Zeldovich: a Lagrangian approximation for growing cosmic density perturbations

What is recorded here?

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. A nearly uniform early universe eventually develops dense regions and large empty regions. Following that change in three dimensions is difficult. Zeldovich instead labels each piece of matter by its initial position and approximates how its displacement grows with cosmic expansion. Conservation of mass then relates density to how the displacement stretches or compresses local volume. A generic small region reaches extreme density by collapsing first along one direction, producing a sheet-like shape rather than a perfectly spherical collapse. The paper is useful as an interpretable approximation with visible conditions. It also explains where the picture stops: pressure, heating, shocks and uncertain nonlinear gravity cannot all be hidden in the same simple displacement formula. This gives later researchers a structured starting model without claiming to explain the entire formation of galaxies.

Source-linked catalogue note. A detailed explanatory guide has not yet been prepared for this entry.

Scientific scope

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.

Read the original work

• Zeldovich, Gravitational Instability: An Approximate Theory for Large Density Perturbations; exact1970 original hosted by NASA GISS
• INSPIRE curated identity for exact1970 Zeldovich perturbation paper

This English explanation is an editorial reading view. It does not replace the complete original work or certify its science.

People and systems

Ya. B. Zeldovich

Source-listed contributors to this scoped work. Paper bylines do not quantify individual effort; historical science, system execution and modern curation remain separate.