Initial Conditions for Vector Inflation

Recently, a model of inflation using non-minimally coupled massive vector fields has been proposed. For a particular choice of non-minimal coupling parameter and for a flat FRW model, the model is reduced to the model of chaotic inflation with massive scalar field. We study the effect of non-zero curvature of the universe on the onset of vector inflation. We find that in a curved universe the dynamics of vector inflation can be different from chaotic inflation, and the fraction of the initial conditions leading to inflationary solutions is reduced compared with the chaotic inflation case.Comment: 12 pages, 5 figures, version to be published in JCA

Primordial statistical anisotropy generated at the end of inflation

We present a new mechanism for generating primordial statistical anisotropy of curvature perturbations. We introduce a vector field which has a non-minimal kinetic term and couples with a waterfall field in hybrid inflation model. In such a system, the vector field gives fluctuations of the end of inflation and hence induces a subcomponent of curvature perturbations. Since the vector has a preferred direction, the statistical anisotropy could appear in the fluctuations. We present the explicit formula for the statistical anisotropy in the primordial power spectrum and the bispectrum of curvature perturbations. Interestingly, there is the possibility that the statistical anisotropy does not appear in the power spectrum but does appear in the bispectrum. We also find that the statistical anisotropy provides the shape dependence to the bispectrum.Comment: 9 pages, This version supersedes the JCAP version. Minor revision

Noether Symmetry Approach in "Cosmic Triad" Vector Field Scenario

To realize the accelerations in the early and late periods of our universe, we need to specify potentials for the dominant fields. In this paper, by using the Noether symmetry approach, we try to find suitable potentials in the "cosmic triad" vector field scenario. Because the equation of state parameter of dark energy has been constrained in the range of $-1.21\leq \omega\leq -0.89$ by observations, we derive the Noether conditions for the vector field in quintessence, phantom and quintom models, respectively. In the first two cases, constant potential solutions have been obtained. What is more, a fast decaying point-like solution with power-law potential is also found for the vector field in quintessence model. For the quintom case, we find an interesting constraint $\tilde{C}V_{p}'=-CV_{q}'$ on the field potentials, where $C$ and $\tilde{C}$ are constants related to the Noether symmetry.Comment: 15 pages, no figures, accepted by Classical and Quantum Gravity

On cosmic inflation in vector field theories

We investigate the longitudinal ghost issue in Abelian vector inflation. It turns out that, within the class of Lorentz-invariant vector field theories with three degrees of freedom and without any extra (scalar) fields, the possibilities are essentially exhausted by the classical solution due to Larry Ford with an extremely flat potential which doesn't feel the fast roll of its argument. And, moreover, one needs to fulfil an extra condition on that potential in order to avoid severe gradient instability. At the same time, some Lorentz-violating modifications are worth to be explored.Comment: 10 pages; a few minor typos corrected; published versio

Higher Curvature Corrections to Primordial Fluctuations in Slow-roll Inflation

We study higher curvature corrections to the scalar spectral index, the tensor spectral index, the tensor-to-scalar ratio, and the polarization of gravitational waves. We find that the higher curvature corrections can not be negligible in the dynamics of the scalar field, although they are energetically negligible. Indeed, it turns out that the tensor-to-scalar ratio could be enhanced and the tensor spectral index could be blue due to the Gauss-Bonnet term. We estimate the degree of circular polarization of gravitational waves generated during the slow-roll inflation. We argue that the circular polarization can be observable with the help both of the Gauss-Bonnet and parity violating terms. We also present several examples to reveal observational implications of higher curvature corrections for chaotic inflationary models.Comment: 12 pages, 4 figure

Statistical Anisotropy from Anisotropic Inflation

We review an inflationary scenario with the anisotropic expansion rate. An anisotropic inflationary universe can be realized by a vector field coupled with an inflaton, which can be regarded as a counter example to the cosmic no-hair conjecture. We show generality of anisotropic inflation and derive a universal property. We formulate cosmological perturbation theory in anisotropic inflation. Using the formalism, we show anisotropic inflation gives rise to the statistical anisotropy in primordial fluctuations. We also explain a method to test anisotropic inflation using the cosmic microwave background radiation (CMB).Comment: 32 pages, 5 figures, invited review for CQG, published versio

Inflationary buildup of a vector field condensate and its cosmological consequences

Light vector fields during inflation obtain a superhorizon perturbation spectrum when their conformal invariance is appropriately broken. Such perturbations, by means of some suitable mechanism (e.g. the vector curvaton mechanism), can contribute to the curvature perturbation in the Universe and produce characteristic signals, such as statistical anisotropy, on the microwave sky, most recently surveyed by the Planck satellite mission. The magnitude of such characteristic features crucially depends on the magnitude of the vector condensate generated during inflation. However, in the vast majority of the literature the expectation value of this condensate has so-far been taken as a free parameter, lacking a definite prediction or a physically motivated estimate. In this paper, we study the stochastic evolution of the vector condensate and obtain an estimate for its magnitude. Our study is mainly focused in the supergravity inspired case when the kinetic function and mass of the vector boson is time-varying during inflation, but other cases are also explored such as a parity violating axial theory or a non-minimal coupling between the vector field and gravity. As an example, we apply our findings in the context of the vector curvaton mechanism and contrast our results with current observations