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Zeldovich: a Lagrangian approximation for growing cosmic density perturbations

Contribution grade

Cosmology · Cosmology

Reference score160,000Provisional editorial estimate of this exact contribution; its grade is assessed separately.

What changed

Zeldovich extrapolates a growing-mode Lagrangian displacement from linear pressureless Newtonian cosmology and obtains density through its deformation Jacobian, predicting generic first compression into sheet-like structures while explicitly retaining uncertain nonlinear accuracy and post-compression limits.

Scientific scope

Zeldovich extrapolates a growing-mode Lagrangian displacement from linear pressureless Newtonian cosmology and obtains density through its deformation Jacobian, predicting generic first compression into sheet-like structures while explicitly retaining uncertain nonlinear accuracy and post-compression limits. Exact 1970 Astronomy and Astrophysics 5,84-89 paper, received September 1969. Pressureless Newtonian growing-mode assumptions and the stated cosmological epoch/scales matter. Extrapolating the displacement does not solve all nonlinear gravitational dynamics: the source says its real accuracy is unknown pending a proposed force comparison. Density follows mass conservation while the map remains locally invertible; after caustic compression the same single-fluid formula cannot simply be continued for affected particles. Shock heating/pressure requires additional treatment. Generic first sheet-like compression assumes nondegenerate deformation eigenvalues and specified perturbation statistics; perfectly symmetric simultaneous collapse is an exception. The paper does not provide a complete galaxy-formation theory or guarantee that its sheets persist in observed galaxies. Small-scale pressure-dominated entropy fluctuations are explicitly outside the approximation. Several thermodynamic numbers are only order-of-magnitude estimates with detailed calculations deferred. Historical Hubble/redshift assumptions are not present-day measurements. Later simulations, dark-matter interpretations and higher-order Lagrangian methods retain separate credit. Original numerical estimates, Gaussian eigenvalue percentages and figures were not independently replayed.

Evidence

Source-linked, scoped account of the original work. The published scope states the scientific assumptions and remaining verification limits. WRS has not independently certified the full proof, experimental result or system benchmark.

Contributors

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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