Einstein's static universe

• 1. Introduction

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  Einstein's static universe is the cosmological model Albert Einstein proposed in 1917, only months after finishing his general theory of relativity. It described a universe that neither grew nor shrank. To make the equations work, Einstein had to insert an extra term of his own invention. That fix would not last through the next decade. What forced Einstein toward a universe standing still, and what finally convinced him to let it go?

• 2. The Static Solution

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  Spherical spatial curvature is what general relativity produced once Einstein applied it to the whole universe, assuming even matter and no change over time. That combination gave Einstein a universe that was finite in size, closed back on itself rather than stretching out forever.

  The cosmological constant is the term Einstein introduced to keep this static, matter-filled universe from collapsing under its own gravity. Einstein tied this constant, written as Λ, to two other quantities: the universe's radius R and its matter density ρ. The relation was Λ equals 1 over R squared, and also equals κ times ρ divided by 2, where κ is the Einstein gravitational constant. That relationship would soon meet a challenge from observations Einstein had not built into his equations.

• 3. Hubble's Challenge

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  In 1929, Edwin Hubble discovered a linear relationship between the redshifts of galaxies and how far away they sat. Faced with this evidence, Einstein abandoned his static model for universes that could expand, including the Friedmann-Einstein universe and the Einstein-de Sitter universe. In both new models he set the cosmological constant to zero, calling it "no longer necessary... and theoretically unsatisfactory."

  Many Einstein biographies claim that he later called the cosmological constant his "biggest blunder." The astrophysicist Mario Livio has cast doubt on this claim, suggesting it may be exaggerated. Whether Einstein ever spoke those exact words remains unresolved, leaving one of physics' most quoted lines still unverified.