Li, TJ (reprint author), Chinese Acad Sci, State Key Lab Theoret Phys, Inst Theoret Phys, Beijing 100190, Peoples R China.
Supergravity (SUGRA) theories with exact global U(1) symmetry or shift symmetry in Kahler potential provide natural frameworks for inflation. However, quadratic inflation is disfavoured by the new results on primordial tensor fluctuations from the Planck Collaboration. To be consistent with the new Planck data, we point out that the explicit. symmetry breaking is needed, and study these two SUGRA inflation in detail. For SUGRA inflation with global U(1) symmetry, the symmetry breaking term leads to a trigonometric modulation on inflaton potential. Coefficient of the U(1) symmetry breaking term is of order 10(-2), which is sufficient large to improve the inflationary predictions while its higher order corrections are negligible. Such models predict sizeable tensor fluctuations and highly agree with the Planck results. In particular, the model with a linear U(1) symmetry breaking term predicts the tensor-to-scalar ratio around r similar to 0.01 and running spectral index alpha(s) similar to -0.004, which comfortably fit with the Planck observations. For SUGRA inflation with breaking shift symmetry, the inflaton potential is modulated by an exponential factor. The modulated linear and quadratic models are consistent with the Planck observations. In both types of models the tensor-to-scalar ratio can be of order 10(-2) which will be tested by the near future observations.