Big-bang nucleosynthesis and gamma-ray constraints on cosmic strings with a large Higgs condensate

We consider constraints on cosmic strings from their emission of Higgs particles, in the case that the strings have a Higgs condensate with amplitude of order the string mass scale, assuming that a fraction of the energy of the condensate can be turned into radiation near cusps. The injection of energy by the decaying Higgs particles affects the light element abundances predicted by standard big-bang nucleosynthesis (BBN) and also contributes to the diffuse gamma-ray background (DGRB) in the Universe today. We examine the two main string scenarios (Nambu-Goto and field theory) and find that the primordial helium and deuterium abundances strongly constrain the string tension and the efficiency of the emission process in the NG scenario, while the strongest BBN constraint in the FT scenario comes from the deuterium abundance. The Fermi-LAT measurement of the DGRB constrains the field theory scenario even more strongly than previously estimated from EGRET data, requiring that the product of the string tension $\mu$ and Newton’s constant $G$ is bounded by $G\mu \lesssim 2.7\times {10}^{-11}{\beta }_{\mathrm{ft}}^{-2}$, where ${\beta }_{\mathrm{ft}}^2$ is the fraction of the strings’ energy going into Higgs particles.

Figure 1

Diagram of cusp annihilation, showing the core of the string (solid lines) overlapping over a length ${\sigma }_c\sim \sqrt{L/M}$, with the Higgs condensate (dashed) interacting over a length $\mathrm{\Delta }\sigma \sim \sqrt{L/m_h}$.

Figure 2

Constraints on cosmic string tension $G\mu$, in the NG scenario, plotted in the $({\beta }_c,G\mu )$ plane for $\nu =0.2$ and $\mathrm{\Gamma }=50$. The plot on the left shows constraints due to nonperturbative emission of Higgs at cusps, and on the right due to two-particle emission. In both plots, green represents constraints due to ${}^4\mathrm{He}$ and blue those due to D, while light and dark colors represent bounds from low and high estimates of the abundances. Note that there is no bound due to two-Higgs emission from the high ${}^4\mathrm{He}$ abundance estimate for physical values ${\beta }_c<1$.

Figure 3

Constraints on cosmic string tension $G\mu$, in the FT scenario, derived from BBN [20] and the DGRB [43], plotted in the $({\beta }_{\mathrm{ft}},G\mu )$ plane. Deuterium is the only element that provides constraints in this case. Thereby, the light blue region bounded below by the blue dashed line is excluded by the low D bound. The red region bounded below by the solid red line is excluded by the combination of the low D and DGRB bounds while the purple region bounded below by the solid purple line is excluded by the low D, DGRB and high D bounds.