Sphaleron and gravitational wave with the Higgs-Dilaton potential in the Standard Model Two-Time Physics

By introducing a Higgs-Dilaton potential, the 2T model has a trigger for a first order electroweak phase transition, namely for the mass of Dilaton between $300$ GeV and $550$ GeV. We have also compared the transition strengths in the case with and without daisy loops, the difference being always less than $0.2$. The effective Higgs potential has given a sphaleron energy less than $8.4$ TeV. The timescale of phase transition $(\beta/H^*)$ is larger than $25$ and less than $34$ in all cases that are sufficient to trigger the first order electroweak phase transition. Gravitational wave energy density caused by this transition, may be detected by future detectors, could indirectly confirm Dilaton.