Will expanding space rupture an empty box floating in outer space

Question

Under the theory that space itself is expanding, but the space inside of atoms and molecules doesn't expand because nuclear and electromagnetic bonding forces exceed the forces that expand space, would a closed empty box floating in outer space eventually rupture because of the expanding space inside of it?

Answer 1

The box would only be ripped apart if dark energy is "phantom energy", which increases in energy density as the Universe expands. In that case, the destruction of the box would occur right before the Big Rip.

If the dark energy is a cosmological constant (which is consistent with current data), then its energy density remains constant over time, and so does the repulsive influence it exerts on a box of fixed volume. Thus, a box that survives now will survive indefinitely (neglecting material degradation). For a spherical box of radius $r$ (which I assume to be much smaller than the cosmological horizon), dark energy at its measured value induces an outward gravitational acceleration of $$g=H_0^2\Omega_\Lambda r\simeq (3\times 10^{-36}\mathrm{sec}^{-2})r,$$ where $H_0\simeq 68$ km/s/Mpc is the Hubble constant and $\Omega_\Lambda\simeq 0.69$ is the dark energy density parameter. For example, this means that if the radius were 1 meter, the acceleration would be $3\times 10^{-36} \mathrm{m}/\mathrm{s}^2$ (36.5 orders of magnitude weaker than Earth's surface gravity). Indeed, for any object denser than $$\frac{3H_0^2}{4\pi G}\Omega_\Lambda\simeq 10^{-29}~\text{gram}/\text{cm}^3\simeq 7~\text{keV}/\text{cm}^3$$ ($10^{-29}$ times the density of water), its own self-gravity is stronger than dark energy's repulsion.

Note that these effects arise from gravitational repulsion from the dark energy. "Expanding space" is not itself a physical phenomenon; as discussed in other answers:

• Space expansion is a description of the coordinates and not the physics.
• There is no concept of "expanding space" in general relativity.
• Expansion of space is not distinguishable from objects moving away.

For example, without dark energy, there would be no expansion force on the box, even as the Universe expands.