I found this article 1 about the production of particles in a time-dependent gravitational field. I have a few questions about it:
According to the standard model of cosmology and our current physical theories and models, can gravitational fields in our expanding universe create particles?
If in our current model of the universe particles could be created (despite at very low rates), would the production inside our Hubble horizon continue as long as spacetime keeps expanding?
Yes, there is particle production in de Sitter space by the Hawking/Unruh mechanism, and the current state of the universe is close to de Sitter space, so I imagine it would already be happening. Unruh radiation can also appear when there is no horizon, as the paper you linked says. I think the paper is probably correct, since it seems physically well motivated.
The number of particles and their energy is extremely small. The de Sitter radiation is at a temperature of roughly $10^{-30}\text{ K}$, and because it's a fixed temperature and there is no infinity for the particles to escape to, the particle count doesn't grow indefinitely but reaches an equilibrium level. I'm not sure of the equilibrium particle count, but according to this answer by Luboš Motl, it's roughly $1$. There is also Unruh radiation from smaller-scale inhomogeneities, most obviously Hawking radiation from black holes, at a much higher but still undetectably tiny temperature. That accumulates, but only until the black hole evaporates, and the total mass of the radiation equals the mass of the former hole.
There is quite a lot more cosmological particle production by other mechanisms, such as the boatloads of photons and neutrinos produced by stars, and black hole mergers like GW190521, which emitted roughly $10^{79}$ gravitons.
