论文标题
Higgs通货膨胀为非线性Sigma模型，而Scalaron作为其$σ$ -Meson
Higgs Inflation as Nonlinear Sigma Model and Scalaron as its $σ$-meson
论文作者
论文摘要
我们指出，具有与RICCI标量较大的非微小耦合（例如Higgs膨胀）具有标量字段的模型，可以视为非线性Sigma模型（NLSM）。不仅包括标量场，还包括度量标准模式，我们对NLSM目标空间的定义在帧转换下是不变的。我们表明，将此NLSM线性化为线性Sigma模型（LSM）的$σ$ -Meson对应于Scalaron，这与Jordan框架中的$ R^2 $项相关的自由度。我们证明，量子校正不可避免地会以$ n $限制引起$σ$ -Meson，从而为Scalaron的出现提供了独立的框架图片。所得的LSM仅涉及可恢复的相互作用，因此，除非击中Landau Pole，否则其扰动的单位性能达到Planck量表，这与二次重力的重量化性一致。
We point out that a model with scalar fields with a large nonminimal coupling to the Ricci scalar, such as Higgs inflation, can be regarded as a nonlinear sigma model (NLSM). With the inclusion of not only the scalar fields but also the conformal mode of the metric, our definition of the target space of the NLSM is invariant under the frame transformation. We show that the $σ$-meson that linearizes this NLSM to be a linear sigma model (LSM) corresponds to the scalaron, the degree of freedom associated to the $R^2$ term in the Jordan frame. We demonstrate that quantum corrections inevitably induce this $σ$-meson in the large-$N$ limit, thus providing a frame independent picture for the emergence of the scalaron. The resultant LSM only involves renormalizable interactions and hence its perturbative unitarity holds up to the Planck scale unless it hits a Landau pole, which is in agreement with the renormalizability of quadratic gravity.
