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Space DOES NOT Expand Everywhere

PBS Space Time·
6 min read

Based on PBS Space Time's video on YouTube. If you like this content, support the original creators by watching, liking and subscribing to their content.

TL;DR

Cosmic expansion is captured by an evolving scale factor in the FLRW metric, producing the Hubble flow where recession speed increases with distance.

Briefing

Cosmic expansion doesn’t mean every gravitationally bound system is getting pulled apart in lockstep with the universe’s overall growth. On the largest scales, distant galaxies recede in the Hubble flow, and general relativity ties that recession to an evolving “scale factor” in the Friedmann–Lemaître–Robertson–Walker (FLRW) model. But once gravity binds matter into structures—planets, stars, galaxies—the local spacetime geometry stops behaving like the smooth, evenly expanding FLRW background. The result is a universe that expands globally while remaining locally stable inside bound systems like the Milky Way.

The key distinction is between the idealized FLRW picture and the spacetime around real, clumped mass. FLRW assumes matter is homogeneous and isotropic, so the metric’s spatial grid expands or contracts uniformly everywhere. That uniformity is what makes the “space is expanding everywhere” slogan sound plausible. Yet zooming in reveals that massive objects warp spacetime in ways that the FLRW approximation cannot capture. Near a compact object, the Schwarzschild metric describes a static, inwardly “pinched” geometry rather than an expanding one. Crucially, the spacetime inside a gravitationally bound system doesn’t “fight” the surrounding expansion, because there isn’t an extra expanding grid underneath the gravitational field. Gravity isn’t something laid on top of spacetime; it is the spacetime geometry itself. So the Milky Way’s internal structure doesn’t thin out or get stretched like rubber as the universe grows.

The balloon analogy—galaxies glued to a balloon and carried apart as it inflates—helps illustrate how recession speeds scale with distance, but it breaks down when applied to bound systems. In the balloon picture, the galaxy seems held together against an expanding material substrate. The transcript reframes that: the bound system’s own spacetime geometry is what matters, and it stays effectively static relative to the system even as the broader universe evolves.

To address what “new space” means, the transcript leans on the mathematical flexibility of general relativity: space can be subdivided indefinitely, so expanding coordinates can be re-gridded without requiring new patches to appear between existing ones. Every point in today’s universe can be traced back along geodesics to earlier times, linking the present to the big bang without “popping” new regions into existence. At the smallest scales, however, general relativity conflicts with quantum mechanics, introducing the Planck length as a minimum meaningful scale. The discussion notes that the Planck length is built from constants (G, ħ, c), so it would remain fixed if those constants don’t change; expansion would then correspond to adding more Planck-scale “units” rather than stretching them.

Finally, dark energy enters as a subtle twist: its energy density in empty space stays constant as space expands, so the total dark energy content grows with the amount of space. That growth matters only on cosmic scales—where vast regions of empty space dominate over matter—not inside bound systems, where the matter-to-empty-space ratio stays effectively unchanged. The upshot: the universe likely expands forever, but the Milky Way remains a relatively static bubble, isolated from other regions as cosmic horizons recede.

Cornell Notes

On the largest scales, the universe’s expansion shows up as the Hubble flow: distant galaxies recede faster the farther away they are. General relativity models that behavior with the FLRW metric, where an evolving scale factor grows or shrinks uniformly under assumptions of homogeneity and isotropy. But those assumptions fail inside gravitationally bound systems. Around massive objects, the Schwarzschild metric (static, inwardly pinched geometry) replaces the FLRW description, and the spacetime inside bound structures doesn’t “stretch like rubber” due to the surrounding expansion. “New space” is largely a coordinate/geometry effect in GR, while quantum gravity issues (Planck length, transplanckian problem) complicate what the smallest “stuff” of space really is. Dark energy’s constant density increases total energy with more volume, yet it doesn’t disrupt bound systems like the Milky Way.

What observational pattern signals cosmic expansion, and how is it distinguished from local motion?

Distant galaxies show recession speeds that increase with distance—the Hubble flow. Local motions from gravity (planets orbiting stars, stars orbiting within galaxies, galaxy interactions in clusters) are called “peculiar velocity,” and they’re small compared with the systematic recession at large distances. The further away a distant point is, the faster it recedes, producing the Hubble flow.

Why does the FLRW model imply uniform expansion, and what assumptions make that possible?

The FLRW metric provides a geometric description of an expanding universe using a scale factor that changes over time. In GR, tracking the FLRW metric forward or backward forces the scale factor to grow or shrink everywhere evenly. That conclusion depends on FLRW’s big assumptions: matter is homogeneous (spread out evenly) and isotropic (looks the same in all directions). Those assumptions work well on the largest scales, but they break down when matter clumps.

How does the Schwarzschild metric change the story inside gravitationally bound systems?

Near a compact massive object, spacetime is described by the Schwarzschild metric rather than FLRW. The transcript emphasizes that the Schwarzschild geometry is static in time and “pinched” inward; space there does not expand. When that local geometry is embedded in a larger FLRW universe, there isn’t an additional expanding spacetime grid underneath the gravitational field that the system must resist. The gravitational field is the spacetime geometry itself, so the bound system’s internal spacetime doesn’t get stretched by the universe’s global expansion.

What does it mean to say “space expands” without stretching space like rubber?

In the FLRW picture, expansion is encoded in the growth of the scale factor and the divergence of the FLRW coordinate grid. The transcript argues that spacetime doesn’t behave like elastic material that thins out or builds tension. Instead, bound systems maintain their internal separations: nearby grid lines in a gravitational field remain effectively parallel while distant ones diverge. The “tug of war” between expansion and gravity is not ongoing inside bound structures; it happened earlier, when some regions were dense enough for gravity to win and others were not.

How can “new space” appear if GR lets spacetime be subdivided indefinitely?

General relativity treats space as infinitely divisible, so one can imagine starting with a small, finely gridded universe and watching the grid diverge as it expands. Because coordinates can be redefined, the expansion can be represented without requiring new patches to appear between existing ones. The transcript links this to geodesic completeness: spacetime paths can be traced to the infinite past or future until they hit singularities like the big bang or black holes, rather than geodesics “popping out” from nowhere.

Why doesn’t dark energy’s constant density automatically tear apart galaxies?

Dark energy in empty space has a very weak but constant energy density. As space expands, the density per unit volume stays the same, so the total dark energy content increases with the amount of space. That effect becomes significant only when empty space dominates over matter on enormous scales. Inside galaxies and other bound systems, the ratio of empty space to matter doesn’t change much, so the expansion-driven dark-energy influence doesn’t produce a comparable disruptive effect.

Review Questions

  1. What role do the FLRW assumptions of homogeneity and isotropy play in predicting uniform expansion, and where do those assumptions fail?
  2. Explain why the Schwarzschild metric implies that space inside a gravitationally bound system doesn’t participate in the global expansion in the same way as the FLRW background.
  3. How does the transcript reconcile “space expansion” with the idea that geodesics don’t originate or terminate by new patches appearing?

Key Points

  1. 1

    Cosmic expansion is captured by an evolving scale factor in the FLRW metric, producing the Hubble flow where recession speed increases with distance.

  2. 2

    Local gravitationally bound systems (planets, stars, galaxies) do not keep stretching with the universe’s global expansion.

  3. 3

    The FLRW description assumes matter is homogeneous and isotropic; clumping breaks that approximation and changes the relevant spacetime geometry.

  4. 4

    Around compact masses, the Schwarzschild metric replaces FLRW and yields a static, inwardly pinched spacetime rather than an expanding one.

  5. 5

    The gravitational field is the spacetime geometry itself, so there isn’t an extra expanding “background grid” that bound systems must resist.

  6. 6

    “New space” is largely a geometric/coordinate effect in GR, consistent with tracing spacetime paths (geodesics) back to the big bang without requiring new regions to appear between old ones.

  7. 7

    Dark energy’s constant density increases total energy with more volume, but it doesn’t disrupt bound systems like the Milky Way because matter-to-empty-space ratios there remain effectively stable.

Highlights

The universe can expand globally while the Milky Way stays effectively stable, because bound systems follow their own spacetime geometry rather than the smooth FLRW expansion.
Schwarzschild spacetime near compact masses is static and inwardly pinched—so “space expansion everywhere” doesn’t apply inside gravitationally bound regions.
The balloon analogy misleads by implying galaxies are glued to an expanding material substrate; in GR, gravity is geometry, not a separate force acting on top of space.
Dark energy’s constant energy density means total dark energy grows with the amount of space, yet its disruptive effects show up mainly on the largest, emptiest scales.

Topics

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