Perturbation theory, effective field theory, and oscillations in the power spectrum

Abstract

We explore the relationship between the nonlinear matter power spectrum and the various Lagrangian and Standard Perturbation Theories (LPT and SPT). We first look at it in the context of one dimensional (1-d) dynamics, where 1LPT is exact at the perturbative level and one can exactly resum the SPT series into the 1LPT power spectrum. Shell crossings lead to non-perturbative effects, and the PT ignorance can be quantified in terms of their ratio, which is also the transfer function squared in the absence of stochasticity. At the order of PT we work, this parametrization is equivalent to the results of effective field theory (EFT), and can thus be expanded in terms of the same parameters. We find that its radius of convergence is larger than the SPT loop expansion. The same EFT parametrization applies to all SPT loop terms and if stochasticity can be ignored, to all N-point correlators. In 3d, the LPT structure is considerably more complicated, and we find that LPT models with parametrization motivated by the EFT exhibit running with k and that SPT is generally a better choice. Since these transfer function expansions contain free parameters that change with cosmological model their usefulness for broadband power is unclear. For this reason we test the predictions of these models on baryonic acoustic oscillations (BAO) and other primordial oscillations, including string monodromy models, for which we ran a series of simulations with and without oscillations. Most models are successful in predicting oscillations beyond their corresponding PT versions, confirming the basic validity of the model. We show that if primordial oscillations are localized to a scale q, the wiggles in power spectrum are approximately suppressed as exp[−k 2 Σ 2 (q)/2], where Σ(q) is rms displacement of particles separated by q, which saturates on large scales, and decreases as q is reduced. No oscillatory features survive past k ∼ 0.5h/Mpc at z = 0.

The reconstructed power spectrum in the Zeldovich approximation

“…Figure 11 shows three possible linear wiggle power spectra, based on no-wiggle spectra computed using the fitting formula from ref. [60], B-splines [61] or a Savitsky-Golay filter; even the latter two, which agree asymptotically with the full linear theory power spectrum, exhibit noticeably different oscillatory behavior. This indicates that extracting the corresponding wiggle spectra from the data is Figure 11.…”

Non-linear damping of superimposed primordial oscillations on the matter power spectrum in galaxy surveys

“…Our results complement analytic approximations based on a perturbative treatment, see Refs. [24][25][26], and show a larger non-linear damping with respect to analytic results to leading order. We stress that these effects are relevant for current galaxy surveys like BOSS and eBOSS [78], DESI [79], DES [80], as well as for future experiments such as Euclid and PSF-Subaru.…”

An EFT description of galaxy intrinsic alignments

“…It turns out that is possible to perform the resummation of such long (IR) displacement modes, and such procedure is known under the name of IR-resummation. For the statistics of number density field the natural setting to perform such IR-resummation is the Lagrangian perturbation theory [81][82][83][84], however the equivalent task can be performed also in the Eulerian settings [85][86][87][88].…”