Abstract
We study inflation and cosmological electroweak phase transitions utilizing the Standard model augmented by $N$ scalars respecting a global $O(N)$ symmetry. We observe that the representation of the global symmetry is restricted by the inflationary observables and the condition of a strongly first order electroweak phase transition. Theoretical constraints including the stability, perturbativity and unitarity are used to bound the model parameter space. The Electroweak precision observables and Higgs precisions limit the representation of the symmetry. We evaluate the possibility to simultaneously address the inflation and the dark matter after considering the experimental constraints from the future leptonic colliders. When the $O (N)$ symmetry respected by the N-scalar is spontaneously broken to the $O (N-1)$ symmetry, both the one-step and two-step SFOEWPT can occur within the inflation viable parameter regions, which will be tested by the future CEPC, ILC and FCC-ee. The relation between the number of Goldstones and the SFOEWPT condition depends on phase transition patterns. The situation of Goldstone faking neutrinos and contributing to the dark radiation are investigated.
Highlights
To our knowledge, the standard model of particle physics (SM) is incapable of explaining the three longstanding problems of particle physics and cosmology, i.e., the horizon, flatness, and monopole problems of the Universe, the baryon asymmetry of the Universe (BAU), and the existence of dark matter
Previous studies of N scalars with an exact OðNÞ symmetry suggest that a one-step strongly first-order electroweak phase transition (SFOEWPT) can be realized with a relatively large N, which results in detectable gravitational wave signals with typical frequency of ∼Oð10−3 − 10−1Þ Hz [50,51,52] and a substantial triple Higgs coupling deviation to be probed by the future colliders [51,52]
Our study shows that the electroweak precision observable (EWPOs) constraints invalidate the inflation explanation when N > 4 for the OðNÞ scalars that shout down the window to accommodate a SFOEWPT
Summary
The standard model of particle physics (SM) is incapable of explaining the three longstanding problems of particle physics and cosmology, i.e., the horizon, flatness, and monopole problems of the Universe, the baryon asymmetry of the Universe (BAU), and the existence of dark matter. Previous studies of N scalars with an exact OðNÞ symmetry suggest that a one-step SFOEWPT can be realized with a relatively large N, which results in detectable gravitational wave signals with typical frequency of ∼Oð10−3 − 10−1Þ Hz [50,51,52] and a substantial triple Higgs coupling deviation to be probed by the future colliders [51,52]. Our study shows that the electroweak precision observable (EWPOs) constraints invalidate the inflation explanation when N > 4 for the OðNÞ scalars that shout down the window to accommodate a SFOEWPT. The paper is organized as follows: In Sec. II, we introduce the model including the case of the scalars respecting the OðNÞ symmetry and the scenario where the OðNÞ is spontaneously broke to the OðN − 1Þ, the relevant theoretical constraints and the Higgs precision constraints are explored.
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