Thermal production of superheavy magnetic monopoles in the new inflationary-Universe scenario

In the new inflationary-Universe scenario monopoles are created in rare, very energetic particle collisions, and their predicted abundance, which is $\propto \exp (-\frac{2m_0}{T_{\mathrm{RH}}})$, is tiny, where $m_0=\mathrm{monopole}\mathrm{mass}$, $T_{\mathrm{RH}}=\mathrm{reheat}\mathrm{temperature}$. During the reheating process the effective monopole mass oscillates about $m_0$ as the vacuum expectation value of the scalar field oscillates about the symmetry-breaking minimum of the scalar potential. We find that owing to this effect monopole production is greatly increased, with $\frac{2m_0}{T_{\mathrm{RH}}}$ being replaced by $\frac{2f_{*}{m}_0}{T_{\mathrm{RH}}}$, where $0<\mathrm{}{f}_{*}<1\mathrm{}$ depends upon the form of the scalar potential and the details of reheating.