Color breaking in the early universe

We explore the possibility that $\mathrm{SU}(3{)}_C$ was not an exact symmetry at all times in the early Universe, using minimal extensions of the standard model that contain a color triplet scalar field and perhaps other fields. We show that, for a range of temperatures, there can exist a phase in which the free energy is minimized when the color triplet scalar has a nonvanishing vacuum expectation value, spontaneously breaking color. At very high temperatures and at lower temperatures, color symmetry is restored. The breaking of color in this phase is accompanied by the spontaneous breaking of $B-L$ if the color triplet scalar Yukawa couples to quarks and/or leptons. We discuss the requirements on the minimal extensions needed for consistency of this scenario with present collider bounds on new colored scalar particles.

Figure 1

Regions in parameter space where color is broken and possibly subsequently restored in the early Universe. Color shading, separated by solid curves, indicates the vacuum structure at zero temperature: yellow (upper-right) represents the region where the $\mathrm{SU}(3{)}_{\mathrm{C}}$-breaking phase is tachyonic, and blue (thinner diagonal region) indicates regions where the $\mathrm{SU}(3{)}_{\mathrm{C}}$-breaking phase is metastable. In the white (lower-left) regions, the standard electroweak phase is metastable, and the $\mathrm{SU}(3{)}_{\mathrm{C}}$-breaking phase is stable. For $(m_C,{\lambda }_C)$ inside the yellow hatched area, the Universe first cools into a color-breaking phase, followed by a transition to the color-preserving EW phase. For the blue hatched region, the Universe may remain in the color-breaking phase. Left panel is for ${\lambda }_{HC}=0.9$, and right panel is for ${\lambda }_{HC}=1.0$.

Figure 2

The free energy for the color-breaking (CoB) and SM electroweak (EW) phases in the $Z_2$-symmetric limit, as a function of temperature $T$. Within this class of parameter choice, the desired pattern of parameter breaking does not happen.

Figure 3

The free energy for the color-breaking (CoB) and SM electroweak (EW) phases as a function of $T$ for nonzero $Z_2$-breaking $e$ parameters. For the choice of parameters labeled above the figure, the critical temperature is $T_{\mathrm{crit}}\simeq 1550\mathrm{GeV}$.

Figure 4

The free energy for the CoB and EW phases as a function of $T$ for the same choice of parameters as in Fig. 3, but with coupling constant, top panel: ${\lambda }_{CS}=0.08$ and bottom panel: ${\lambda }_{CS}=0.12$. Raising ${\lambda }_{CS}$ has the effect of lowering $T_{\mathrm{crit}}$ and lengthening (in temperature) the duration of spontaneous color breaking in the early Universe.