Chapter 1. Schumann and Schubert's “Immortal” Piano Trio in E Flat, D. 929

Daverio, John

doi:10.1093/acprof:oso/9780195132960.003.0002

Cited by 3 publications

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“…This is what has been done for most full GR calculations of cosmological structure to date (Refs. [8,9,22] are exceptions to this). However, such fluid descriptions break down as soon as multi-stream regions emerge, which of course are generic features of structure formation.…”

Section: Introductionmentioning

confidence: 95%

“…Recently, there has been a growing interest in quantifying the importance of effects that are both nonlinear and relativistic on the large scale evolution and development of structure in the Universe [1][2][3][4][5][6][7][8][9]. This means studying effects that may be missed by the standard tool for studying cosmological structure formation: Newtonian N -body simulations.…”

Section: Introductionmentioning

confidence: 99%

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Einstein-Vlasov calculations of structure formation

2019

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We study the dynamics of small inhomogeneities in an expanding universe collapsing to form bound structures using full solutions of the Einstein-Vlasov (N -body) equations. We compare these to standard Newtonian N -body solutions using quantities defined with respect to fiducial observers in order to bound relativistic effects. We focus on simplified initial conditions containing a limited range of length scales, but vary the inhomogeneities from small magnitude, where the Newtonian and GR calculations agree quite well, to large magnitude, where the background metric receives an order one correction. For large inhomogeneities, we find that the collapse of overdensities tends to happen faster in Newtonian calculations relative to fully general-relativistic ones. Even in this extreme regime, the differences in the spacetime evolution outside the regions of large gravitational potential and velocity are small. For standard cosmological values, we corroborate the robustness of Newtonian N -body simulations to model large scale perturbations and the related cosmic variance in the local expansion rate.

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

Einstein-Vlasov calculations of structure formation

2019

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“…However, this treatment is only an approximation, as general relativity (GR) is inherently a nonlinear system which couples different scales. Recently, there has been much interest in applying advances in numerically solving the full Einstein equations to study inhomogeneous cosmologies [1][2][3][4][5]. Such studies are motivated by assessing "backreaction" effects-that is the potential for smaller-scale inhomogeneities to effect the overall expansion of the Universe, a topic that remains controversial [6][7][8][9][10] -and, in general, quantifying relativistic effects and their possible impact on making measurements in the era of precision cosmology.…”

Section: Introductionmentioning

confidence: 99%

Comparing fully general relativistic and Newtonian calculations of structure formation

2018

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In the standard approach to studying cosmological structure formation, the overall expansion of the Universe is assumed to be homogeneous, with the gravitational effect of inhomogeneities encoded entirely in a Newtonian potential. A topic of ongoing debate is to what degree this fully captures the dynamics dictated by general relativity, especially in the era of precision cosmology. To quantitatively assess this, we directly compare standard N-body Newtonian calculations to full numerical solutions of the Einstein equations, for cold matter with various magnitude initial inhomogeneities on scales comparable to the Hubble horizon. We analyze the differences in the evolution of density, luminosity distance, and other quantities defined with respect to fiducial observers. This is carried out by reconstructing the effective spacetime and matter fields dictated by the Newtonian quantities, and by taking care to distinguish effects of numerical resolution. We find that the fully general relativistic and Newtonian calculations show excellent agreement, even well into the nonlinear regime. They only notably differ in regions where the weak gravity assumption breaks down, which arise when considering extreme cases with perturbations exceeding standard values.

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“…The numerical accuracy of this indirect integration method of the fluid dynamics, e.g. in capturing shock waves, will be addressed in future work [53].…”

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confidence: 99%

A numerical relativity scheme for cosmological simulations

Daverio¹,

Dirian²,

Mitsou³

2017

Class. Quantum Grav.

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Cosmological simulations involving the fully covariant gravitational dynamics may prove relevant in understanding relativistic/non-linear features and, therefore, in taking better advantage of the upcoming large scale structure survey data. We propose a new 3+1 integration scheme for General Relativity in the case where the matter sector contains a minimally-coupled perfect fluid field. The original feature is that we completely eliminate the fluid components through the constraint equations, thus remaining with a set of unconstrained evolution equations for the rest of the fields. This procedure does not constrain the lapse function and shift vector, so it holds in arbitrary gauge and also works for arbitrary equation of state. An important advantage of this scheme is that it allows one to define and pass an adaptation of the robustness test to the cosmological context, at least in the case of pressureless perfect fluid matter, which is the relevant one for late-time cosmology. IntroductionThe upcoming large scale structure observations will provide a powerful probe of relativistic/nonlinear effects in cosmology, such as those encountered in alternative descriptions of the dark sector, backreaction, matter-radiation interactions, neutrinos, cosmic defects, the inflationary phase, etc. This motivated some very recent developments in going beyond the standard simulation techniques that are the linear-Boltzmann and Newtonian N -body approaches. These include the first relativistic N -body code [1][2][3][4], where the gravitational field is treated through an appropriately truncated secondorder perturbation theory [1,5,6], Newtonian N -body simulations that include linearized radiation [7,8] or a more sophisticated estimate of the scale factor [9], and a Boltzmann method for describing non-linear effects of massive neutrinos [10]. At the same time, fully non-linear simulations of General Relativity (GR) have been performed to study aspects of both the early and late universe, using wellestablished schemes of numerical relativity (NR, [11-16] for reviews). There are simulations of the inflationary epoch in 1 + 1 [17-20] and 3 + 1 [21-23] dimensions, while for late-time cosmology there are 1 + 1 spherical collapse simulations [24, 25] and 3 + 1 simulations involving a pressureless perfect fluid field [26-31] (see also [32]). The latter are mainly motivated by the issue of cosmic backreaction which, until recently, was addressed numerically only through lattice configurations [33][34][35][36][37][38][39]. Finally, there is also a renewal of interest in 3 + 1 NR N -body simulations of the collapse dynamics [40], after the earlier work of Shibata [41,42] and the even earlier, but lower-dimensional, works of Shapiro and Teukolsky using both N -body and Boltzmann approaches [43][44][45][46][47][48] (see also [49]).Our interest here lies in 3 + 1 NR applied to cosmology. A first observation is that NR has been mostly developed to deal with strong gravity phenomena at astrophysical scales, in which case the scenarios of inte...

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Chapter 1. Schumann and Schubert's “Immortal” Piano Trio in E Flat, D. 929

Cited by 3 publications

References 0 publications

Einstein-Vlasov calculations of structure formation

Einstein-Vlasov calculations of structure formation

Comparing fully general relativistic and Newtonian calculations of structure formation

A numerical relativity scheme for cosmological simulations

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