# Will expanding space rupture an empty box floating in outer space

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?

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:

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

• Thank you Sten. Under your example where if the box survives now it will survive indefinitely, would that indicate that the size and composition of the box is relevant, where size could be increased to an equilibrium point whereby accumulated forces of space expansion exactly equal the nuclear and electromagnetic binding forces of the matter the box is composed of, allowing the box to survive forever, but if the box is made any bigger it would immediately rupture? Just wondering if an experiment could be devised using cardboard boxes to see if a certain size ruptures and smaller size survives. Commented Jul 9 at 6:20
• Also wondering if we already have measurements of the the force of expanding space versus nuclear and electromagnetic force of the matter the box is composed of to allow for a prediction of what the equilibrium size should be? Commented Jul 9 at 6:27
• @mdswartz I might be wrong, but I don't think one should think about it in terms of classical force. Think about "the big rip" scenarios in terms of an effective weakening of the other forces. The speed of sound in materials would start decreasing and it would, eventually, become zero. At that point all internal cohesion of a classical object would be lost and it would literally start flowing apart like as if it was melting. Commented Jul 9 at 7:47
• @mdswartz The outward gravitational acceleration induced on a spherical box of radius $r$ is $g=H_0^2\Omega_\Lambda r$, where $H_0\simeq 68$ km/s/Mpc is the Hubble constant and $\Omega_\Lambda\simeq 0.69$ is the dark energy density parameter. That works out to be about $3\times 10^{-36}r/\mathrm{sec}^2$ (so if the radius were 1 meter, the acceleration would be $3\times 10^{-36} \mathrm{m}/\mathrm{s}^2$).
– Sten
Commented Jul 9 at 21:35
• if the box has the size of the Hubblesphere the force in order to stay constant should be infinite since it would require local speed of light to keep a contant distance, while in your equation g stays finite even if the box was larger than that. the proper acceleration or force required to stay stationary at distance r is F=cr√(((H²(c-Hr)+Ḣc)(H²(c+Hr)+Ḣc))/(c²-r²H²)²) for a time dependend H and F=cH²r/√(c²-r²H²) for a constant H (Ḣ=0), so if the diameter of the box was c/H the force would be infinite (F=1/0). Commented Jul 10 at 3:15