We consider homogeneous abelian vector fields in an expanding universe. We find a mechanical analogy in which the system behaves as a particle moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. For simple power-law potentials of the form V=\lambda (A^\mu A_\mu)^n, the average equation of state is found to be w=(n-1)/(n+1). This implies that vector coherent oscillations could act as natural dark matter or dark energy candidates. Finally, we show that under very general conditions, the average energy-momentum tensor of a rapidly evolving bounded vector field in any background geometry is always isotropic and has the perfect fluid form for any locally inertial observer.Comment: 5 pages, 1 figure. Final version to appear as Rapid Communication in Phys. Rev.

Abstract:We study the dynamics of cosmological perturbations in models of dark matter based on ultralight coherent vector fields. Very much as for scalar field dark matter, we find two different regimes in the evolution: for modes with k 2 Hma, we have a particle-like behaviour indistinguishable from cold dark matter, whereas for modes with k 2Hma, we get a wave-like behaviour in which the sound speed is non-vanishing and of order c 2 s k 2 /m 2 a 2 . This implies that, also in these models, structure formation could be suppressed on small scales. However, unlike the scalar case, the fact that the background evolution contains a non-vanishing homogeneous vector field implies that, in general, the evolution of the three kinds of perturbations (scalar, vector and tensor) can no longer be decoupled at the linear level. More specifically, in the particle regime, the three types of perturbations are actually decoupled, whereas in the wave regime, the three vector field perturbations generate one scalar-tensor and two vector-tensor perturbations in the metric. Also in the wave regime, we find that a non-vanishing anisotropic stress is present in the perturbed energy-momentum tensor giving rise to a gravitational slip of order (Φ − Ψ)/Φ ∼ c 2 s . Moreover in this regime the amplitude of the tensor to scalar ratio of the scalar-tensor modes is also h/Φ ∼ c 2 s . This implies that small-scale density perturbations are necessarily associated to the presence of gravity waves in this model. We compare their spectrum with the sensitivity of present and future gravity waves detectors.

We show that the energy-momentum tensor of homogeneous fields of arbitrary spin in an expanding universe is always isotropic in average provided the fields remain bounded and evolve rapidly compared to the rate of expansion. An analytic expression for the average equation of state is obtained for Lagrangians with generic power-law kinetic and potential terms. As an example we consider the behavior of a spin-two field in the standard Fierz-Pauli theory of massive gravity. The results can be extended to general space-time geometries for locally inertial observers. 98.80.Cq

We consider homogeneous non-abelian vector fields with general potential terms in an expanding universe. We find a mechanical analogy with a system of N interacting particles (with N the dimension of the gauge group) moving in three dimensions under the action of a central potential. In the case of bounded and rapid evolution compared to the rate of expansion, we show by making use of a generalization of the virial theorem that for arbitrary potential and polarization pattern, the average energy-momentum tensor is always diagonal and isotropic despite the intrinsic anisotropic evolution of the vector field. We consider also the case in which a gauge-fixing term is introduced in the action and show that the average equation of state does not depend on such a term. Finally, we extend the results to arbitrary background geometries and show that the average energy-momentum tensor of a rapidly evolving Yang-Mills fields is always isotropic and has the perfect fluid form for any locally inertial observer.

The cold dark matter (CDM) scenario has proved successful in cosmology. However, we lack a fundamental understanding of its microscopic nature. Moreover, the apparent disagreement between CDM predictions and subgalactic-structure observations has prompted the debate about its behaviour at small scales. These problems could be alleviated if the dark matter is composed of ultralight fields m ∼ 10 −22 eV, usually known as fuzzy dark matter (FDM). Some specific models, with axion-like potentials, have been thoroughly studied and are collectively referred to as ultralight axions (ULAs) or axion-like particles (ALPs). In this work we consider anharmonic corrections to the mass term coming from a repulsive quartic self-interaction. Whenever this anharmonic term dominates, the field behaves as radiation instead of cold matter, modifying the time of matter-radiation equality. Additionally, even for high masses, i.e. masses that reproduce the cold matter behaviour, the presence of anharmonic terms introduce a cut-off in the matter power spectrum through its contribution to the sound speed. We analyze the model and derive constraints using a modified version of class and comparing with CMB and large-scale structure data.