Relativity and Cosmology

Einstein and the Static Universe

When Einstein first applied his field equations to cosmology in 1917, he expected to find a static, unchanging universe, consistent with the prevailing scientific view of the time. Instead, he found that his equations predicted a dynamic universe that would either expand or contract. Unable to accept this result, Einstein introduced a term called the cosmological constant (denoted by the Greek letter Lambda) to balance gravitational attraction and produce a static solution.

In 1929, Edwin Hubble discovered that distant galaxies are moving away from us at speeds proportional to their distance, a relationship now known as Hubble law. This observational evidence for an expanding universe meant that Einstein static model was unnecessary. Einstein reportedly called the cosmological constant his greatest blunder. Ironically, the cosmological constant would return decades later in a different role, as the simplest mathematical description of dark energy.

The Friedmann Equations and the Expanding Universe

In the early 1920s, Russian physicist Alexander Friedmann solved Einstein field equations under the assumption that the universe is homogeneous (the same everywhere) and isotropic (the same in every direction) at large scales. His solutions, known as the Friedmann equations, describe a universe that evolves over time, with the rate of expansion depending on the density of matter, radiation, and any cosmological constant present.

The Friedmann equations predict three possible geometries for the universe depending on its total energy density relative to a critical value. If the density exceeds the critical value, the universe has positive spatial curvature (like the surface of a sphere) and is closed, eventually contracting back to a point. If the density is below the critical value, the universe has negative curvature (like a saddle shape) and expands forever. If the density exactly equals the critical value, the universe is spatially flat and expands forever, but at an ever-decreasing rate. Observations, particularly from the cosmic microwave background, indicate that the universe is very close to spatially flat.

The Friedmann-Lemaitre-Robertson-Walker (FLRW) metric is the mathematical description of these expanding universe models. It incorporates a time-dependent scale factor a(t) that describes how distances between galaxies change over time. The ratio of the scale factor at two different times determines the cosmological redshift: light emitted by a distant galaxy is stretched (redshifted) by the expansion of space during its journey to us.

The Big Bang

Running the expansion backward in time, the Friedmann equations imply that the universe was once much smaller, hotter, and denser than it is today. Extrapolating all the way back leads to a singularity at the initial moment, commonly called the Big Bang. In the standard cosmological model, the Big Bang occurred approximately 13.8 billion years ago.

The Big Bang model makes several testable predictions. It predicts that the universe should be filled with thermal radiation left over from its hot early phase, the cosmic microwave background (CMB), which was discovered in 1965 by Arno Penzias and Robert Wilson. It predicts specific abundances of the lightest elements (hydrogen, helium, deuterium, lithium) produced during the first few minutes of the universe, which match observations. And it predicts that the distribution of galaxies and other large-scale structures should reflect tiny density fluctuations from the early universe, which has been confirmed by detailed CMB measurements from satellites like COBE, WMAP, and Planck.

It is important to note that the Big Bang is not an explosion in space. It is an expansion of space itself. There is no center of the Big Bang and no edge to the expanding universe. Every point in space sees all other points receding from it, a consequence of the uniform expansion described by the FLRW metric.

Dark Energy and Accelerating Expansion

In 1998, two independent teams studying distant Type Ia supernovae discovered that the expansion of the universe is not slowing down (as gravity would cause) but accelerating. This discovery, which earned Saul Perlmutter, Brian Schmidt, and Adam Riess the 2011 Nobel Prize in Physics, implies the existence of a mysterious component of the universe called dark energy that exerts a repulsive gravitational effect.

In the framework of general relativity, dark energy is most simply described by Einstein cosmological constant, a constant energy density that pervades all of space. This energy density is extremely small, corresponding to about 6 x 10^-10 joules per cubic meter, but because it fills all of space, it dominates the energy budget of the universe. Current observations indicate that dark energy constitutes about 68% of the total energy content of the universe, with dark matter making up about 27% and ordinary (baryonic) matter only about 5%.

The nature of dark energy remains one of the most profound unsolved problems in physics. If it is truly a cosmological constant, its value is incredibly difficult to explain from fundamental physics. Quantum field theory predicts a vacuum energy density roughly 10¹²⁰ times larger than what is observed, a discrepancy sometimes called the worst prediction in the history of physics.

Relativity and the Ultimate Fate of the Universe

General relativity, combined with observations of the universe energy content, predicts the ultimate fate of the cosmos. If dark energy is a true cosmological constant and remains unchanged, the universe will continue to expand at an accelerating rate forever. Galaxies beyond our local group will eventually recede faster than light (due to the expansion of space, not motion through space), becoming permanently unobservable. In the very distant future, the observable universe will contain only our local group of galaxies, surrounded by an empty, cold void.

Alternative models of dark energy, where its density changes over time, could lead to different fates. If dark energy strengthens over time, the universe could end in a Big Rip, where the expansion becomes so violent that it tears apart galaxies, stars, atoms, and eventually spacetime itself. If dark energy weakens, the expansion could eventually reverse, leading to a Big Crunch. Current observations favor a cosmological constant, but the precision is not yet sufficient to definitively rule out slowly changing dark energy.