Einstein–de Sitter model

Einstein–de Sitter model
Name	Einstein–de Sitter model

Einstein–de Sitter model is a historical cosmological model proposing a spatially flat, matter-dominated universe with zero cosmological constant, introduced in the early 20th century. It serves as a simplified benchmark in the study of Friedmann equations, Big Bang, cosmological constant, general relativity, and cosmology more broadly. The model influenced observational programs and theoretical work connected to Albert Einstein, Willem de Sitter, Alexander Friedmann, Georges Lemaître, and later debates involving Edwin Hubble, George Gamow, and Alan Guth.

Overview

The Einstein–de Sitter model assumes a homogeneous and isotropic spacetime described by the Friedmann–Lemaître–Robertson–Walker metric, with vanishing cosmological constant and critical matter density matching spatial flatness, linking to concepts in Friedmann equations, Robertson–Walker metric, Robertson–Walker coordinates, and the Hubble law. It was advocated in responses to observations by Edwin Hubble and theoretical work by Alexander Friedmann, and it played a role in discussions at institutions such as Princeton University, Institut d'Astrophysique de Paris, University of Göttingen, and Kavli Institute for Cosmological Physics. Debates over the model engaged figures like Albert Einstein, Willem de Sitter, Howard Percy Robertson, Arthur Eddington, and Subrahmanyan Chandrasekhar.

Mathematical formulation

The model arises from the Friedmann equations specialized to zero curvature term and zero cosmological constant, producing a scale factor a(t) ∝ t^{2/3} solution first noted by Alexander Friedmann and discussed by Einstein and de Sitter. Its energy content is pressureless dust represented in the stress–energy tensor formalism used by Albert Einstein in general relativity, with critical density ρ_c = 3H^2/(8πG) defined using Hubble parameter H, Newton's constant G, and constants appearing in work by Paul Dirac and Arthur Eddington. The model's dynamics are often derived employing methods from tensor calculus developed by Gregorio Ricci-Curbastro and Tullio Levi-Civita and expounded in texts by S. Weinberg and Misner, Thorne, and Wheeler.

Physical properties and predictions

The Einstein–de Sitter universe predicts a deceleration parameter q0 = 1/2, a matter-dominated thermal history connected to Big Bang nucleosynthesis studies by George Gamow, Ralph Alpher, and Robert Herman, and a specific relation between age and Hubble time t0 = 2/(3H0) referenced in observational work by Allan Sandage and G. de Vaucouleurs. It implies a scale-invariant growth of linear density perturbations used in structure formation theory advanced by Peebles, Press–Schechter formalism of William Press and Paul Schechter, and later elaborated by James Peebles and P. J. E. Peebles. Predictions about the cosmic microwave background anisotropy patterns relate to calculations by Ralph Alpher and later measurements by COBE, WMAP, and Planck missions, and influence expectations in studies by John Mather and George Smoot.

Observational tests and constraints

Empirical tests contrasted Einstein–de Sitter expectations with observations from Type Ia supernovae surveys led by teams including Saul Perlmutter, Brian Schmidt, and Adam Riess, cosmic microwave background experiments such as COBE, WMAP, and Planck, and large-scale structure surveys like the Sloan Digital Sky Survey and the Two-degree Field Galaxy Redshift Survey. Measurements of cosmic acceleration and inferred dark energy from supernova results, combined with CMB determinations of the acoustic scale and baryon acoustic oscillation detections by teams at Baryon Oscillation Spectroscopic Survey and WiggleZ, disfavored the pure Einstein–de Sitter case in favor of models including a cosmological constant or dark energy as in Lambda-CDM advocated in literature by Peebles and Ratra and observational analyses by Planck Collaboration. Cluster abundance studies by groups using data from ROSAT, Chandra X-ray Observatory, and XMM-Newton also constrained the matter density away from the Einstein–de Sitter critical value, informing work by Vera Rubin and Fritz Zwicky on mass estimates.

Historical development and influence

Historically, the model synthesized insights from Albert Einstein's field equations and Willem de Sitter's cosmological solutions and was part of early 20th-century cosmology debates involving Alexander Friedmann, Georges Lemaître, Arthur Eddington, and Hermann Weyl. It served as a reference for mid-century theoretical work by George Gamow, Ralph Alpher, and observational programs by Edwin Hubble and later Allan Sandage; it influenced pedagogical treatments by Steven Weinberg and research agendas at institutions such as Princeton University and California Institute of Technology. Declines in its favor followed late 20th-century advances led by Saul Perlmutter, Brian Schmidt, and Adam Riess, along with precision cosmology from WMAP and Planck, though it remains a useful idealization in textbooks by Kolb and Turner and reviews by Peebles.

Alternatives and extensions

Alternatives include Lambda-CDM with a positive cosmological constant and cold dark matter, open models with negative curvature as considered by Robertson and Walker, and inflationary scenarios introduced by Alan Guth and developed by Andrei Linde, Andreas Albrecht, and Paul Steinhardt. Extensions combine Einstein–de Sitter initial conditions with baryonic physics, neutrino mass effects investigated by Fermi National Accelerator Laboratory collaborations, and modified gravity proposals by Clifton and Nojiri and Odintsov inspired by work of Milgrom. Numerical and analytical studies employ tools from N-body simulations work at Max Planck Institute for Astrophysics and cosmological parameter estimation methods used by the Planck Collaboration and the Dark Energy Survey.

Category:Cosmology