TY - JOUR

T1 - Anisotropic inflation reexamined

T2 - Upper bound on broken rotational invariance during inflation

AU - Naruko, Atsushi

AU - Komatsu, Eiichiro

AU - Yamaguchi, Masahide

N1 - Publisher Copyright:
© 2015 IOP Publishing Ltd and Sissa Medialab srl.

PY - 2015/4/27

Y1 - 2015/4/27

N2 - 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 N2, 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(εH+4ηH)/3 - 4(c - 1)]-2, where εH and ηH 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).

AB - 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 N2, 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(εH+4ηH)/3 - 4(c - 1)]-2, where εH and ηH 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).

KW - CMBR theory

KW - cosmological perturbation theory

KW - inflation

UR - http://www.scopus.com/inward/record.url?scp=84928745692&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928745692&partnerID=8YFLogxK

U2 - 10.1088/1475-7516/2015/04/045

DO - 10.1088/1475-7516/2015/04/045

M3 - Article

AN - SCOPUS:84928745692

VL - 2015

JO - Journal of Cosmology and Astroparticle Physics

JF - Journal of Cosmology and Astroparticle Physics

SN - 1475-7516

IS - 4

M1 - 045

ER -