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引力本身，没有额外的R项，其中R是Ricci标量)已经被证明等同于具有非零宇宙常数和额外的无质量标量场的爱因斯坦引力。这种等价性是通过*自发地打破其标度对称性而发生的(它实际上拥有一个更大的对称性，称为限制性韦尔对称性)。无质量标量场被认为是破碎扇区的戈德斯通玻色子。非零的宇宙常数意味着，在*爱因斯坦作用中，真空或背景时空具有非零的利玛窦标量，可以是de Sitter(DS)或anti-de Sitter(ADS)，但不是Minkowski*时空。在连续扇区，真空解的R=0，Minkowski*时空是背景解。然而，以前的作者*已经证明，关于Minkowski时空的线性化R^2引力不会产生引力子*，而只产生一个传播的标量。简而言之，在这个理论中，明可夫斯基并没有在线性化的层面上“引力”。我们计划的目标之一是研究在原始作用中添加一个与Ricci标量非最小耦合的*希格斯场的含义。*希格斯场最初必须是无质量的，以保持受限的Weyl*对称性，但在对称性自发破缺后，它在爱因斯坦作用量中获得了质量。加入希格斯场有两个至关重要的后果。首先，在爱因斯坦作用量中，在希格斯粒子和额外的无质量标量场之间出现了一个新的*相互作用项。其次，尽管没有希格斯场的原始纯R^2理论没有可行的Minkowski背景，但当Higgs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，人们就可以在爱因斯坦引力下研究磁单极子。我和我的合作者已经在数值上获得了Minkowski、DS和ADS背景下具有非最小耦合的爱因斯坦-杨-米尔斯-希格斯*(EYMH)磁单极子。我们现在想用相互作用项来研究EYMH磁单极子，这是迄今为止还没有进行过的事情。*我们可以用一个无质量的希格斯二重数把*所有的标准模型场包括在我们的原始动作中。在自发对称性破缺后，我们将恢复通常的*标准模型，其中有一个大质量的希格斯粒子，但在标量场和希格斯双重态之间有一种新的相互作用。将这作为超越标准模型的物理学的一部分进行研究将是非常有意义的。

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.