The δN formula for the primordial curvature perturbation ζ is extended to include vector as well as scalar fields. Formulas for the tree-level contributions to the spectrum and bispectrum of ζ are given, exhibiting statistical anisotropy. The one-loop contribution to the spectrum of ζ is also worked out. We then consider the generation of vector field perturbations from the vacuum, including the longitudinal component that will be present if there is no gauge invariance. Finally, the δN formula is applied to the vector curvaton and vector inflation models with the tensor perturbation also evaluated in the latter case.

A new model realisation of the vector curvaton paradigm is presented and analysed. The model consists of a single massive Abelian vector field, with a Maxwell type kinetic term. By assuming that the kinetic function and the mass of the vector field are appropriately varying during inflation, it is shown that a scale invariant spectrum of superhorizon perturbations can be generated. These perturbations can contribute to the curvature perturbation of the Universe. If the vector field remains light at the end of inflation it is found that it can generate substantial statistical anisotropy in the spectrum and bispectrum of the curvature perturbation. In this case the non-Gaussianity in the curvature perturbation is predominantly anisotropic, which will be a testable prediction in the near future. If, on the other hand, the vector field is heavy at the end of inflation then it is demonstrated that particle production is approximately isotropic and the vector field alone can give rise to the curvature perturbation, without directly involving any fundamental scalar field. The parameter space for both possibilities is shown to be substantial. Finally, toy-models are presented which show that the desired variation of the mass and kinetic function of the vector field can be realistically obtained, without unnatural tunings, in the context of supergravity or superstrings.

The Higgs-inflaton coupling plays an important role in the Higgs field dynamics in the early Universe. Even a tiny coupling generated at loop level can have a dramatic effect on the fate of the electroweak vacuum. Such Higgs-inflaton interaction is present both at the trilinear and quartic levels in realistic reheating models. In this work, we examine the Higgs dynamics during the preheating epoch, focusing on the effects of the parametric and tachyonic resonances. We use lattice simulations and other numerical tools in our studies. We find that the resonances can induce large fluctuations of the Higgs field which destabilize the electroweak vacuum. Our considerations thus provide an upper bound on quartic and trilinear interactions between the Higgs and the inflaton. We conclude that there exists a favorable range of the couplings within which the Higgs field is stabilized during both inflation and preheating epochs.

A vector curvaton model with a Maxwell kinetic term and varying kinetic function and mass during inflation is studied. It is shown that, if light until the end of inflation, the vector field can generate statistical anisotropy in the curvature perturbation spectrum and bispectrum, with the latter being predominantly anisotropic. If by the end of inflation the vector field becomes heavy, then particle production is isotropic and the vector curvaton can alone generate the curvature perturbation. The model does not suffer from instabilities such as ghosts and is the only concrete model, to date, which can produce the curvature perturbation without direct involvement of fundamental scalar fields.There has been a recent outburst of activity in the cosmological implications of vector fields. In particular, the possible contribution of vector fields to the curvature perturbation ζ is receiving growing attention [1,2,3], with emphasis on characteristic signatures such as statistical anisotropy in the spectrum and bispectrum of ζ [4, 5,6,7]. The forthcoming observations of Planck satellite may well detect statistical anisotropy in the near future. On the theoretical side, it is a challenge to investigate whether the curvature perturbation can be generated without fundamental scalar fields. Even though theories beyond the standard model are abundant in scalar fields, no scalar field has ever been observed. The LHC may or may not confirm the existence of scalar fields. In the latter case it is imperative to find alternatives for the generation of ζ.The pioneering work in Ref.[1] offered such a possibility by showing that a massive Abelian vector field alone can, in principle, generate ζ following the curvaton mechanism, originally introduced for scalar fields [8]. The only requirement is that some suitable mechanism breaks the conformality of the vector field during inflation, such that an (almost) scale invariant spectrum of vector field perturbations is generated. This was firstly attempted by introducing a non-minimal coupling to gravity, of the form 1 6 RA 2 [2]. In another attempt, a non-trivial variation of the kinetic function was considered [3]. However, in these early works on the vector curvaton, statistical anisotropy was ignored. But, as shown in Ref.[4], if particle production of the vector field perturbations is strongly anisotropic the statistical anisotropy in the spectrum can be excessive. In this case observational bounds force the vector field contribution to ζ to be subdominant. This was found to be the case for the 1 6 RA 2 model [4]. Moreover, the model was criticised for giving rise to instabilities, such as ghosts [9]. In view of these developments, here we reexamine the model of Ref.[3] taking statistical anisotropy fully into account. * Electronic address: k.dimopoulos1@lancaster.ac.uk † Electronic address: m.karciauskas@lancaster.ac.uk ‡ Electronic address: wagstafj@exchange.lancs.ac.uk A massive, Abelian vector field has Lagrangian densitywhere f is the kinetic function and the field strength te...

It is shown that a massive Abelian vector boson field can generate the curvature perturbation in the Universe, when coupled non-minimally to gravity, through an RA 2 coupling. The vector boson acts as a curvaton field imposing the curvature perturbation after the end of inflation, without generating a large-scale anisotropy. The parameter space of the model is fully explored, obtaining the relevant bounds on the inflation scale and the decay constant of the vector curvaton.

We suppose that a vector field perturbation causes part of the primordial curvature perturbation. The non-Gaussianity parameter fNL is then, in general, statistically anisotropic. We calculate its form and magnitude in the curvaton scenario and in the end-of-inflation scenario. We show that this anisotropy could easily be observable.Comment: 10 pages; v2: minor sign mistake corrected which affected Eqs. (18), (28) and (29

Abstract. Apparent metastability of the electroweak vacuum poses a number of cosmological questions. These concern evolution of the Higgs field to the current vacuum, and its stability during and after inflation. Higgs-inflaton and non-minimal Higgs-gravity interactions can make a crucial impact on these considerations potentially solving the problems. In this work, we allow for these couplings to be present simultaneously and study their interplay. We find that different combinations of the Higgs-inflaton and non-minimal Higgs-gravity couplings induce effective Higgs mass during and after inflation. This crucially affects the Higgs stability considerations during preheating. In particular, a wide range of the couplings leading to stable solutions becomes allowed.

The coupling RA 2 /6 of a vector field to gravity was proposed as a mechanism for generating a primordial magnetic field, and more recently as a mechanism for generating a statistically anisotropic contribution to the primordial curvature perturbation. In either case, the vector field's perturbation has both a transverse and a longitudinal component, and the latter has some unusual features which call into question the health of the theory. We calculate for the first time the energy density generated by the longitudinal field perturbations, and go on to argue that the theory may well be healthy in at least some versions. * Electronic address: m.karciauskas@lancaster.ac.uk † Electronic address: d.lyth@lancaster.ac.uk