Cosmological Constant and Vacuum Energy

The simplest form of dark energy is a constant energy of empty space, Einstein's cosmological constant, but its observed value is fantastically smaller than theory predicts.

Definition

The cosmological constant is a constant term in Einstein's field equations corresponding to a uniform energy density of the vacuum with negative pressure; identified with dark energy, it produces accelerated expansion, and its observed magnitude is many orders of magnitude below naive theoretical expectations.

Scope

This topic covers the cosmological constant as a term in Einstein's equations and its interpretation as the energy density of the vacuum, the way a constant negative-pressure component drives acceleration, and the cosmological-constant problem posed by the enormous mismatch between the observed value and quantum-field-theory estimates.

Core questions

• What is the cosmological constant and how does it relate to vacuum energy?
• Why does a constant vacuum energy cause acceleration?
• Why is the cosmological-constant problem so severe?

Key concepts

• Cosmological constant
• Vacuum energy
• Negative pressure
• Equation of state w equals minus one
• Cosmological-constant problem
• Anthropic argument
• Lambda-CDM

Key theories

Vacuum energy as Lambda

Quantum field theory predicts the vacuum carries energy, which gravitates like a cosmological constant with negative pressure, providing a natural candidate for dark energy within general relativity.

The cosmological-constant problem

Estimates of the vacuum energy from particle physics exceed the observed dark-energy density by many tens of orders of magnitude, a discrepancy that is one of the deepest unsolved problems linking gravity and quantum theory.

Mechanisms

A cosmological constant corresponds to an energy density that does not dilute as the universe expands; because its pressure equals minus its energy density, the second Friedmann equation gives accelerated expansion once it dominates, while summing zero-point energies of quantum fields yields a vastly larger value than observed.

Clinical relevance

The cosmological constant is the foundation of the standard Lambda-CDM model and fits all current data, yet the unexplained smallness of its value sits at the intersection of cosmology, particle physics, and quantum gravity, motivating ideas from supersymmetry to the multiverse.

History

Einstein introduced the constant in 1917 and later regretted it; after the discovery of expansion it was largely set aside, but Zeldovich connected it to vacuum energy in the 1960s, Weinberg sharpened the problem in 1989, and the 1998 acceleration discovery brought a small positive value back to center stage.

Debates

Why is Lambda so small but nonzero?

Explaining the tiny, nonzero value of the cosmological constant has driven proposals ranging from unknown cancellation mechanisms to anthropic selection in a multiverse, none of which is established, leaving the problem open.

Key figures

• Albert Einstein
• Steven Weinberg
• Yakov Zeldovich
• Wolfgang Pauli

Seminal works

• weinberg1989

Frequently asked questions

Is the cosmological constant the same as dark energy?

The cosmological constant is the simplest possible form of dark energy, a constant vacuum energy; dark energy is the broader term that also includes dynamical alternatives, so the constant is one specific, currently favored, model of dark energy.

Why is the cosmological-constant problem called the worst prediction in physics?

Because naive quantum-field-theory estimates of the vacuum energy exceed the observed value by something like 120 orders of magnitude, an unprecedented mismatch between theory and observation that no accepted mechanism yet resolves.