Einstein's 1917 Static Model of the Universe: A Centennial Review

Abstract: We present a historical review of Einstein's 1917 paper 'Cosmological Considerations in the General Theory of Relativity' to mark the centenary of a key work that set the foundations of modern cosmology. We find that the paper followed as a natural next step after Einstein's development of the general theory of relativity and that the work offers many insights into his thoughts on relativity, astronomy and cosmology. Our review includes a description of the observational and theoretical background to the paper; a paragraph-by-paragraph guided tour of the work; a discussion of Einstein's views of issues such as the relativity of inertia, the curvature of space and the cosmological constant. Particular attention is paid to little-known aspects of the paper such as Einstein's failure to test his model against observation, his failure to consider the stability of the model and a mathematical oversight concerning his interpretation of the role of the cosmological constant. We recall the response of theorists and astronomers to Einstein's cosmology in the context of the alternate models of the universe proposed by Willem de Sitter, Alexander Friedman and Georges Lemaitre. Finally, we describe the relevance of the Einstein World in today's 'emergent' cosmologies.

• The paper critically reexamines Einstein's introduction of the cosmological constant as a stabilizer for a static, homogeneous universe.
• It highlights the absence of observational testing and quantitative predictions, reflecting early challenges in applying relativistic ideas to cosmology.
• The review demonstrates how the instability of Einstein’s model paved the way for dynamic cosmological theories and modern universe models.

Centenary Review of Einstein’s Static Model of the Universe

The paper "Einstein’s 1917. Static Model of the Universe: A Centennial Review" by Cormac O’Raifeartaigh et al. provides a comprehensive analysis of Einstein's influential 1917 paper, which introduced the first relativistic model of the universe. This significant work laid the groundwork for modern cosmology, offering insights into the conceptual developments following Einstein's formulation of the general theory of relativity (GTR). The review meticulously examines both the strengths and oversights of Einstein's model and situates it within the broader context of early 20th-century cosmological theories.

Historical and Theoretical Context

Einstein's landmark 1917 paper, presented shortly after his completion of the general theory of relativity, signaled the extension of relativistic principles to cosmological scales. The review emphasizes Einstein's innovative attempt to model the universe as a static, isotropic, and homogeneous sphere—later referred to as "Einstein’s Static Universe" or "Einstein World"—characterized by a uniform distribution of matter. The proposal was a direct challenge to Newtonian cosmology, which had inherent issues with infinite matter distributions and gravitational instability.

The centennial review outlines the theoretical motivations leading Einstein to introduce a cosmological constant (λ) to his field equations. This modification was analogous to the alterations made to Newtonian gravitational equations, intending to stabilize the universe against gravitational collapse, given that Einstein assumed a cosmologically static state.

Key Insights and Critical Analysis

O’Raifeartaigh et al. point out several critical aspects and oversights in Einstein’s paper:

1. Introduction of the Cosmological Constant: The addition of λ was Einstein’s attempt to reconcile his equations with a static universe, a concept he felt was required to align with observational understandings of the cosmos at that time. However, subsequent theoretical and empirical developments, most notably Hubble's expansion observations, eventually shifted perspectives towards dynamic models.
2. Lack of Observational Testing: Interestingly, Einstein did not attempt to quantitatively match his model's predictions with astronomical observations. The review highlights correspondence in which Einstein estimated a cosmic radius far exceeding astronomical expectations but chose not to publish this calculation.
3. Stability Concerns: The paper neglects the stability analysis of his static model. Later studies demonstrated that Einstein’s Static Universe is inherently unstable to perturbations in density, leading either to expansion or collapse without strict balancing forces.

Broader Implications and Historical Context

The review contextualizes Einstein's model amidst alternative rising cosmological theories, such as those by Willem de Sitter and Alexander Friedman. While de Sitter’s solution offered a universe devoid of matter, offering pathways for later theoretical development, Friedman's work introduced non-static solutions to the Einstein equations, anticipating cosmological expansion. The correspondence between these developments is explored, emphasizing the debates and discussions that shaped early relativistic cosmology.

Prospects for Future Research

Despite its early dismissal post-Hubble's discovery of the universe's expansion, Einstein's model resurfaces in contemporary cosmological discourse in the context of emergent universe scenarios. Here, the idea that the universe scales from a quasi-static phase offers new approaches to addressing the initial singularity and horizon problems in cosmology. Exploring the stability of such models within quantum frameworks continues to be a topic of considerable interest.

In conclusion, the historical review by O’Raifeartaigh et al. exemplifies a thorough examination of Einstein’s cosmological vision, its theoretical underpinnings, and its longstanding impact on the evolution of cosmic models. This centennial reflection not only sheds light on the intricate historical narrative of early cosmology but also highlights the considerable importance of historical scientific analyses in informing current theoretical explorations.