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The initial energy density at the end of hybrid inflation is given by: ρ$_{0}$ = m $^{2}$v$^{2}$/ 4, with m 2 = λv $^{2}$, where v is the VEV of the Higgs field (water-field), so the fractional energy density in gravitational waves is r is roughly given by [779]: 

where 〈 ˙ h$_{ij}$ ˙ h ij 〉 $_{V}$, defined as a volume average like 1 V ∫ d $^{3}$x ˙ h$_{ij}$ ˙ h $^{ij}$, is extracted from the nu- merical simulations. 

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There are three stages of preheating which contribute to gravity waves. First, an expo- nential growth driven by the tachyonic instability of the long-wave modes of the Higgs field. Second, the Higgs field oscillates around the true vacuum, as the Higgs’ bubbles collide and scatter off each other. Third, a period of turbulence is reached, during which the inflaton oscillates around its minimum and the Higgs is already settled in its vacuum [725, 779, 796]. In Ref. [808], it was pointed out that the turbulence phase does not contribute to any en- hancement in gravity waves, but if one includes the gauge fields in the stress-energy tensor it is possible to mimic the results of [779]. 

Gravity wave production has also been studied in a potential given by Eq. (395). The 

