There are many different ways to explain the cosmic matter–antimatter asymmetry, says Géraldine Servant, but the Higgs boson plays a key role in essentially all of them.

Precision measurements of the Higgs boson open the possibility to explore the moment in cosmological history when electroweak symmetry broke and elementary particles acquired mass. Ten years after the Higgs-boson discovery, it remains a possibility that the electroweak phase transition happened as a rather violent process, with a large departure from thermal equilibrium, via Higgs-bubble nucleations and collisions. This is a fascinating scenario for three reasons: it provides a framework for explaining the matter–antimatter asymmetry of the universe; it predicts the existence of at least one new weak-scale scalar ﬁeld and thus is testable at colliders; and it would leave a unique signature of gravitational waves detectable by the future space-based interferometer LISA.

One major failure of the Standard Model (SM) is its inability to explain the baryon-to-photon ratio in the universe: η ≈ 6 × 10^{–10}. Measurements of this ratio from two independent approaches – anisotropies in the cosmic microwave background and the abundances of light primordial elements – are in beautiful agreement. In a symmetric universe, however, the prediction for η is a billion times smaller; big-bang nucleosynthesis could not have occurred and structures could not have formed. This results from strong annihilations between nucleons and antinucleons, which deplete their number densities very efficiently. Only in a universe with a primordial asymmetry between nucleons and antinucleons can these annihilations be prevented. There are many different models to explain such “baryogenesis”. Interestingly, however, the Higgs boson plays a key role in essentially all of them.

**Accidental symmetry**

It is worth recalling how baryon number B gets violated by purely SM physics. B is an “accidental” global symmetry in the SM. There are no B-violating couplings in the SM Lagrangian. But the chiral nature of electroweak interactions, combined with the non-trivial topology of the SU(2) gauge theory, results in non-perturbative, B-violating processes. Technically, these are induced by extended gauge-ﬁeld conﬁgurations called sphalerons, whose energy is proportional to the value of the Brout–Englert–Higgs (BEH) field. The possibility of producing these conﬁgurations is totally suppressed at zero temperature, such that B is an extremely good symmetry today. However, at high temperature, and in particular at 100 GeV or so, when the electroweak symmetry is unbroken, the baryon number is violated intensively as there is no energy cost. Since both baryons and antibaryons are created by sphalerons, charge–parity (CP) violation is needed. Indeed, as enunciated by Sakharov in 1967, a theory of baryogenesis requires three main ingredients: B violation, CP violation and a departure from equilibrium, otherwise the baryon number will relax to zero.

The conclusion is that baryogenesis must take place either from a mechanism occurring before the electroweak phase transition (necessitating new sources of B violation beyond the SM) or from a mechanism where B-violation relies exclusively on SM sphalerons and occurring precisely at the electroweak phase transition (provided that it is sufficiently out-of-equilibrium and CP-violating). The most emblematic example in the ﬁrst category is leptogenesis, where a lepton asymmetry is produced from the decay of heavy right-handed neutrinos and “reprocessed” into a baryon asymmetry by sphalerons. This is a popular mechanism motivated by the mystery of the origin of neutrino masses, but is difficult to test experimentally. The second category, electroweak baryogenesis, involves electroweak-scale physics only and is therefore testable at the LHC.

Electroweak baryogenesis requires a ﬁrst-order electroweak phase transition to provide a large departure from thermal equilibrium, otherwise the baryon asymmetry is washed out. A prime example of this type of phase transition is boiling water, where bubbles of gas expand into the liquid phase. During a ﬁrst-order electroweak phase transition, symmetric and broken phases coexist until bubbles percolate and the whole universe is converted into the broken phase (see “Bubble nucleation” image). Inside the bubble, the BEH field has a non-zero vacuum expectation value; outside the bubble, the electroweak symmetry is unbroken. As the wall is passing, chiral fermions in the plasma scatter off the Higgs at the phase interface. If some of these interactions are CP-violating, a chiral asymmetry will develop inside and in front of the bubble wall. The resulting excess of left-handed fermions in front of the bubble wall can be converted into a net baryon number by the sphalerons, which are unsuppressed in the symmetric phase in front of the bubble. Once inside the bubble, this baryon number is preserved as sphalerons are frozen there. In this picture, the baryon asymmetry is determined by solving a diffusion system of coupled differential equations.

**New scalar required**

The nature of the electroweak phase transition in the SM is well known: for a 125 GeV Higgs boson, it is a smooth crossover with no departure from thermal equilibrium. This prevents the possibility of electroweak baryogenesis. It is, however, easy to modify this prediction to produce a ﬁrst-order transition by adding an electroweak-scale singlet scalar ﬁeld that couples to the Higgs boson, as predicted in many SM extensions. Notably, this is a general feature of composite-Higgs models, where the Higgs boson emerges as a “pseudo Nambu–Goldstone” boson of a new strongly-interacting sector.

An important consequence of such models is that the BEH field is generated only at the TeV scale; there is no field at temperatures above that. In the minimal composite Higgs model, the dynamics of the electroweak phase transition can be entirely controlled by an additional scalar Higgs-like ﬁeld, the dilaton, which has experimental signatures very similar to the SM Higgs boson. In addition, we expect modiﬁcations of the Higgs boson’s couplings (to gauge bosons and to itself) induced by its mixing with this new scalar. LHC Run 3 thus has excellent prospects to fully test the possibility of a ﬁrst-order electroweak phase transition in the minimal composite Higgs model.

The properties of the additional particle required to modify the electroweak phase transition also suggest new sources of CP violation, which is welcome as CP-violating SM processes are not sufficient to explain the baryon asymmetry. In particular, this would generate non-zero electric dipole moments (EDMs). The most recent bounds on the electron EDM from the ACME experiment in the US placed stringent constraints on a large number of electroweak baryogenesis models, in particular two-Higgs-doublet models. This is forcing theorists to consider new paths such as dynamical Yukawa couplings in composite Higgs models, a higher temperature for the electroweak phase transition, or the use of dark particles as the new source of CP violation. Here, there is a tension. To evade the stringent EDM bounds, the new scalar has to be heavy. But if it is too heavy, it reheats the universe too much at the end of the electroweak phase transition and washes out the just-produced baryon asymmetry. During the next decade, precise measurements of the Higgs boson at the LHC will enable a deﬁnitive test of the electroweak baryogenesis paradigm.

**Gravitational waves **

There is a further striking consequence of a ﬁrst-order electroweak phase transition: fluid velocities in the vicinity of colliding bubbles generate gravitational waves (GWs). Today, these would appear as a stochastic background that is homogeneous, isotropic, Gaussian and unpolarised – the superposition of GWs generated by an enormous number of causally-independent sources, arriving at random times and from random directions. It would appear as noise in GW detectors with a frequency (in the mHz region) corresponding to the typical inverse bubble size, redshifted to today (see “Primordial peak” figure). There has been a burst of activity in the past few years to evaluate the chances of detecting such a peaked spectrum at the future space interferometer LISA, opening the fascinating possibility of learning about Higgs physics from GWs.

The results from the LHC so far have pushed theorists to question traditional assumptions about where new physics beyond the SM could lie. Electroweak baryogenesis relies on rather conservative and minimal assumptions, but more radical approaches are now being considered, such as the intriguing possibility of a cosmological interplay between the Higgs boson and a very light and very weakly-coupled axion-like particle. Through complementarity of studies in theory, collider experiments, EDMs, GWs and cosmology, probing the electroweak phase transition will keep us busy for the next two decades. There are exciting times ahead.