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The paper Lyman-alpha Constraints on Ultralight Scalar Dark Matter by Kobayashi et al. says, at the beginning of Section 3.1:

A light scalar field stays frozen at its initial field value in the early Universe. Hence, any initial displacement from the potential minimum gives rise to a scalar dark matter density in the later universe.

I don't understand this statement. Can someone explain its meaning? Why would such a configuration give rise to matter later in the universe? Is it due to the fact that later in the universe the scalar field would oscillate and oscillations can be seen as particles?

Sorry if the question is not clear, I studied physics quite a long time ago and study these things in my free time so there are many gaps in my understanding of fundamental physics and Cosmology. Feel free to be as technical as you wish but please remember I'm not expert or anything.

This question is the same question I have posted here oh physics SE but it didn't receive an answer that I could really understand. My main doubt is how this field misalignment at early times becomes a non-negligible matter density at late times, how does this work?

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If the scalar field freezes it has a nonzero value (like the Higgs field). If this field is not a vacuum field (like the Higgs field which is a false vacuum field state) then it corresponds to real particles (contrary to the scalar Higgs field).

Inflation picked out a nonzero fluctuation of the scalar field just as it could have picked out a nonzero fluctuation of the normal (quarks and lepton) fields. Inflation can even be caused by the fluctuating vacuum fields (just as dark energy can be thought as the the energy of the virtual matter field of which it's not sure yet what's the associated energy).

So what happens? The vacuum fluctuations of the scalar field freeze into a state of a real field configuration of scalar particles. Scalar particles are used because they interact with matter only weakly like spinor neutrinos. That's why a spinor particle is not considered because they are already covered for in the standard model. The vacuum scalar field confuguration can be excited by the negative curvature of spacetime back then at the beginning just as a field can be excited around a black hole giving rise to Hawking radiation (in which case it's the positive curvature that is the source, i.e. the immense tidal forces).

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  • $\begingroup$ It's a bit clearer now, thanks. You say "If this field is not a vacuum field" . What is a vacuum field exactly. Sorry if my questions are trivial $\endgroup$ Jun 23 at 13:43
  • $\begingroup$ @AstroFedale The very fact that you ask this is already non trivial! :) The vacuum field is the field with no excitations corresponding to real particles. For the Higgs this is also a scalar field (like the one you talk about) but with particles already present in the lowest energy mode (the vacuum mode). That's why the vacuum is called false. Its different from a true vacuum field for which the lowest possible energy state has true virtual particles only (true vacuum). The false vacuum is false indeed and said to cause mass (Higgs mechanism). A true scalar vacuum contains zero excitations $\endgroup$ Jun 23 at 14:53
  • $\begingroup$ @AstroFedale Only fluctuations. These can get real by the same mechanism as Hawking radiation gets real. $\endgroup$ Jun 23 at 14:54
  • $\begingroup$ @AstroFedale So there is a difference between a false vacuum and a true vacuum. The false vacuum (like that of the Higgs) contains fluctuations that are no different from a true vacuum. But the vacuum fluctuations in a false vacuum could enter a enter a lower true vacuum. The Higgs field has a maximum energy when the field is zero (the top of the Mexican hat). So in this case you can say that a true vacuum decays into a false vacuum. A bit confusing indeed! $\endgroup$ Jun 23 at 15:06
  • $\begingroup$ @AstroFedale Is the scalar field in your question a Higgs like field? Or is it a field like quark fields? The alledged Higgs field is supposed to be frozen in one of its vacuum states (after symmetry breaking and when the temperature gets high enough symmetry is restored and the field will become one with maximum top of the hat potential for a zero field...). Excitations around the minimum values for the energies (the false vacuum) give you real particles. $\endgroup$ Jun 23 at 15:21

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