Evolution of vacuum states and phase transitions in the two Higgs doublet model during cooling of the Universe

We consider the evolution of the ground state in the two Higgs doublet model during cooling down of the Universe after the big bang. Different regions in the space of free parameters of this model correspond to different sequences of thermal phase transitions. We discuss different paths of thermal evolution and corresponding evolution of physical properties of the system for different modern values of the parameters.

Figure 1

First correction to the Gibbs potential.

Figure 2

The second sheet of the $(\mu ,\delta )$ plane. Dotted rays are curves of physical states at the first sheet of this plane, which begin at the modern zero-temperature point $({\mu }_0,{\delta }_0)$ or $({\mu }_0^{\prime },{\delta }_0^{\prime })$. Solid lines are their high-temperature continuations on the second sheet. The left and right panels correspond to $|P|<1$ and $|P|>1$, respectively. At points where the solid lines intersect the circle $\mathbb{C}$ the system experiences EWSB phase transitions.

Figure 3

Parameters of the vacuum state for the case with a single phase transition $\mathrm{EWs}\to CPc$. Shown are the vacuum and extremum energies (upper left), $\tan \beta$ (upper right), as well as $v_1$, $v_2$ and $v$ in the lower row.

Figure 4

The same as in Fig. 3 but for another set of ${\lambda }_i$.

Figure 5

Evolution of the parameters of the vacuum state for sector II, ray II. Upper row: Extremum energy, $\tan \beta$, total vacuum expectation value $v$. Lower row: $v_1$ and $v_2$ shown separately.

Figure 6

The same as in Fig. 5 but for another set of ${\lambda }_i$

Figure 7

The $(\mu ,\delta )$ plane for sector II.

Figure 8

The $(\mu ,\delta )$ plane for sector III.

Figure 9

Evolution of the parameters of the vacuum state through the double $CP$-violating and $CP$-restoring phase transition. Upper row: Vacuum energy evolution (left), $\tan \beta$ (center); $v$ (right). Lower row: $v_1$ (left); $v_2$ (center); ${sin}^2\xi$ (right).

Figure 10

The same as in Fig. 9 for another set of parameters.

Figure 11

The $(\mu ,\delta )$ plane for sector IV.

Figure 12

Evolution of physical quantities during transition through the charge-breaking vacuum.