Cosmological Vlasov–Poisson equations for dark matter

Rampf, Cornelius

doi:10.1007/s41614-021-00055-z

Cited by 16 publications

(9 citation statements)

References 208 publications

(246 reference statements)

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“…Moreover, since LPT is a Taylor series in powers of a, the temporal regime of convergence is spanned by |a| < a , where the radius of convergence a is set by the nearest singularity(ies) in the complex-time plane around the expansion point a = 0. In the case of spherical symmetry, the nearest singularity occurs at the real-valued collapse time a where, specifically, the velocity v = ẋ blows up [25,61]. This explains the exact coincidence between the collapse time and the loss of convergence in the case of spherical symmetry.…”

Section: Lagrangian Perturbation Theorymentioning

confidence: 94%

“…Cosmological perturbation theory (CPT; [21][22][23][24][25]) provides highly accurate predictions on large cosmological scales, and in particular plays a crucial role in connecting early-with latetime cosmology, such as by providing initial conditions for numerical simulations [26][27][28][29][30]. However, CPT struggles to accurately predict the small-scale collapse to gravitationally bound structures, a process that is intimately tied to the shellcrossing singularity-the crossing of trajectories of collisionless matter, which comes with extreme matter densities.…”

Section: Introductionmentioning

confidence: 99%

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Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

Rampf,

Hahn

2022

Preprint

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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 to collapsed 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 Padé 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.

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Section: Lagrangian Perturbation Theorymentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

Rampf,

Hahn

2022

Preprint

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“…In order to understand the results exposed above, we will use the LPT formalism [6,13,16] to compute approximate expressions for the power spectra that go into equation (3.3) and their variances; this will allow us to see what are the effects of fixing or pairing on the structure of these quantities. Let us call F (q) a field in Lagrangian space such that…”

Section: Theoretical Explorationmentioning

confidence: 99%

Statistics of biased tracers in variance-suppressed simulations

Francisco¹,

Angulo²,

Zennaro³

2022

Preprint

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Cosmological simulations play an increasingly important role in analysing the observed large-scale structure of the Universe. Recently, they have been particularly important in building hybrid models that combine a perturbative bias expansion with displacement fields extracted from N-body simulations to describe the clustering of biased tracers. Here, we show that simulations that employ a technique referred to as "Fixing-and-pairing" (F&P) can dramatically improve the statistical precision of such hybrid models. Specifically, by numerical and analytic means, we show that F&P simulations provide unbiased estimates for all statistics employed by hybrid models while reducing, by up to two orders of magnitude, their uncertainty on large scales. This roughly implies that an EUCLID-like survey could be analysed using simulations of 2Gpc a side -a 10% of the survey volume. Our work establishes the robustness of F&P for current hybrid theoretical models for galaxy clustering, an important step towards achieving an optimal exploitation of large-scale structure measurements.

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“…Nonetheless, there exist by now various algorithms that can incorporate the gravitational interactions efficiently; to a good approximation even after the appearance of the first singularities [32,33]; see e.g. [34] for a review.…”

Section: Discussionmentioning

confidence: 99%

Eye of the Tyger: early-time resonances and singularities in the inviscid Burgers equation

Rampf¹,

Frisch²,

Hahn³

2022

Preprint

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We chart a singular landscape in the temporal domain of the inviscid Burgers equation in one space dimension for sine-wave initial conditions. These so far undetected complex singularities are arranged in an eye shape centered around the origin in time. Interestingly, since the eye is squashed along the imaginary time axis, complex-time singularities can become physically relevant at times well before the first real singularity-the pre-shock. Indeed, employing a time-Taylor representation for the velocity around t = 0, loss of convergence occurs roughly at 2/3 of the pre-shock time for the considered single-and multi-mode models. Furthermore, the loss of convergence is accompanied by the appearance of initially localized resonant behaviour which, as we claim, is a temporal manifestation of the so-called tyger phenomenon, reported in Galerkin-truncated implementations of inviscid fluids [Ray et al., Phys. Rev. E 84, 016301 (2011)]. We support our findings of early-time tygers with two complementary and independent means, namely by an asymptotic analysis of the time-Taylor series for the velocity, as well as by a novel singularity theory that employs Lagrangian coordinates.Finally, we apply two methods that reduce the amplitude of early-time tygers, one is tyger purging which removes large Fourier modes from the velocity, and is a variant of a procedure known in the literature. The other method realizes an iterative UV completion, which, most interestingly, iteratively restores the conservation of energy once the Taylor series for the velocity diverges. Our techniques are straightforwardly adapted to higher dimensions and/or applied to other equations of hydrodynamics.

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Cosmological Vlasov–Poisson equations for dark matter

Cited by 16 publications

References 208 publications

Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

Renormalization group and UV completion of cosmological perturbations: Gravitational collapse as a critical phenomenon

Statistics of biased tracers in variance-suppressed simulations

Eye of the Tyger: early-time resonances and singularities in the inviscid Burgers equation

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