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 （R^2引力单独存在，没有额外的R项，其中R是里奇标量） 被证明是等效于爱因斯坦引力与非零宇宙 常数场和无质量标量场这种等效性通过 它的尺度对称性的自发破缺（它实际上拥有一个更大的对称性，称为限制外尔 对称性）。无质量标量场被确定为戈德斯通玻色子， 破碎的扇区非零的宇宙学常数意味着， 在爱因斯坦作用下，真空或背景时空具有非零的Ricci标量，可以是de Sitter（dS）或反de Sitter（AdS），但不是Minkowski 时空在不间断扇区中，真空解具有R=0和Minkowski 时空是一种背景解决方案。然而，先前的作者表明， 关于闵可夫斯基时空的线性化R^2引力并不产生引力子 而仅仅是传播标量。简单地说，闵可夫斯基并不“吸引”在 这个理论中的线性化水平。 我们计划的目标之一是研究增加一个 希格斯场是非最小耦合的Ricci标量在原来的行动。 希格斯场必须是无质量的，才能保持受限制的外尔 对称性，但它获得了质量后，在爱因斯坦的行动对称性是 自发破裂。加入希格斯场有两个关键的后果。首先，在爱因斯坦作用量中， 希格斯粒子和额外无质量标量之间的相互作用项 领域第二，虽然没有希格斯场的原始纯R^2理论不可行， 在闵可夫斯基背景下，当希格斯场获得非零真空期望值时，它确实有一个。如果希格斯玻色子是三重标量场， 在爱因斯坦引力下。我 我和我的合作者已经从数字上得到了爱因斯坦-杨-米尔斯-希格斯 （EYMH）磁单极子在闵可夫斯基，dS和AdS背景中具有非最小耦合。我们现在要研究 EYMH磁单极子与相互作用项，一些东西， 至今从未实施过。 我们可以包括 所有标准模型中的场都与无质量的希格斯粒子作用 双重的在自发对称破缺之后， 具有大质量希格斯粒子但具有新颖相互作用的标准模型 在标量场和希格斯偶线之间。这将是非常有趣的 来研究标准模型之外的物理学

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.