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 $-{\lambda }_{HS}$ 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 $y_t$, the potential along the valley becomes negative since the Higgs quartic coupling ${\lambda }_H$ becomes negative at inflationary scale. Then slow-roll inflation cannot occur. For inflation to definitely occur, we render the coupling $-{\lambda }_{HS}$ positive at inflationary scale and consider the $S$-inflation case. This is achieved by introducing a new singlet scalar $\eta$ with the large coupling ${\lambda }_{H\eta }$ to $H$. By this extension, ${\lambda }_H$ can also always be positive, and we consider this case as the simplest case. We consider inflation with the nonminimal coupling ${\xi }_S$ between $S$ and gravity. Although ${\xi }_S$ is large such as ${\xi }_S\simeq {𝒪}(10^3)$, unitarity is not violated since couplings between $S$ and other fields are sufficiently small. $\eta$ is odd under a new symmetry $Z_2$ not to mix with $H$ regardless of largeness of ${\lambda }_{H\eta }$. Because of this symmetry, $\eta$ may have its relic abundance ${\mathrm{\Omega }}_{\eta }{ĥ}^2$ comparable with the observational value ${\mathrm{\Omega }}^{\mathrm{\text{obs}}}{ĥ}^2\simeq 0.12$ of the dark matter relic abundance. However, the spin-independent elastic cross-section ${\sigma }_{\mathrm{\text{SI}}}^{\eta }$ of $\eta$ exceeds the observational bound ${\sigma }_{\mathrm{\text{SI}}}^{\mathrm{\text{obs}}}\sim {𝒪}(10^{-47})$ cm². Hence, we impose the resonance condition $m_{\eta }\simeq m_S/2$ and reduce ${\mathrm{\Omega }}_{\eta }{ĥ}^2$ to much smaller than ${\mathrm{\Omega }}^{\mathrm{\text{obs}}}{ĥ}^2$. Constraints from the electroweak scale physics and inflationary scale physics are much strong, and the allowed parameter space is very narrow.

我们扩展了一个经典的尺度不变模型，其中电弱对称破坏是由隐藏 QCD 扇区中的动态手征对称破坏触发的，以及一个真正的单线态标量 $秒$中介这两个部门。此外，我们的模型可以解释宇宙膨胀而不会违反幺正性。缓慢的膨胀发生在标量势的谷底。在原始模型中，联轴器$-{\lambda }_{H秒}$ 希格斯场之间 $H$ 和 $秒$ 总是负面的，因此，潜力在 $H$——$秒$混合方向。大值顶级汤川联轴器${是}_{吨}$，由于希格斯四次耦合，沿谷的电位变为负 ${\lambda }_H$在通胀规模上变为负值。那么慢速通胀就不会发生。为了肯定会发生通货膨胀，我们渲染了耦合$-{\lambda }_{H秒}$ 在通胀规模上为正，并考虑 $秒$- 通货膨胀情况。这是通过引入新的单线态标量来实现的$\eta$ 大联轴器 ${\lambda }_{H\eta }$ 到 $H$. 通过这个扩展，${\lambda }_H$也可以总是正数，我们认为这种情况是最简单的情况。我们考虑非最小耦合的通货膨胀${\xi }_{秒}$ 之间 $秒$和重力。虽然${\xi }_{秒}$ 大如 ${\xi }_{秒}\simeq {𝒪}(10^3)$，不违反单一性，因为之间的耦合 $秒$ 和其他领域足够小。 $\eta$ 在新的对称性下是奇数 $Z_2$ 不可混用 $H$ 不管有多大 ${\lambda }_{H\eta }$. 由于这种对称性，$\eta$ 可能有它的遗迹丰富 ${\mathrm{\Omega }}_{\eta }{H}^2$ 与观测值相当 ${\mathrm{\Omega }}^{\mathrm{\text{观测}}}{H}^2\simeq 0.12$暗物质遗迹的丰度。然而，与自旋无关的弹性截面${\sigma }_{\mathrm{\text{SI}}}^{\eta }$ 的 $\eta$ 超出观察范围 ${\sigma }_{\mathrm{\text{SI}}}^{\mathrm{\text{观测}}}～{𝒪}(10^{-47})$厘米²。因此，我们强加共振条件${米}_{\eta }\simeq {米}_{秒}/2$ 并减少 ${\mathrm{\Omega }}_{\eta }{H}^2$ 远小于 ${\mathrm{\Omega }}^{\mathrm{\text{观测}}}{H}^2$. 来自电弱尺度物理和暴胀尺度物理的约束非常强，并且允许的参数空间非常狭窄。