it is quantum FIELDS, extended versions of particles, that expand in space with expanding space and can become 'particles', which we describe as quanta [localized versions] of fields...what we detect. There are a variety of ideas about how this might happen.
For an overview:
Gravitational fluctuations in accelerated expansion is what gives rise to the primordial perturbations. The idea is usually pitched in terms of particle/anti-particle pairs that pop out of the vacuum, only to get pulled apart by the rapidly inflating background. Eventually they are pulled outside the horizon, never to meet again. Of course, this description has the same conceptual shortcomings as the description of the Hawking effect {for Black Holes} in terms of particle/anti-particle pairs -- it isn't quite right.
and
Quantum fluctuations in the inflationary vacuum become quanta [particles]
at super horizon scales...it seems that expansion of geometry itself, especially inflation, can produce matter...The evolution of quantum fluctuations is from their birth [at Planck Scale] in the inflationary vacuum and their subsequent journey out to superhorizon scales where they become real life perturbations...[particles at detection]
So we have quantum field perturbations...what do they mean:
[These quotes may be from MTW..I did not keep the reference source]
... there is no preferred vacuum state, and the interpretation of the field states in term of particles appears to be difficult...Such arbitrariness and ambiguity of the particle concept have led some theoreticians like Davies to affirm that “particles do not exist” , a view shared by several relativists. ... other theoreticians ... hold that QFT is fundamentally a formalism for describing processes involving particles, such as scattering or decays...
This view similar to that I posted aready from Rovelli: there are some fundamental differences among theorists about what particles are...they are not easy to define.
Here is a closely related view:
... there are two distinct notions of particles in QFT. Local particle states correspond to the real objects observed by finite size detectors. ... On the other hand, global particle states...can be defined only under certain conditions. Global particle states are simpler to define and they approximate well the local particle states detected by local measurements. Therefore the global particle states, when they are available, give a good approximate description of the physics of the “real” particles recorded by local detectors...In the paper we illustrate the difference between these two classes of states, and discuss their relation. The precise sense in which global states approximate local particle states is subtle...
Here is a quote I liked from Wikipedia. Keep in mind the quantum fluctuations that are grown with accelerated cosmological expansion can be thought of as a mix of 'real and virtual particles' ...which are also field amplitudes...[analogous to the real and imaginary numbers I mentioned in my first post.]
There is not a definite line differentiating virtual particles from real particles — the equations of physics just describe particles (which includes both equally). The amplitude that a virtual particle exists interferes with the amplitude for its non-existence; whereas for a real particle the cases of existence and non-existence cease to be coherent with each other and do not interfere any more. In the quantum field theory view, "real particles" are viewed as being detectable excitations of underlying quantum fields. ... In this sense, virtual particles are an artifact of perturbation theory, and do not appear in a non-perturbative treatment.
That last sentence AGAIN alludes to the difficulty of defining and modeling a 'particle'. What you 'see' depends on your model.