### Abstract

The presence of a light vector field coupled to a scalar field during inflation makes a distinct prediction: the observed correlation functions of the cosmic microwave background (CMB) become statistically anisotropic. We study the implications of the current bound on statistical anisotropy derived from the Planck 2013 CMB temperature data for such a model. The previous calculations based on the attractor solution indicate that the magnitude of anisotropy in the power spectrum is proportional to N^{2}, where N is the number of e-folds of inflation counted from the end of inflation. In this paper, we show that the attractor solution is not necessarily compatible with the current bound, and derive new predictions using another branch of anisotropic inflation. In addition, we improve upon the calculation of the mode function of perturbations by including the leading-order slow-roll corrections. We find that the anisotropy is roughly proportional to [2(ε_{H}+4η_{H})/3 - 4(c - 1)]^{-2}, where ε_{H} and η_{H} are the usual slow-roll parameters and c is the parameter in the model, regardless of the form of potential of an inflaton field. The bound from Planck implies that breaking of rotational invariance during inflation (characterized by the background homogeneous shear divided by the Hubble rate) is limited to be less than O(10^{-9}). This bound is many orders of magnitude smaller than the amplitude of breaking of time translation invariance, which is observed to be O(10^{-2}).

Original language | English |
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Article number | 045 |

Journal | Journal of Cosmology and Astroparticle Physics |

Volume | 2015 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2015 Apr 27 |

### Keywords

- CMBR theory
- cosmological perturbation theory
- inflation

### ASJC Scopus subject areas

- Astronomy and Astrophysics

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## Cite this

*Journal of Cosmology and Astroparticle Physics*,

*2015*(4), [045]. https://doi.org/10.1088/1475-7516/2015/04/045