The large scale structure of the universe I. General properties. One-and two-dimensional models

Arnold, Vladimir I.; Shandarin, Sergei F.; Zel’dovich, Ya. B.

doi:10.1080/03091928208209001

Cited by 230 publications

(234 citation statements)

References 20 publications

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“…On large scales, and even well into the nonlinear regime, the velocity field remains a potential flow and can be expressed as the gradient of a velocity potential [4,5,15]. In the linear Lagrangian regime and at high redshifts, where dark energy contribution to the expansion rate is small relative to the contribution from the dark matter, this is the same as the gravitational potential.…”

Section: Introductionmentioning

confidence: 94%

Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constant

Liu¹,

Mohayaee²,

Naselsky³

2016

J. Cosmol. Astropart. Phys.

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Abstract. The existence of critical points for the peculiar velocity field is a natural feature of the correlated vector field. These points appear at the junctions of velocity domains with different orientations of their averaged velocity vectors. Since peculiar velocities are the important cause of the scatter in the Hubble expansion rate, we propose that a more precise determination of the Hubble constant can be made by restricting analysis to a subsample of observational data containing only the zones around the critical points of the peculiar velocity field, associated with voids and saddle points. On large-scales the critical points, where the first derivative of the gravitational potential vanishes, can easily be identified using the density field and classified by the behavior of the Hessian of the gravitational potential. We use high-resolution N-body simulations to show that these regions are stable in time and hence are excellent tracers of the initial conditions. Furthermore, we show that the variance of the Hubble flow can be substantially minimized by restricting observations to the subsample of such regions of vanishing velocity instead of aiming at increasing the statistics by averaging indiscriminately using the full data sets, as is the common approach.

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Section: Introductionmentioning

confidence: 94%

Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constant

Liu¹,

Mohayaee²,

Naselsky³

2016

J. Cosmol. Astropart. Phys.

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“…This question was studied by L P Grishchuk [26]. Later V I Arnold, S F Shandarin and Ya B Zeldovich [27] have used the caustics for the explanation of the initial clustering of the dust, which though does not create physical singularities, is nevertheless responsible for the creation of the so called pancakes. These pancakes represent the initial stage of the development of the large scale structure of the universe.…”

Section: Landau Theorem About the Singularitymentioning

confidence: 99%

“…The random nature of this process arises because of the rules (26)- (27) which define the transitions from one era to another in the infinite sequence of values of u. If all this infinite sequence begins since some initial value u…”

Section: Landau Theorem About the Singularitymentioning

confidence: 99%

The problem of singularities and chaos in cosmology

Kamenshchik¹

2010

Phys.-Usp.

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We consider different aspects of the problem of cosmological singularity such as the BKL oscillatory approach to the singularity, the new features of the cosmological dynamics in the neighbourhood of the singularity in multidimensional and superstring cosmological models and their connections with such a modern branch of mathematics as infinite-dimensional Lie algebras. The chaoticity of the oscillatory approach to the cosmological singularity is also discussed. The Conclusion contains some thoughts about the past and the future of the Universe in the light of the oscillatory approach to the Big Bang and the Big Crunch cosmological singularities.

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“…For the unforced Burgers equation there is the representation (3). Let the function w(a) = W (a, x * , t * ) have a collection…”

Section: Shock Recognitionmentioning

confidence: 99%

“…This is a model of formation of the large-structure of the Universe or the so-called "Zel ′ dovich approximation" [2], [3]. According to this model, after some time the density becomes infinite because the fastest particles overrun the slowest ones.…”

Section: Introductionmentioning

confidence: 99%

Perestroikas of shocks and singularities of minimum functions

Bogaevsky

2002

Physica D: Nonlinear Phenomena

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The shock discontinuities, generically present in inviscid solutions of the forced Burgers equation, and their bifurcations happening in the course of time ( perestroikas) are classified in two and three dimensions -the one-dimensional case is well known. This classification is a result of selecting among all the perestroikas occurring for minimum functions depending generically on time, the ones permitted by the convexity of the Hamiltonian of the Burgers dynamics. Topological restrictions on the admissible perestroikas of shocks are obtained. The resulting classification can be extended to the so-called viscosity solutions of a Hamilton-Jacobi equation, provided the Hamiltonian is convex.

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The large scale structure of the universe I. General properties. One-and two-dimensional models

Cited by 230 publications

References 20 publications

Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constant

Critical points of the cosmic velocity field and the uncertainties in the value of the Hubble constant

The problem of singularities and chaos in cosmology

Perestroikas of shocks and singularities of minimum functions

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