Dilatonic Inflation, Gravitino and Reheating in Modified Modular invariant Supergravity

A new modified string-inspired modular invariant supergravity model is proposed and is applied to realize the slow roll inflation in Einstein frame, so that the model explains WMAP observations very well. Gravitino mass and their production rate from scalar fields are estimated at certain values of parameters in the model. Seven cases of parameter choices are discussed here, among which some examples show the possibility of observation of gauginos by LHC experiments, which will give some hints of identity of dark matters. The reheating temperature, which is estimated by the stability condition of Boltzmann equation by using the decay rates of the dilaton $S$ into gauginos, is lower than the mass of gravitino. Therefore no thermal reproduction of gravitinos happens. The ratio between the scalar and tensor power spectrum is predicted to be almost the same for the seven cases under study, and its value $r \sim 6.8 \times 10^{-2}$ seems in the range possibly observed by the Planck satellite soon. The plausible supergravity model of inflation, which will be described here, will open the hope to construct a realistic theory of particles and cosmology in this framework, including yet undetected objects.Comment: 12 pages, 4 figures, 2 table

Supersymmetry Breaking and Gravitino Production after Inflation in Modular Invariant Supergravity

By using a string-inspired modular invariant supergravity, which was proved well to explain WMAP observations appropriately, a mechanism of supersymmetry breaking (SSB) and Gravitino Production just after the end of inflation are investigated. Supersymmetry is broken mainly by F-term of the inflaton superfield and the Goldstino is identified to be inflatino in this model, which fact is shown numerically. By using the canonically normalized and diagonalized scalars, the decay rates of these fields are calculated, for both the $T$ and $Y$ into gravitinos. Non-thermal production of gravitinos is not generated from the inflaton (dilaton), since the inflaton mass is lighter than gravitino, but they are produced by the decay of modular field $T$ and scalar field $Y$. Because the reheating temperature $T_R$ is about order $\sim O(10^{10})$ GeV and the mass of gravitino is $3.16 \times 10^{12}$ GeV, it is not reproduced after the reheating of the universe. The gravitinos are produced almost instantly just after the end of inflation through $Y$ and $T$, not from inflaton. Because the decay time appears very rapid, gravitinos disappear before the BBN stage of the universe. The effects of the lightest supersymmetric particles (LSP) produced by gravitinos may be important to investigate more carefully, if the LSP's are the candidate of dark matter.Comment: 11 pages, 1 figure