Does Rapid Space Expansion Produce an Effect Similar to Hawking Radiation?

Question

As we know that due to quantum fluctuations, virtual particle pairs constantly pop in and out of existence for incredibly short period of time. If such a pair forms near the event horizon of a Black Hole, one particle can fall into the black hole while the other escapes, leading to what we call as Hawking radiation.

I was wondering whether the same thing can happen for a rapidly expanding region of space, where the rate of expansion is so extreme that even if the virtual particle pair tried to annihilate each other, the space between them expands so fast (faster than the distance a photon can travel in that time) that they are permanently separated? If so, would this result in something analogous to Hawking radiation in regions of space that are expanding faster than the speed of light?

Answer 1

This effect indeed happens. It is sometimes referred to as the Unruh effect in curved spacetime, or the Gibbons–Hawking effect. In de Sitter spacetime with Hubble parameter $H$, inertial observers measure a temperature $T$ of $$k_B T = \hbar H. \tag{1}$$ Hence, the faster the expansion rate, the larger the temperature (as you would expect).

I agree with Ghoster's comment that virtual particles are just an illustration. The actual calculations work with quantum fields in curved spacetime and compute the temperature I gave above. There is no need to resort to particles. However, a given observer would interpret this phenomenon as due to a particle bath at a given temperature.

To understand the meaning of this, let us consider an inertial observer in de Sitter spacetime. If you give them a particle detector, it turns out the particle detector will "click" in the same way it would if the observer was in Minkowski spacetime in a thermal bath with temperature $T = \frac{\hbar H}{k_B}$. Similarly, a thermometer would indicate such a temperature. The quantum state for the fields on de Sitter spacetime is a thermal state at temperature given by Eq. (1). Hence, in this sense, $\hbar H$ is a thermal energy associated to the state of the field.