Tracking down the route to the SM with inflation and gravitational waves

We explore supersymmetric SO(10) models predicting observable proton decay and various topological defects which produce different shapes and strengths of gravitational wave backgrounds depending on the scales of intermediate symmetry breaking and inflation as well. We compare these to their nonsupersymmetric counterparts. By identifying the scales at which gravitational wave signals appear, we would be able to track down a particular breaking chain and discern if it has a supersymmetric origin or not. It would also be useful to observe gravitational waves from more than one source among all possible topological defects and first order phase transitions for a realistic breaking chain. For these purposes, we work out specific examples in which the grand unification and relevant intermediate scales are calculable explicitly. It turns out that examples with gravitational waves from different sources are quite difficult to obtain, and the predicted gravitational wave profiles from domain walls and first order phase transitions obtained in some examples will require detectors in the kHz to MHz region.

Figure 1

The signals from the breaking of supersymmetric SO(10) via an SU(5) route depending on when the inflation takes place. Taking $M_{B-L}={10}^{14}\mathrm{GeV}$ we show the usual stable CS signal by the dotted orange line, and the diluted CS signal by the dashed purple line. The solid red line shows the decaying CS signal with $M_{B-L}=2.5\times {10}^{14}\mathrm{GeV}$ and $\sqrt{k}=7.5$ [see Eq. (2)]. For information about the experimental backgrounds please check Appendix pp1.

Figure 2

(Left plot: supersymmetric case) The stable CS signal after inflation ($T_{RH}>M_R$) is shown by the orange band corresponding to $M_R=(2,4)\times {10}^{13}\mathrm{GeV}$. The profile of the diluted CS is shown in the dashed purple line with $M_R=3\times {10}^{13}\mathrm{GeV}$ (see the text for the details). The decaying CS signal cannot occur due to the large gap between $M_{\mathrm{GUT}}$ and $M_R$. The blue solid line shows the signal from FOPT at the scale ${10}^{13}\mathrm{GeV}$ which is, unfortunately, out of the future experimental reach. (Right plot: nonsupersymmetric case) We show the signals from nonsupersymmetric version of the model predicting the intermediate scale at $9.5\times {10}^9\mathrm{GeV}$ corresponding to $G\mu =7.6\times {10}^{-20}$.

Figure 3

(Left plot: supersymmetric case) The solid purple line represents the profile of a GW generated by a DW after inflation at a scale about ${10}^{14}\mathrm{GeV}$. We have used the parametric formula of Eq. (e1) with the values of Tab. 2. The tension has been taken between $(3\times {10}^{14}\mathrm{GeV}{)}^3$ (top line) and $(1\times {10}^{14}\mathrm{GeV}{)}^3$ (bottom line). The solid orange line is the signal from CS produced at about $3.7\times {10}^{13}\mathrm{GeV}$, corresponding to $G\mu ={10}^{-12}$. (Right plot: nonsupersymmetric case) DW are formed above ${10}^{15}\mathrm{GeV}$ and hence are not observable. CS (solid orange line) for this case are produced at $2\times {10}^{12}\mathrm{GeV}$, corresponding to a tension $G\mu$ approximately equal to $3\times {10}^{-15}$.