http://arxiv.org/abs/2211.02053
Cosmological perturbation theory is known to converge poorly for predicting the spherical collapse and void evolution of collisionless matter. Using the exact parametric solution as a testing ground, we develop two asymptotic methods in spherical symmetry that resolve the gravitational evolution to much higher accuracy than Lagrangian perturbation theory (LPT), which is the current gold standard in the literature. One of the methods selects a stable fixed-point solution of the renormalization-group flow equation, thereby predicting already at the leading order the critical exponent of the phase transition of collapsing structures. The other method completes the truncated LPT series far into the ultra-violet (UV) regime, by adding a non-analytic term that captures the critical nature of the gravitational collapse. We find that the UV method most accurately resolves the evolution of the non-linear density as well as its one-point probability distribution function. Similarly accurate predictions are achieved with the renormalization-group method, especially when paired with Pad\’e approximants. Further, our results yield new, very accurate, formulae to relate linear and non-linear density contrasts. Finally, we chart possible ways on how to adapt our methods to the case of cosmological random field initial conditions.
C. Rampf and O. Hahn
Mon, 7 Nov 22
60/67
Comments: 11 pages + appendices and references, 10 figures
You must be logged in to post a comment.