Quantum Fluctuations of Vector Fields and the Primordial Curvature Perturbation in the Universe

Understand

The \delta N formalism is extended to include the perturbation of the vector field.

• The latter is quantized in de Sitter space-time and it is found that in general the particle production process of the vector field is anisotropic.
• This anisotropy is parametrized by introducing two parameters p and q, which are determined by the conformal invariance breaking mechanism.
• If any of them are non-zero, generated \zeta is statistically anisotropic.