5. Discussions
In this work, we presented a model of inflation in which the Higgs scalar is the inflaton. In our model, we have assumed Higgs is non-minimally coupled to Gauss-Bonnet Gravity in 4- dimensions. We have shown analytically that scalar field with φ4 potential term leads to power-law inflation, however, adding a mass leads to the exit of inflation. We have explicitly shown that the exit is close to the Electroweak scale. Power-spectrum generated from our model is consistent with the PLANCK observations. There have been earlier attempts to look for an inflationary model at electro-weak scales [46–51]. Our model leads to inflation with exit at Electroweak scale due to non-minimal coupling of the Higgs to Gauss-Bonnet gravity term. In the model proposed by German et al.Ref. [49], thermal effects lead to low-scale inflation in supersymmetric or large extra dimensions. It is intriguing that Gauss-Bonnet gravity which are higherderivative gravity corrections to Einstein gravity and hence are expected to have strong effects only in the early universe. However,we have explicitly shown that Gauss-Bonnet gravity leads a dynamical model at low-energies. Our model is in spirit with Chaotic inflationary model of Linde [44]. Our model does not require an extension of standard model but is a natural phenomenon within standard model at the cost of a non minimal coupling of Higgs field with the Gauss-Bonnet coupling. Our analysis also indicate possible implications of the GaussBonnet coupling at LHC.1 As mentioned in the previous section, PLANCK observations constrain all parameters of our model, however, it does not constrain the epoch of inflation. Using the non-Gaussianity constraints of PLANCK may help to break the degeneracy between h0 and t0. This is currently under investigation.
