Azrul Pohan, Michael Joyce, David Benhaiem, Francesco Sylos Labini
We generalize previously derived analytic results for the one-loop power spectrum (PS) in scale-free models (with linear PS P(k)∝kn) to a broader class of such models in which part of the matter-like component driving the Einstein de Sitter expansion does not cluster. These models can be conveniently parametrized by α, the constant logarithmic linear growth rate of fluctuations (with α=1 in the usual case). For-3<n<-1, where the one-loop PS is both infrared and ultraviolet convergent and thus explicitly self-similar, it is characterized conveniently by a single numerical coefficient c(n,α). We compare the analytical predictions for c(n=-2,α) with results from a suite of N-body simulations with α∈[0.25,1] performed with an appropriately modified version of the gadget code. Although the simulations are of small (2563) boxes, the constraint of self-similarity allows the identification of the converged PS at a level of accuracy sufficient to test the analytical predictions for the α dependence of the evolved PS. Good agreement for the predicted dependence on α of the PS is found. To treat the UV sensitivity of results which grows as one approaches n=-1, we derive exact results incorporating a regularization kc and obtain expressions for c(n,α,kc/k). Assuming that this regularization is compatible with self-similarity allows us to infer a predicted functional form of the PS equivalent to that derived in effective field theory (EFT). The coefficient of the leading EFT correction at one loop has a strong dependence on α, with a change in sign at α≈0.16, providing a potentially stringent test of EFT. © 2023 American Physical Society.
Laboratoire de Physique Nucléaire et de Hautes Energies, UPMC, IN2P3, CNRS, UMR 7585, Sorbonne Université, 4, place Jussieu, Paris, Cedex 05 75252, France; Laboratory of Theoretical Physics, Institut Teknologi Sumatera, Lampung, 35365, Indonesia; Centro Ricerche Enrico Fermi, Via Panisperna 89a, Roma, I-00184, Italy
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