Abstract
Supergravity (SUGRA) theories with exact global U(1) symmetry or shift symmetry in Kähler 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∼0.01 and running spectral index αs∼ −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.
Highlights
To realize inflation [1, 2] in supergravity (SUGRA) theory, the flat conditions give strong constraints on the F-term scalar potential with an exponential factor eK(Φ,Φ) which is too steep to generate inflation by the field close or above the reduced Planck scale
The coefficient of the U (1) symmetry breaking term is of the order 10−2, which is sufficient large to improve the inflationary predictions while its higher order corrections are negligible
We found that by introducing small symmetry breaking term the inflationary predictions are significantly improved, in the the η problem remains absent even though the symmetry is approximate
Summary
To realize inflation [1, 2] in supergravity (SUGRA) theory, the flat conditions give strong constraints on the F-term scalar potential with an exponential factor eK(Φ,Φ) which is too steep to generate inflation by the field close or above the reduced Planck scale. In this work we will show that by introducing a small U(1) symmetry breaking term, the phase potential will be slightly modulated by a trigonometric factor, and their predictions on inflation are highly consistent with the new Planck results. In the SUGRA inflation with breaking shift symmetry, the modulated linear and quadratic models agree with the Planck observations due to the additional exponential factor in the inflaton potential. In these two kinds of models, the tensor-to-scalar ratio can be of the order 10−2, which will be tested by the near future experiments.
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