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Spectrum of Perturbations in Anisotropic Inflationary Universe with Vector Hair

Burak Himmetoglu

Abstract

We study both the background evolution and cosmological perturbations of anisotropic inflationary models supported by coupled scalar and vector fields. The models we study preserve the U(1) gauge symmetry associated with the vector field, and therefore do not possess instabilities associated with longitudinal modes (which instead plague some recently proposed models of vector inflation and curvaton). We first intoduce a model in which the background anisotropy slowly decreases during inflation; we then confirm the stability of the background solution by studying the quadratic action for all the perturbations of the model. We then compute the spectrum of the $h_{\times}$ gravitational wave polarization. The spectrum we find breaks statistical isotropy at the largest scales and reduces to the standard nearly scale invariant form at small scales. We finally discuss the possible relevance of our results to the large scale CMB anomalies.

Spectrum of Perturbations in Anisotropic Inflationary Universe with Vector Hair

Abstract

We study both the background evolution and cosmological perturbations of anisotropic inflationary models supported by coupled scalar and vector fields. The models we study preserve the U(1) gauge symmetry associated with the vector field, and therefore do not possess instabilities associated with longitudinal modes (which instead plague some recently proposed models of vector inflation and curvaton). We first intoduce a model in which the background anisotropy slowly decreases during inflation; we then confirm the stability of the background solution by studying the quadratic action for all the perturbations of the model. We then compute the spectrum of the gravitational wave polarization. The spectrum we find breaks statistical isotropy at the largest scales and reduces to the standard nearly scale invariant form at small scales. We finally discuss the possible relevance of our results to the large scale CMB anomalies.

Paper Structure

This paper contains 13 sections, 96 equations, 8 figures.

Table of Contents

  1. Introduction
  2. Anisotropic inflationary expansion due to coupled vector and scalar fields
  3. Single Scalar Field Inflationary Background
  4. Two Scalar Field Inflationary Background
  5. Perturbations
  6. Decomposition of Perturbations
  7. General Properties of Coupled System of Perturbations
  8. 2d Vector Perturbations
  9. Power Spectrum
  10. Conclusions
  11. Appendices
  12. Appendix I
  13. Appendix II

Figures (8)

  • Figure 1: The left panel shows the evolution of anisotropy during inflation and the right panel after inflation (during when the scalar field is oscillating). $H \equiv \dot\alpha$ and $h \equiv \dot\sigma$. The black dashed curve represents the approximate slow-roll solution during inflation and the straight red curves the numerical solution.
  • Figure 2: The left panel shows the evolution of the average Hubble rate ($H\equiv \dot\alpha$) and the right panel is the phase plot of the scalar field. Again, the black dashed lines are the slow-roll solutions. Time is measured in units of $m$.
  • Figure 3: The left panel shows the evolution of the average Hubble expansion. The right panel shows the evolution of anisotropy, where $H \equiv \dot\alpha$ and $h \equiv \dot\sigma$.
  • Figure 4: The phase portrait for the two scalar fields. The straight red line represents $\phi$ and the dashed black line represents $\phi_1$. Time is measured in units of $m$.
  • Figure 5: Parts of the power spectrum for $h_{\times}$ are shown for $\xi=0$ (straight line), $\xi=0.5$ (dashed line) and $\xi=1$(dotted line).
  • ...and 3 more figures