Recently an inflationary model with a vector field coupled to the inflaton was proposed and the phenomenology studied for the Bianchi type I spacetime. It was found that the model demonstrates a counter-example to the cosmic no-hair theorem since there exists a stable anisotropically inflationary fix-point. One of the great triumphs of inflation, however, is that it explains the observed flatness and isotropy of the universe today without requiring special initial conditions. Any acceptable model for inflation should thus explain these observations in a satisfactory way. To check whether the model meets this requirement, we introduce curvature to the background geometry and consider axisymmetric spacetimes of Bianchi type II,III and the Kantowski-Sachs metric. We show that the anisotropic Bianchi type I fix-point is an attractor for the entire family of such spacetimes. The model is predictive in the sense that the universe gets close to this fix-point after a few e-folds for a wide range of initial conditions. If inflation lasts for N e-folds, the curvature at the end of inflation is typically of order ∼ e −2N . The anisotropy in the expansion rate at the end of inflation, on the other hand, while being small on the one-percent level, is highly significant. We show that after the end of inflation there will be a period of isotropization lasting for ∼ 2 3 N e-folds. After that the shear scales as the curvature and becomes dominant around N e-folds after the end of inflation. For plausible bounds on the reheat temperature the minimum number of e-folds during inflation, required for consistency with the isotropy of the supernova Ia data, lays in the interval (21, 48). Thus the results obtained for our restricted class of spacetimes indicates that inflation with anisotropic hair is cosmologically viable.

Motivated by the couplings of the dilaton in four-dimensional effective actions, we investigate the cosmological consequences of a scalar field coupled both to matter and a Maxwell-type vector field. The vector field has a background isotropy-violating component. New anisotropic scaling solutions which can be responsible for the matter and dark energy dominated epochs are identified and explored. For a large parameter region the universe expands almost isotropically. Using that the CMB quadrupole is extremely sensitive to shear, we constrain the ratio of the matter coupling to the vector coupling to be less than 10 −5 . Moreover, we identify a large parameter region, corresponding to a strong vector coupling regime, yielding exciting and viable cosmologies close to the ΛCDM limit.

Horndeski derived a most general vector-tensor theory in which the vector field respects the gauge symmetry and the resulting dynamical equations are of second order. The action contains only one free parameter, λ, that determines the strength of the non-minimal coupling between the gauge field and gravity. We investigate the cosmological consequences of this action and discuss observational constraints. For λ < 0 we identify singularities where the deceleration parameter diverges within a finite proper time. This effectively rules out any sensible cosmological application of the theory for a negative nonminimal coupling. We also find a range of parameter that gives a viable cosmology and study the phenomenology for this case. Observational constraints on the value of the coupling are rather weak since the interaction is higher-order in space-time curvature.

In this paper the dynamics of free gauge fields in Bianchi type I–VIIh space-times is investigated. The general equations for a matter sector consisting of a p-form field strength (), a cosmological constant (4-form) and perfect fluid in Bianchi type I–VIIh space-times are computed using the orthonormal frame method. The number of independent components of a p-form in all Bianchi types I–IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions, ‘Wonderland (λ)’ appears generally in type V and in type I for . Depending on the value of the equation of state parameter other new stable solutions are also found (‘The Rope’ and ‘The Edge’) containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.

We study the Horndeski vector-tensor theory that leads to second order equations of motion and contains a non-minimally coupled abelian gauge vector field. This theory is remarkably simple and consists of only 2 terms for the vector field, namely: the standard Maxwell kinetic term and a coupling to the dual Riemann tensor. Furthermore, the vector sector respects the U(1) gauge symmetry and the theory contains only one free parameter, M2, that controls the strength of the non-minimal coupling. We explore the theory in a de Sitter spacetime and study the presence of instabilities and show that it corresponds to an attractor solution in the presence of the vector field. We also investigate the cosmological evolution and stability of perturbations in a general FLRW spacetime. We find that a sufficient condition for the absence of ghosts is M2 > 0. Moreover, we study further constraints coming from imposing the absence of Laplacian instabilities. Finally, we study the stability of the theory in static and spherically symmetric backgrounds (in particular, Schwarzschild and Reissner-Nordström-de Sitter). We find that the theory, quite generally, do have ghosts or Laplacian instabilities in regions of spacetime where the non-minimal interaction dominates over the Maxwell term. We also calculate the propagation speed in these spacetimes and show that superluminality is a quite generic phenomenon in this theory.