Title: Symmetry protection of superhorizon perturbations from small-scale loops
Speaker: Ryusuke Jinno
Abstract:
Small-scale scalar perturbations can be strongly enhanced in inflationary scenarios relevant to primordial black holes and induced gravitational waves. A central question is whether such enhanced modes can feed back into superhorizon scalar and tensor perturbations through scale-invariant one-loop corrections. I will discuss this problem using the Schwinger–Keldysh formalism in the r/a basis and the corresponding soft effective field theory obtained by integrating out hard scalar modes. For tensor perturbations, the dangerous operator in the soft tensor EFT is forbidden by the residual spatial diffeomorphism invariance of general relativity. For scalar perturbations, the dilatation symmetry of zeta, together with the tadpole cancellation condition and the associated symmetry-preserving counterterm, removes the corresponding scale-invariant contribution. I will also explain how the explicit one-loop cancellation follows from an identity among statistical and retarded Green’s functions, valid for arbitrary time-dependent inflationary backgrounds. These results show that, including transient ultra-slow-roll scenarios, enhanced small-scale scalar perturbations do not generate scale-invariant one-loop corrections to the large-scale scalar or tensor power spectra in the soft limit.
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