Inflation based on a classically scale invariant extended standard model
Abstract
We extend a classically scale invariant model where the electroweak symmetry breaking is triggered by the dynamical chiral symmetry breaking in a hidden QCD sector, and a real singlet scalar S mediates these two sectors. Our model can explain cosmic inflation without unitarity violation in addition. Slow-roll inflation occurs along a valley in scalar potential. In the original model, the coupling −λHS between the Higgs field H and S is always negative and therefore, the potential has its valleys in H-S mixed directions. For large value of the top Yukawa coupling yt, the potential along the valley becomes negative since the Higgs quartic coupling λH becomes negative at inflationary scale. Then slow-roll inflation cannot occur. For inflation to definitely occur, we render the coupling −λHS positive at inflationary scale and consider the S-inflation case. This is achieved by introducing a new singlet scalar η with the large coupling λHη to H. By this extension, λH can also always be positive, and we consider this case as the simplest case. We consider inflation with the nonminimal coupling ξS between S and gravity. Although ξS is large such as ξS≃𝒪(103), unitarity is not violated since couplings between S and other fields are sufficiently small. η is odd under a new symmetry Z2 not to mix with H regardless of largeness of λHη. Because of this symmetry, η may have its relic abundance Ωηĥ2 comparable with the observational value Ωobsĥ2≃0.12 of the dark matter relic abundance. However, the spin-independent elastic cross-section σηSI of η exceeds the observational bound σobsSI∼𝒪(10−47) cm2. Hence, we impose the resonance condition mη≃mS/2 and reduce Ωηĥ2 to much smaller than Ωobsĥ2. Constraints from the electroweak scale physics and inflationary scale physics are much strong, and the allowed parameter space is very narrow.
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