vacua

Vacua are states of a physical system that minimize or locally minimize its energy, describing the properties of empty space or the low-energy configuration of fields in a theory. In cosmology and particle physics, the term often refers to the vacuum state of the underlying quantum fields.

In quantum field theory, the vacuum is not truly empty; it exhibits fluctuations due to the Heisenberg uncertainty principle. These quantum vacuum fluctuations give rise to zero-point energy and contribute to vacuum energy that influences the gravitational dynamics described by general relativity, potentially appearing as a cosmological constant. Observables such as the Casimir effect provide empirical manifestations of the quantum vacuum. In gravitation, vacua can correspond to different spacetime geometries, including Minkowski (flat), anti-de Sitter (AdS), and de Sitter (dS) vacua.

The energy landscape of a field can contain multiple minima. A true vacuum is the global minimum, while a false (metastable) vacuum is a local minimum that can decay to a deeper one. Decay proceeds through bubble nucleation and, in a gravitational setting, through Coleman–De Luccia processes. Such transitions can have profound cosmological consequences, including phase transitions in the early universe and the generation of gravitational waves.

In particle physics, fields may have nonzero vacuum expectation values (VEVs). The Higgs field, for example, acquires a nonzero VEV that breaks electroweak symmetry and endows particles with mass. In theories with supersymmetry or extra dimensions, the set of possible vacua—the vacuum manifold or landscape—can be vast, with different low-energy constants. Stabilizing moduli selects particular vacua and shapes the predicted physics.

The study of vacua intersects with inflation, the cosmological constant problem, and attempts to connect fundamental theory to observed cosmic acceleration, highlighting both the richness and the challenges of understanding empty space.