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

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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.