Inflation based on a classically scale invariant extended standard model

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 [Formula: see text] 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 [Formula: see text] between the Higgs field [Formula: see text] and [Formula: see text] is always negative and therefore, the potential has its valleys in [Formula: see text]-[Formula: see text] mixed directions. For large value of the top Yukawa coupling [Formula: see text], the potential along the valley becomes negative since the Higgs quartic coupling [Formula: see text] becomes negative at inflationary scale. Then slow-roll inflation cannot occur. For inflation to definitely occur, we render the coupling [Formula: see text] positive at inflationary scale and consider the [Formula: see text]-inflation case. This is achieved by introducing a new singlet scalar [Formula: see text] with the large coupling [Formula: see text] to [Formula: see text]. By this extension, [Formula: see text] can also always be positive, and we consider this case as the simplest case. We consider inflation with the nonminimal coupling [Formula: see text] between [Formula: see text] and gravity. Although [Formula: see text] is large such as [Formula: see text], unitarity is not violated since couplings between [Formula: see text] and other fields are sufficiently small. [Formula: see text] is odd under a new symmetry [Formula: see text] not to mix with [Formula: see text] regardless of largeness of [Formula: see text]. Because of this symmetry, [Formula: see text] may have its relic abundance [Formula: see text] comparable with the observational value [Formula: see text] of the dark matter relic abundance. However, the spin-independent elastic cross-section [Formula: see text] of [Formula: see text] exceeds the observational bound [Formula: see text] cm2. Hence, we impose the resonance condition [Formula: see text] and reduce [Formula: see text] to much smaller than [Formula: see text]. Constraints from the electroweak scale physics and inflationary scale physics are much strong, and the allowed parameter space is very narrow.