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 precision 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 situations of Goldstone faking neutrinos and contributions to dark radiation are investigated.

• Received 18 November 2018
• Revised 22 January 2019

DOI:https://doi.org/10.1103/PhysRevD.99.035038

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

Published by the American Physical Society