[Li, Mingzhe] Univ Bielefeld, Fak Phys, D-33615 Bielefeld, Germany
; [Li, Mingzhe] Nanjing Univ, Dept Phys, Nanjing 210093, Peoples R China
; [Li, Mingzhe] Nanjing Univ, Purple Mt Observ, Joint Ctr Particle Nucl Phys & Cosmol, Nanjing 210093, Peoples R China
; [Zhang, Xinmin] Chinese Acad Sci, Inst High Energy Phys, Beijing 100049, Peoples R China
A dark energy scalar (or a function of the Ricci scalar) coupled with the derivative to the matter fields will violate the CPT symmetry during the expansion of the Universe. This type of cosmological CPT violation helps to generate the baryon number asymmetry and gives rise to the rotation of the photon polarization which can be measured in the astrophysical and cosmological observations, especially the experiments of the cosmic microwave background radiation. In this paper, we derive the rotation angle in a fully general relativistic way and present the rotation formulas used for the cosmic microwave background data analysis. Our formulas include the corrections from the spatial fluctuations of the scalar field. We also estimate the magnitude of these corrections in a class of dynamical dark energy models for quintessential baryo/leptogenesis.