Implications of a Higgs field for the spontaneously broken pure R^2 gravity: magnetic monopoles, new interactions and dark radiation

纯R^2引力 (不带附加R项的R^2重力，其中R是Ricci标量) 被证明等同于爱因斯坦引力与非零宇宙学 常量和一个额外的无质量标量场。这种等价性通过 自发地打破了它的标度对称性(它实际上拥有一个更大的对称性，称为受限韦尔 对称性)。这个无质量的标量场被认为是 支离破碎的部门。非零的宇宙常数意味着在宇宙中 爱因斯坦作用量真空或背景时空具有非零的利玛窦标量，可以是德西特(DS)或反德西特(ADS)，但不是明可夫斯基 时空。在连续区，真空解具有R=0和Minkowski 时空是一种背景解决方案。然而，它是由以前的作者展示的 关于Minkowski时空的线性化R^2引力不会产生引力子 但只是一个传播的标量。简而言之，明科夫斯基不会对 这一理论中的线性化程度。 我们计划的目标之一是研究添加一个 在原始作用中非最小耦合到Ricci标量的希格斯场。 希格斯场最初必须是无质量的，才能保持受限制的Weyl 对称性，但它在爱因斯坦作用量中获得了质量 自发破裂的。加入希格斯场有两个至关重要的后果。首先，在爱因斯坦的行动中，有一个新的 在希格斯粒子和额外无质量标量粒子之间产生的相互作用项 菲尔德。其次，尽管没有希格斯场的原始纯R^2理论是不可行的 Minkowski背景，当希格斯场获得非零真空期望值时，它确实有一个。如果希格斯粒子是三重标量场，人们就可以研究磁单极子 在爱因斯坦引力下。我的 我和合作者已经得到了爱因斯坦-杨-米尔斯-希格斯的数值结果 在Minkowski、DS和ADS背景中具有非最小耦合的(EYMH)磁单极子。我们现在想要研究一下 EYMH磁单极子与相互作用项，它有 到目前为止从未实施过。 我们可以包括 无质量希格斯粒子的原始运动中的所有标准模型场 双人套装。在自发对称性破缺后，我们将恢复通常的对称性 具有大质量希格斯粒子但具有新的相互作用的标准模型 在标量场和希格斯二重态之间。这将是非常有意义的 作为超越标准模型的物理学的一部分进行研究。

Pure R^2 gravity (R^2 gravity alone with no additional R term where R is the Ricci scalar) has been shown to be equivalent to Einstein gravity with non-zero cosmological constant and an extra massless scalar field. This equivalence occurs via the spontaneous breaking of its scale symmetry (it actually possesses a larger symmetry called restricted Weyl symmetry). The massless scalar field is identified as the Goldstone boson of the broken sector. The non-zero cosmological constant implies that in the Einstein action the vacuum or background spacetime have non-zero Ricci scalar and can be either de Sitter (dS) or anti-de Sitter (AdS) but not Minkowski spacetime. In the unbroken sector, the vacuum solution has R=0 and Minkowski spacetime is a background solution. However, it was shown by previous authors that linearized R^2 gravity about Minkowski spacetime does not yield gravitons but only a propagating scalar. Simply put, Minkowski does not “gravitate” at the linearized level in this theory. One of the objectives of our program is to study the implications of adding a Higgs field that is non-minimally coupled to the Ricci scalar in the original action. The Higgs field must be originally massless to preserve the restricted Weyl symmetry but it acquires a mass in the Einstein action after the symmetry is spontaneously broken. There are two crucial consequences to adding the Higgs field. First, in the Einstein action, there is a new interaction term that arises between the Higgs and the extra massless scalar field. Secondly, though the original pure R^2 theory without Higgs field has no viable Minkowski background, it does have one when the Higgs field acquires a non-zero vacuum expectation value. If the Higgs is a triplet of scalar fields, one can study magnetic monopoles under Einstein gravity. My collaborator and I already obtained numerically Einstein-Yang-Mills-Higgs (EYMH) magnetic monopoles with non-minimal coupling in Minkowski, dS and AdS backgrounds. We would now like to study the EYMH magnetic monopoles with the interaction term, something which has never been carried out to date. We can include all the Standard Model fields in our original action with a massless Higgs doublet. After spontaneous symmetry breaking we would recover the usual Standard Model with a massive Higgs but with a novel interaction between the scalar field and the Higgs doublet. This would be of great interest to study as part of physics beyond the Standard Model.