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

Konstantinos Dimopoulos

TL;DR

This work explores the vector curvaton scenario, asking whether a massive vector field can generate the Universe's curvature perturbations without producing large-scale anisotropy. It shows that a tachyonic mass around the Hubble scale during inflation can yield a nearly scale-invariant spectrum, while post-inflation oscillations in a positive-mass regime behave like pressureless matter, preserving isotropy even if the vector dominates. The perturbation transfer to curvature perturbations is analyzed within a curvaton framework, highlighting conditions under which the vector can imprint adiabatic perturbations after decay. Realising these conditions in concrete theories, notably supergravity, is possible in principle but requires substantial fine-tuning or additional field dynamics to ensure stability and correct post-inflation behaviour. Overall, the paper demonstrates a conceptually viable, though technically challenging, alternative to scalar-field perturbations for explaining cosmic structure.

Abstract

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 possibilitiy of realising this scenario in supergravity is also outlined.

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

TL;DR

This work explores the vector curvaton scenario, asking whether a massive vector field can generate the Universe's curvature perturbations without producing large-scale anisotropy. It shows that a tachyonic mass around the Hubble scale during inflation can yield a nearly scale-invariant spectrum, while post-inflation oscillations in a positive-mass regime behave like pressureless matter, preserving isotropy even if the vector dominates. The perturbation transfer to curvature perturbations is analyzed within a curvaton framework, highlighting conditions under which the vector can imprint adiabatic perturbations after decay. Realising these conditions in concrete theories, notably supergravity, is possible in principle but requires substantial fine-tuning or additional field dynamics to ensure stability and correct post-inflation behaviour. Overall, the paper demonstrates a conceptually viable, though technically challenging, alternative to scalar-field perturbations for explaining cosmic structure.

Abstract

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 possibilitiy of realising this scenario in supergravity is also outlined.

Paper Structure

This paper contains 12 sections, 85 equations, 1 figure.

Table of Contents

  1. Introduction
  2. The equations of motion
  3. Particle production
  4. The transverse component
  5. The longitudinal component
  6. Evolution during and after Inflation
  7. The evolution of the vector field
  8. The energy momentum tensor
  9. Generating the curvature perturbation
  10. The "physical" vector field
  11. Vector Curvaton in Supergravity
  12. Conclusions

Figures (1)

  • Figure 1: Illustration of the superhorizon spectra of the transverse and longitudinal components of the perturbation of a light vector field. The transverse component corresponds to the vacuum spectrum. The longitudinal component mimics the transverse component at small momenta but at large momenta its spectrum becomes approximately scale invariant.