality and stability is demonstrated, and their formal ghost conditions are related to a singularity of the cosmological background. In general, the Newtonian limit of these models has no apparent conflicts with observations but can provide useful constraints.

Vector Field Models of Inflation and Dark Energy

We consider several new classes of viable vector field alternatives to the inflaton and quintessence scalar fields. Spatial vector fields are shown to be compatible with the cosmological anisotropy bounds if only slightly displaced from the potential minimum while dominant, or if driving an anisotropic expansion with nearly vanishing quadropole today. The Bianchi I model with a spatial field and an isotropic fluid is studied as a dynamical system, and several types of scaling solutions are found. On the other hand, time-like fields are automatically compatible with large-scale isotropy. We show that they can be dynamically important if non-minimal gravity couplings are taken into account. As an example, we reconstruct a vector-Gauss-Bonnet model which generates the concordance model acceleration at late times and supports an inflationary epoch at high curvatures. The evolution of vortical perturbations is considered.