Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-312/3/iii/c/solution

The ultraviolet part of the one-loop matter power spectrum is renormalized by the leading effective field theory of large-scale structure operator proportional to . The analogous velocity-divergence counterterm is
where the time dependence and the nonlinear reference scale may be absorbed into the renormalized coefficient . In the bispectrum it supplies
and permutations, with momentum shape on the corrected leg. This cancels the local ultraviolet dependence of .

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