Bound vs Coupled Systems in Cosmology

The terms "bound" and "coupled" are related and often appear in similar cosmological contexts, but they are not equivalent. They describe different physical mechanisms and states.

Core Definitions

Bound System

A bound system refers to a collection of objects, typically held together by a dominant attractive force (almost always gravity), whose total energy is negative.

The key feature is that the objects are trapped in a potential well. Their kinetic energy is insufficient to escape the mutual attraction.

In cosmology, a system is considered bound if its internal gravitational pull is stronger than the influence of the Hubble expansion. This is often assessed using the Bondi Criterion: the escape velocity within the system (v_esc) is greater than the Hubble flow velocity across it (v_Hub = H₀ × R).

Examples include the Solar System (bound by the Sun's gravity), the Milky Way galaxy (bound by dark matter and stellar gravity), and the Local Group of galaxies (bound and will not be pulled apart by expansion).

Coupled System

A coupled system consists of two or more components of the universe that are interacting with each other through some force or particle exchange. They are in communication and can efficiently exchange energy, momentum, or otherwise influence each other's behavior.

The key feature is that the interaction rate (Γ) between the components is greater than the Hubble expansion rate (H). When Γ > H, the components are tightly coupled. When Γ < H, they decouple or "freeze out."

Examples include the photon-electron plasma before recombination (tightly coupled via constant Thomson scattering), photons after recombination (decoupled from matter, forming the CMB), and neutrinos which decoupled from other particles about one second after the Big Bang.

Comparative Analysis

Feature	Bound System	Coupled System
Governing Force	Almost always Gravity	Can be any force: Electromagnetic, Strong, Weak, Gravity
Key Criterion	Negative total energy; vesc > vHub	Interaction rate > Expansion rate; Γ > H
What it resists	Kinetic Dispersal & Cosmic Expansion	Decoupling & Free Streaming (the tendency for components to stop interacting due to expansion)
Typical Scale	Local (Solar System, Galaxy, Cluster)	Can be local or global (e.g., the entire photon-baryon fluid)
State of Components	Components are trapped in a common potential well	Components are in communication via interactions

How They Relate and Interact

While distinct, the concepts can interact in important ways:

A system can be bound but not coupled

The planets in the Solar System are gravitationally bound to the Sun, but they are not coupled to it in the particle-interaction sense. They follow their orbits without constant "communication" via scattering.

A system can be coupled but not globally bound

The baryon-photon fluid before recombination is the prime example. Photons and electrons were tightly coupled through constant scattering, but this entire fluid was not a gravitationally bound object; it was expanding with the universe.

Coupling can lead to binding

In the early universe, tiny over-densities in the coupled baryon-photon fluid oscillated as sound waves. After photons decoupled, the baryons were no longer pressured by the photons and could collapse into the gravitational potential wells provided by dark matter. Thus, the decoupling of one set of components allowed another set to become bound into the structures we see today.

Conclusion: Complementary but Distinct

In summary, "bound" and "coupled" describe fundamentally different aspects of physical systems in cosmology.

A bound system is a statement about the gravitational energy state of a system. It's about being confined.

A coupled system is a statement about the interaction and communication between components. It's about being connected.

Think of it this way: A bound system is like a solar system where the planets are trapped by the sun's gravity. A coupled system is like a hot gas where the atoms are constantly colliding and interacting.

In cosmology, understanding when systems become bound (like galaxies) and when different components decouple (like the CMB) is fundamental to building the history and structure of our universe. They are two different, crucial threads in the cosmic story.