system
Given the following post, respond as if you're commenting on Reddit:
human
What is vacuum energy and what is the "vacuum catastrophe"?
gpt
Vacuum energy is an energy density associated with empty space. 

You may have heard of 'zero-point energy' of quantum mechanical systems, where the state of lowest energy--the ground state--doesn't have zero energy but instead slightly above zero. For example, a classical harmonic oscillator (think mass on a spring) has zero energy at rest, but a quantum harmonic oscillator has hbar*omega/2 of energy at minimum (where hbar is the reduced Planck constant, and omega is the angular frequency of the oscillator).

When you apply quantum mechanics to relativistic particles (quantum field theory), you find that each particle type (field) acts like an infinite number of harmonic oscillators, one for each possible momentum of the particle. And each of those harmonic oscillators has a zero-point energy. And a finite number times infinity seems to give an infinite contribution to the energy density of empty space! This is the 'vacuum catastrophe.'

But, all is not lost. This sort of thing happens all the time in quantum field theory, and it's actually not a big deal---just an artifact of the way we like to describe the system mathematically. When you work hard enough to only describe *observable* quantities, all of the infinities (including the vacuum energy) go away and become finite. This is called renormalization.

However, all is not won, either. The tradeoff for renormalization rescuing us from infinite vacuum energy is that the *actual* vacuum energy depends very sensitively on the highest-energy particles in the theory. This is not what we like in physics, where we want to describe low-energy physics independently of what's going on at higher energies; planetary motion doesn't really care about the top quark, for example. But the vacuum energy cares about the *highest* energies that we can't even access directly. Naively, then, it should have a value comparable to the Planck scale, where quantum gravity renders quantum field theory incomplete. Or maybe optimistically it should be comparable to a scale just above the reach of the LHC (10 TeV or so) where physics *could* (probably doesn't, but could) change dramatically. Instead it's milli-electronvolts, comparable to the tiniest particle masses we know about.

Who cares what the energy density of empty space is? Gravity does--vacuum energy causes an accelerating expansion of the universe, which we know we live in! So that's good. Except the value we've measured (meV^(4)=10^-12 eV^(4)) is 120 orders of magnitude smaller than what we expect (Planck mass^(4)=10^108 eV^(4)). What. This is the cosmological constant problem, which is the modern version of 'vacuum catastrophe.' Widely considered the biggest problem in theoretical physics, nobody has any good ideas for how to solve it (besides arguing for a multiverse with 10^120 possible universes).