Cosmological constant

• 1. Introduction

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  The cosmological constant is a number so small it nearly vanishes, yet its presence or absence shapes the fate of the entire universe. Albert Einstein first wrote it into his field equations of general relativity in 1917. He added it reluctantly, as a fix he never fully believed in. He later called it his "biggest blunder". And then, decades after his death, observations of distant exploding stars forced physicists to conclude he may have been right the first time.

  What is this constant, and why does it matter so much? It represents the energy density of empty space itself. That sounds abstract, but the consequences are concrete: if its value were even modestly different, galaxies could not form, and life as we know it could not exist. Today it sits at the center of the deepest unsolved problem in physics, where the prediction from one branch of science disagrees with the measured value by a factor of ten to the power of one hundred and twenty. Physicists have called that gap "the worst theoretical prediction in the history of physics." Understanding how that gap opened, and why no one has closed it, is the story this documentary will follow.

• 2. Einstein's Reluctant Addition

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  In 1917, Einstein published a paper titled Cosmological Considerations in the General Theory of Relativity. His equations, finished two years earlier, described a universe that could not hold still. Gravity, left unchecked, would cause any non-expanding universe to collapse inward on itself. That outcome troubled Einstein, because the scientific consensus at the time assumed the universe was static and eternal.

  To prevent that collapse, he inserted a new term into his equations. He gave it a value calculated to hold the cosmos in perfect balance. But the balance was illusory. As physicists later established, the equilibrium his constant created was unstable: a universe nudged even slightly outward would expand further, releasing energy that drove yet more expansion. A universe nudged inward would collapse all the way. There was no stable middle ground.

  Einstein's own feelings about this move were on record. He wrote that since introducing the term he had "always a bad conscience," and added that he was "unable to believe that such an ugly thing is actually realized in nature." The physicist George Gamow later recalled that Einstein described abandoning the constant as his "biggest blunder," a phrase that has echoed through physics ever since.

• 3. Hubble, Friedmann, and the Expanding Sky

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  Alexander Friedmann, a Russian mathematician, had already found a solution to Einstein's equations that described a dynamic, expanding universe. He reached this conclusion while working directly with the Einstein equations of general relativity. His result showed that the equations remained valid whatever value the cosmological constant took, meaning the constant was not needed to save general relativity from a collapsing cosmos.

  In 1927, the Belgian astrophysicist Georges Lemaitre combined general relativity with astronomical observations, drawing on work by Hubble among others, to argue that the universe was in fact expanding. Then in 1929, Edwin Hubble published observations that confirmed the expansion directly. The universe was not static. Einstein's original motivation for adding the constant had evaporated.

  Einstein responded by proposing, in 1931, a model of a continuously expanding universe with the cosmological constant set to zero, the Friedmann-Einstein universe. The following year, working with the Dutch physicist and astronomer Willem de Sitter, he proposed yet another model in which both the constant and the spatial curvature of the universe were set to zero, the Einstein-de Sitter universe. For most physicists, from the 1930s through the late 1990s, the constant was simply zero. The question seemed settled.

• 4. Supernovae and the Shock of Acceleration

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  Saul Perlmutter at Lawrence Berkeley National Laboratory, Brian Schmidt of the Australian National University, and Adam Riess of the Space Telescope Science Institute each led teams hunting for type Ia supernovae in the 1990s. Type Ia supernovae are useful to astronomers because they explode with a known brightness, making them reliable distance markers across billions of light-years.

  When the teams began their work, they expected the data to show the universe decelerating. Gravity from all the matter inside the cosmos should have been slowing the expansion down since the Big Bang. The first reports from one of the teams, published in July 1997, were consistent with that picture. Then the numbers shifted. Both teams announced in 1998 that the supernovae were not slowing down; they were accelerating away. The universe's expansion was speeding up.

  The only way to account for that acceleration within Einstein's framework was to restore the cosmological constant, with a positive value. A positive constant implies a negative pressure from the vacuum of space itself, and that negative pressure drives expansion rather than resisting it. The constant was reinserted into the general relativity equations. For this discovery, Perlmutter, Schmidt, and Riess jointly received the Nobel Prize in Physics in 2011.

• 5. Dark Energy and the LCDM Model

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  Studies since the 1990s, using the cosmological principle as a baseline assumption, have suggested that around 68 percent of the total mass-energy density of the universe can be attributed to dark energy. The cosmological constant is the simplest possible explanation for that dark energy. It is now a load-bearing ingredient in the standard model of cosmology, known as the Lambda-CDM model.

  Cosmologists often express the constant not as a raw number but as a dimensionless ratio: the fraction of the universe's total energy content that dark energy accounts for. The Planck Collaboration published a value for this ratio in 2018, estimating it at 0.714. This parameter is not fixed for all time in the way other constants are. The critical density of the universe changes over cosmic time, but the energy density from the cosmological constant does not. As the universe grows, the total amount of dark energy rises along with the volume, while the amount of matter remains the same. Dark energy therefore becomes a progressively larger share of the total.

  The equation of state of dark energy, denoted w, compares the pressure dark energy exerts to its energy per unit volume. For the cosmological constant, this ratio is exactly negative one. The Planck Collaboration measured a value of negative 1.028 in 2018, consistent with that theoretical expectation. Alternative theories of dark energy, such as quintessence, use different values of w, which means future measurements that pin down w more precisely could distinguish between the cosmological constant and its rivals.

• 6. The Worst Prediction in Physics

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  Quantum field theory, the framework underlying modern particle physics, defines empty space not as truly empty but as a seething collection of quantum fields. These fields all sit in their lowest possible energy state, their ground state, but quantum mechanics forbids that energy from being exactly zero. Zero-point energy, as it is called, fills all of space.

  Those zero-point fluctuations should contribute to the cosmological constant. When physicists perform the calculation using quantum field theory down to the Planck scale, the expected value of the vacuum energy comes out roughly ten to the power of one hundred and twenty times larger than what astronomers actually measure. That factor of ten to the one hundred and twentieth power has no precedent in the history of science. It is the discrepancy between the theory's prediction and the observation that earned the label "the worst theoretical prediction in the history of physics."

  Some supersymmetric theories offer a partial escape: they require the cosmological constant to be exactly zero, which at least avoids the enormous positive prediction. But zero is also wrong, given the observed acceleration. No string theory vacuum is known to support a stable, positive cosmological constant, and in 2018 a group of four physicists put forward a conjecture that would imply no such universe can exist. The cosmological constant problem remains one of the greatest unresolved mysteries in science, with many physicists holding that the vacuum itself holds the key to a full understanding of nature.

• 7. The Anthropic Argument

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  In 1987, the physicist Steven Weinberg proposed an explanation that did not resolve the discrepancy but reframed the question. Following the anthropic principle, Weinberg argued that if vacuum energy varied across different domains of the universe, observers could only find themselves in domains where the value permitted life to exist.

  His reasoning ran in two directions. A strongly negative vacuum energy would close the universe and shorten its lifetime, potentially below what intelligent life needs to evolve. A large positive value would cause the universe to expand so fast that galaxies could never assemble. Either extreme rules out observers. Using this constraint, Weinberg predicted that the cosmological constant would turn out to be less than a hundred times the value then accepted. In 1992, he refined that estimate to between five and ten times the matter density of the universe.

  In 1995, Alexander Vilenkin sharpened the argument further, predicting a value only about ten times the matter density. That is roughly three times the value eventually measured and accepted. Critics of this line of reasoning argue that invoking the anthropic principle to explain fine-tuning commits what logicians call the inverse gambler's fallacy. Multiverse theories, which predict vast numbers of universes with different physical constants, are one framework within which the anthropic argument makes formal sense, but the debate over whether such theories constitute genuine scientific explanation remains unresolved.