Konstantinos Dimopoulos

Statistical anisotropy of the curvature perturbation from vector field perturbations

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.

Can a vector field be responsible for the curvature perturbation in the Universe

I investigate the possibility that the observed curvature perturbation is due to a massive vector field. To avoid generating a large scale anisotropy the vector field is not taken to be driving inflation. Instead it is assumed to become important after inflation when it may dominate the Universe and imprint its perturbation spectrum before its decay, as in the curvaton scenario. It is found that, to generate a scale invariant spectrum of perturbations, the mass-squared of the vector field has to be negative and comparable to the Hubble scale during inflation. After inflation the mass-squared must become positive so that the vector field engages into oscillations. It is shown that such an oscillating vector field behaves as pressureless matter and does not lead to large scale anisotropy when it dominates the Universe. The possibility of realizing this scenario in supergravity is also outlined.

Vector Curvaton with varying Kinetic Function

A new model realization of the vector curvaton paradigm is presented and analyzed. 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 scaleinvariant 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.

Models of inflation liberated by the curvaton hypothesis

It is usually supposed that inflation is of the slow-roll variety and that the inflaton generates the primordial curvature perturbation. According to the curvaton hypothesis, inflation need not be slow-roll, and if it is, the inflaton generates a negligible curvature perturbation. We find that the construction of slow-roll inflation models becomes much easier under this hypothesis. Also, thermal inflation followed by fast-roll becomes viable, with no slow-roll inflation at all.

Vector curvaton without instabilities

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.

Reconciliation of high energy scale models of inflation with Planck

The inflationary cosmology paradigm is very successful in explaining the CMB anisotropy to the percent level. Besides the dependence on the inflationary model, the power spectra, spectral tilt and non-Gaussianity of the CMB temperature fluctuations also depend on the initial state of inflation. Here, we examine to what extent these observables are affected by our ignorance in the initial condition for inflationary perturbations, due to unknown new physics at a high scale M. For initial states that satisfy constraints from backreaction, we find that the amplitude of the power spectra could still be significantly altered, while the modification in bispectrum remains small. For such initial states, M has an upper bound of a few tens of H, with H being the Hubble parameter during inflation. We show that for M ∼ 20H, such initial states always (substantially) suppress the tensor to scalar ratio. In particular we show that such a choice of initial conditions can satisfactorily reconcile the simple 1 m 2 φ 2 chaotic model with the Planck data (1)

Anisotropic non-Gaussianity from vector field perturbations

We suppose that a vector field perturbation causes part of the primordial curvature perturbation. The non-Gaussianity parameter f_NL 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.

Primordial spectrum of gauge fields from inflation

Abstract We show that conformal invariance of gauge fields is naturally broken in inflation, having as a consequence amplification of gauge fields. The resulting spectrum of the field strength is approximately B l ∝l −1 , where l is the relevant coherence scale. One realisation of our scenario is scalar electrodynamics with a scalar whose mass is large enough to evade observational constraints — the obvious candidates being supersymmetric partners of the standard-model fermions. Our mechanism also leads naturally to amplification of the standard-model Z -boson field due to its coupling to the electroweak Higgs field. At preheating, the spectrum of the Z field is transferred to the hypercharge field, which remains frozen in the plasma and is converted into a magnetic field at the electroweak phase transition. With a reasonable model of field evolution one obtains a magnetic field strength of the order of 10 −29 Gauss on a scale of 100 pc, the size of the largest turbulent eddy in a virialised galaxy. Resonant amplification in preheating can lead to primordial fields as large as 10 −24 Gauss, consistent with the seed field required for the galactic dynamo mechanism.

A-term inflation and the minimal supersymmetric standard model

The parameter space for A-term inflation is explored with W = λpp/pMPp−3. With p = 6 and λp~1, the observed spectrum and spectral tilt can be obtained with soft mass of order 102 GeV but not with a much higher mass. The case p = 3 requires λp~10−9 to 10−12. The ratio m/A requires fine-tuning, which may be justified on environmental grounds. An extension of the minimal supersymmetric standard model to include non-renormalizable terms and/or Dirac neutrino masses might support either A-term inflation or modular inflation.The parameter space for A-term inflation is explored with W = �pp /pM p−3 P. With p = 6 andp ∼ 1, the observed spectrum and spectral tilt can be obtained with soft mass of order 10 2 GeV but not with a much higher mass. The case p = 3 requiresp ∼ 10 −9 to 10 −12 . The ratio m/A requires fine-tuning, which may be justified on environmental grounds. An extension of the MSSM to include non-renormalizable terms and/or Dirac neutrino masses might support either A-term inflation or modular inflation.

Particle Production of Vector Fields: Scale Invariance is Attractive

In a model of an Abelian vector boson with a Maxwell kinetic term and non-negative mass-squared it is demonstrated that, under fairly general conditions during inflation, a scale-invariant spectrum of perturbations for the components of a vector field, massive or not, whose kinetic function (and mass) is modulated by the inflaton field is an attractor solution. If the field is massless, or if it remains light until the end of inflation, this attractor solution also generates anisotropic stress, which can render inflation weakly anisotropic. The above two characteristics of the attractor solution can source (independently or combined together) significant statistical anisotropy in the curvature perturbation, which may well be observable in the near future.