^{3}.

The commonly assumed cosmological history of our Universe is that at early times and high temperatures the Universe went through an electroweak phase transition (EWPT). Assuming an EWPT, and depending on its strength, there are many implications for baryogenesis, gravitational waves, and the evolution of the Universe in general. However, it is not true that all spontaneously broken symmetries at zero temperature are restored at high temperature. In particular the idea of “inverse symmetry breaking” has long been established in scalar theories with evidence from both perturbative and lattice calculations. In this Letter we demonstrate that with a simple extension of the standard model it is possible that the EW symmetry was always broken or only temporarily passed through a symmetry-restored phase. These novel phase histories have many cosmological and collider implications that we discuss. The model presented here serves as a useful benchmark comparison for future attempts to discern the phase of our Universe at

Since the discovery of a Standard Model(SM)-like Higgs boson at the LHC

While studying the order of the EWPT provides a compelling research program for high energy experimental physics and GW astronomy, there is an even more basic question that can be investigated. Did an EW phase transition ever occur in the early Universe? The original techniques for studying finite-temperature quantum field theory

In this Letter we will show that with a simple scalar extension of the SM, a nonrestoration phase can occur for the EWS. The existence of such a phase has a number of implications experimentally and cosmologically. First, the cosmological history is very different than the SM. While it is commonly assumed that all SM particles are massless before the standard EWPT, this is not the case in the phase we describe, and masses

To demonstrate SNR for EWSB we exploit the same term used for symmetry restoration

Therefore a contribution to

Additionally in this scaling limit, at high

For an example point with

Top: temperature-dependent VEV,

The existence of SNR, or more complicated phase histories, for the simple model discussed here is robust when looked at from many different vantage points including: RGE stability, thermal decoupling, and thermal fluctuations.

Under RGE evolution for large-

If this phase is robust, then we must also check that the fields stay in thermal equilibrium validating the ansatz of equlibrium local thermal field theory used in describing the phase in the previous section. For our purposes here, it is sufficient that

For

One can not formally take the infinite-

Once the temperature of the Universe drops to the point where

Another concern is the possibility that even though the VEV of the Higgs scales as the temperature

There are a number of cosmological differences for SNR or TR phases compared to the usual SR phase. Some of these effects are due to the VEV of the Higgs boson not vanishing, while others are more connected to the

1. Gravitational waves: One simple cosmological consequence of SNR is that in the absence of a phase transition there will be no GW signal. However, there will be a difference in how this arises compared to the usual SM statement of a second order phase transition. In our model, there

2. Electroweak sphalerons and baryogenesis: EW sphalerons are often a key ingredient in models of baryogenesis ranging from models of EW baryogenesis to leptogenesis. This is due to the fact that they provide a

3. Thermal evolution: For the SNR and TR phases, there can be changes to the overall thermal evolution of the Universe through contributions to

Another interesting cosmological effect concerns the equation of state for any particle which obtains its mass from the Higgs boson. For a particle

The SR thermal history is known to keep all particles in thermal equilibrium from around the electroweak scale to

Thermal effects can also potentially modify freeze-in and freeze-out calculations which have potential effects on the abundance of both SM and DM particles. Neutrinos are a familiar example via their decoupling caused by the massive

The collider phenomenology of this model is very similar to other models with a singlet and a

It is interesting to note that collider measurements consistent with the SM are not sufficient to distinguish between the SM and SNR. Additionally, there can be degeneracies with a FOEWPT as demonstrated in Fig.

Comparison between different SNR points and a FOEWPT in the space of

Collider sensitivities from Fig.

We have outlined a scenario where EWSB is either persistent in the early Universe or can go through a different order parameter history with respect to temperature. There are a number of interesting potential cosmological consequences that we have outlined for baryogenesis and GW studies, and new cosmological phenomena as well. The cosmological effects in this model are generally small because they are coupled to EWSB which sets a scale in the problem. However, just as SNR and ISB have been used for other applications

The phases we have shown in this Letter for EWSB are robust in the large-

We would like to thank David Curtin, Daniel Egana-Ugrinovic, and Marilena LoVerde for useful discussions. The work of P. M. was supported in part by the National Science Foundation Grant No. PHY-1620628. P. M. would like to thank the Aspen Center for Physics, which is supported by National Science Foundation Grant No. PHY-160761, where part of this work was completed. H. R. is supported in part by the DOE under Contract No. DEAC02-05CH11231.