There is only one known scalar field -- the Higgs -- and it is far from a free field.
Any non-gravitational interaction between this proposed field and the rest of the universe (including self-interactions) after the end of inflation is incompatible with this proposal. (One contrast this with other proposals such as WIMPs, which are not free fields, and typically also not scalars) and axions (which are scalars, but are not free); most of these are explicitly non-free because they also try to solve some problems in the Standard Model of Particle Physics via new interactions).
The phase between the end of inflation and before some of the dense matter (mostly the quark-gluon plasma, and ancestors thereof) condensed into nucleons and nuclei is far from the much hotter and much much denser phase in which quantum uncertainties and classical curvature do not obviously play well with one another. Barring very early black holes from direct collapse (perhaps seeded by overdensities in this massive proposed field), touched on in this paper only very briefly as "enhanced structure formation", the post-inflation/pre-BBN universe this paper describes is free from strong curvature requiring any sort of quantum gravity: one is safely in the land of quantum field theory on (classical) curved spacetime, and in practically any small spacetime region after the decay into the proposed massive free scalar, one can even ignore the (global) curvature.
The paper proposes constraints on the mass of the field and on its ancestor field(s) but otherwise does not contemplate the much earlier universe. The central feature of the paper is that it commits totally to minimal-coupling (i.e., the late time field is truly free, other than gravitation). The field contents generate and respond to curvature, and that's it.
The paper also features what appears to be one of the most confusing initial two sentences that science writers have latched onto in many many papers...
Finally, I think it is better to link the abs page than the PDF directly. Speaking only for myself, the abs page has puts significant and useful metadata front-and-centre and other metadata at the same reliable one-click distance from the PDF itself. Not all PDFs make it easy to go to the abs page in a click, and fewer still suggest that the PDF itself may have been superseded by a subsequent revision (or by publication somewhere in final form).
For this paper, the abs link is https://arxiv.org/abs/1905.01214
In fact there are a number of such theories, it's just that AFAIK none of them have predicted something better than the standard model well enough for the singularity model to be definitively replaced, though I think if you polled physicists and asked them about whether they think there was "really" a singularity there or if it's just an artifact of our current poor theories, the vast bulk would say it's the latter. But in the absence of quantum gravity, General Relativity is the best established tool we have for investigating this sort of thing, and that tool says it was a singularity. We have lots of other tools that say other things, but none of them are established like GR is.
This is neither here nor there, but that number would be 0.
It's possible that 'time' has no minimum, but as far as I am aware the solution can be continuously extended to include 0. If not then you might as well say that the universe has existed for all time, the clocks were just running a bit slow at the start.
They're using "Big Bang" to mean the hot, dense, rapidly expanding state that is the earliest state of the universe for which we have good evidence. In models with inflation, this state occurs at the end of inflation, when "reheating" transfers all the energy stored in the inflaton field to the Standard Model fields (quarks, leptons, and radiation).
This is actually the standard definition of "Big Bang" used in cosmology, but unfortunately pop science books and articles still use "Big Bang" to mean "the initial singularity". We don't even know if there was an initial singularity (in eternal inflation models, for example, there isn't one).
As for why we perceive the time with notions of before and after, nobody has an clue. There are philosophical speculations, but nothing that can tested experimentally.
The "arrow of time" is commonly explained as an effect of thermodynamics, i.e. increasing entropy.
I always felt this to be a deeply unsatisfying explanation that implied "nobody has a clue" (a hot, expanding ball of quarks is a "highly ordered state", orly?) but I'm not a physicist.
That dimension is called "time" and it does show up in the equations and models of modern physics.
Perhaps, it is because of
> having different properties than the three others
This is not correct. "Expanding faster than the speed of light" isn't really a good description of the expansion of the universe at any phase, but if you're going to use it, it can happen during all phases--in fact it's happening now relative to us for parts of the universe beyond the Hubble horizon.
The key difference in the inflation period was that all of the energy was in a single field, the inflaton field, whose properties caused exponential expansion of the universe with a very short time constant, so the universe "inflated" by a huge factor in a very small interval of time. At the end of inflation, all that energy got transferred to the Standard Model fields (quarks, leptons, and radiation), which don't have that property (although now the expansion is dominated by dark energy, which does have the "exponential expansion" property but with a much, much longer time constant so the expansion only accelerates very slowly).
That is not to say there wasn't anything (say we as 3D being are unable to experience/imagine 4D).
(sorry, not talking about religion or life-after-death, just about how you go about proving something that can only happen outside your experience, and you have to rely on secondary evidence to deduce it)
I'll try. The tl;dr is at the end before my own footnote. The author certainly doesn't make it easy, even for people familiar with the standard model of cosmology.
The very first sentence of the paper [ https://arxiv.org/abs/1905.01214 ] reads, "Dark matter (DM) may have its origin in a pre-big-bang epoch. It may have been produced, for example, by decays or annihilations of particles during the Big Bang, i.e. by the so-called ’freeze-in’ [1–3] mechanism, or by e.g. the misalignment mechanism which generated a non-zero DM abundance during cosmic inflation (see e.g. Ref.)." which while not strictly speaking self-contradictory is certainly far from clear.
The term "Big Bang" only appears in that first sentence, and the abstract.
If one does a case-independent search for "bang" in the paper's reference , there are no matches at all.
There is hope, however.
Reference  of the paper carefully uses only "big bang nucleosynthesis" and its abbreviation BBN.
BBN occurs after the universe has cooled via expansion ("adiabatic cooling") so that some of the hot, dense matter filling the universe earlier than BBN can "freeze" into atomic nuclei. That probably happened in steps: first quarks and gluons (and perhaps other particles feeling nuclear forces) could freeze into individual protons and neutrons, then those could join into atomic nuclei. It was still too hot for electrons to bind for long with these nuclei, so they were completely ionized.
Reference  uses "big bang nucleosynthesis" and "BBN" too, but also introduces "hot big bang cosmology". With respect to that new term, it defers to a further reference, which describes the typical picture of an arrangement of matter fields that undergo a phase transition wherein the result is BBN preceded by a plausible technical description of pre-BBN matter.
Reference  discusses a particularly speculative particle, the axion, and its role in the lead-up to BBN, compared with "the usual hot big bang"; it also leaves many of the details of "hot big bang cosmology" to other papers (e.g. at footnote 45).
I think it is fair to say that the widely circulated paraphrasings of the paper's first sentence are at best begging the question of whether the big bang is that of the standard model, or one of the variations or extensions in the first four of the paper's references. I also think it is fair to say that the author should have anticipated these paraphrasings, and that most readers would have even more trouble distinguishing exactly what is meant by "pre-big-bang" than working physical cosmologists.
For "professionals", the sentences immediately following equation (1) explain the picture: a field with very little mass gains mass during cosmic inflation, with the result that after inflation stops the field contents have the characteristics of a form of cold dark matter that interacts only gravitationally (it is a "free field", which is more amenable to modelling than an "interacting field" or a "self-interacting field" or a field that is both[a]). The paper considers constraints imposed by other observations, how generic a solution remains after considering those constraints, and that the entire idea would be obliterated by evidence favouring any sort of non-gravitational dark matter interaction (including non-gravitational interactions between DM and itself, or different types of DM).
Given this, one would tend to read "pre-big-bang" as used by the author as a region between the end of inflation and the beginning of big-bang nucleosynthesis. The epoch wherein one runs into conflicts between General Relativity and Quantum Field Theory is well before the end of the inflationary epoch, so one should feel free to completely ignore any sort of explanation which invokes things like the beginning of time, or even the differences in the nature of time in these two sufficiently-fundamental-for-these-purposes theories.
[a] Strictly speaking the field is "minimally coupled to gravity"; it is non-interacting in the sense that there is no associated (non-gravitational) force-carrier, whereas interacting fields generally involve things like gauge bosons. Here because the end of inflation is so far from the part of the early universe that's hot and dense enough that quantum uncertainties and classical curvature cause problems, we can safely use textbook quantum field theory on curved spacetime -- the new physics is in the "decay" from a very light field to a massive field through the inflationary period, as well as the presence of a free field at all (no known fields are "free"). The mass-gaining mechanism is not described, but in the paragraph after the one containing eqn (21), the author claims that a wide range of possible mechanisms is allowed without conflict with other observations, and without conflicting with the central claim that dark matter experiences no non-gravitational interactions (including no self-interactions) after inflation.
Everything in the universe can be considered to be either light/electricity or magnetic (basically an electromagnetic wave). One cannot exist without the other.
Using the above as a base, you can think of vacuum as "noise", basically equal ("minimal") amounts of oscillating magnetic waves that connect and stretch across the whole universe, just like the background radiation. And you could also think of it as a sort of "medium" through which information travels.
Then you can think of objects/particles as our perception of "standing waves". So under this model, the planets can be described as clumps of light/electricity, sorounded by a "magnetic vacuum".
The interesting thing is you can then consider dark matter to be everything magnetic that is not light. However, it all in the end depends on the observer (us), because any light also has a magnetic component and viceversa, so "dark" just means "not in the human-visible light spectrum". But in reality not a single bit of space is "dark", that's just our (very limited) perspective/perception.
So if you ask me what dark matter is, I would say it's just the same stuff as everything else, it's already all around us, but we just can't see it with our human eyes.
Also, can anything in written form not be called playing with words?
A model which is based upon physics, which itself is (according to Wikipedia,) "the natural science that studies matter, its motion and behavior through space and time," and which, being a natural science, ascribes attributes and behavior to the material world and its processes through experimentation and mathematical inference.
>Also, can anything in written form not be called playing with words?
What "playing with words" means in the context of your former comment is that what you presented was a fantasy which ignored any of the observed and known principles (read: actual definitions) of the terms being used, and the science which led to them.
Alternative theories for dark matter are all well and good (MOND is popular) but your alternative only makes sense if one neither knows, nor cares, about actual physics. We already know that planets are not clumps of electricity and light surrounded by a magnetic vacuum which is the medium in which information travels. That's not physics, it's word-salad, it doesn't even make sense.
That said, I still upvoted your comment because ridiculous as it is, fringe theories for dark matter aren't uncommon and they can and should serve as a basis for discussion, not just be quashed. It's understandable that people are uncomfortable or unsatisfied by dark matter and dark energy - particularly since the "dark" in those terms refers to the nature of the phenomena being unknown, and they seem counter-intuitive and humans (and perhaps CS/engineering types in particular) want the universe to not just be intuitive, but elegant and simple.
Unfortunately, the more we study it, the less sense it makes. To reference XKCD, the universe isn't built in Lisp, it's hacked together in Perl.
But that doesn't mean we should just throw out what we know and start again on first principles until we have a model that makes sense to us first, and describes reality second.
Now, regarding physical models, you are assuming there is a universal truth or reality that is the same for everyone. And that is just a belief. I don't think you can force anyone to believe something. You are also free to believe in whatever you want to believe.
There appear to be universal constants which can be experimentally verified and whose attributes and behaviors remain consistent. In other words, the universe appears to have properties which can be known. There is no evidence that the fundamental nature or properties of reality change based on the beliefs of the individual observer. Therefore, it is reasonable to assume that universal physical reality does exist, and that data gathered through repeated observation and measurement more accurately describes that reality than speculation without such evidence.
>I don't think you can force anyone to believe something.
Wasn't trying to. Just pointing out that the universe isn't arbitrary, and not all conjectures are equally valid. You can believe the moon is made of green cheese if you like, just don't expect to be taken seriously, because there is a vast amount of evidence that it isn't.
You yourself must believe in some universal truths, otherwise you would not attempt to communicate with other beings.
So, in order to have any kind of discussion, you must start from a point where you believe that at least a large part of everyday experience (including other beings, their minds, physical objects, their interactions, our observation thereof and many others) exist in a meaningful sense, outside your own cognition.
Now, any extrapolation from these base assumptions, is what we should think of as physics. For example, if I assume my eyes exist and my perception of the world is meaningful, then I must also conclude that the moon I see through a telescope exists to the same extent, and it's motion as I observe it exists, and I can search for explanations of that motion etc.
If I were to not assume that my eyes perceive something which truly exists, I would have no reason to stand in front of a computer screen, hitting keys on my keyboard and watching the letters appear on the screen - it's possible in a very absolutist way, but it's simply not a productive way of looking at the world.
> regarding physical models, you are assuming there is a universal truth or reality that is the same for everyone
which is basically an axiom one must adopt to engage in science. E.g., here's the formulation found in the Wikipedia article "Philosophy of Science":
> that there is an objective reality shared by all rational observers
So if one wishes to engage in an inquiry that doesn't hold this axiom, it's of course a perfectly fine thing to do, but it's best for all concerned not to call it science or scientific. Many issues and lines of inquiry that are important to people aren't amenable to scientific inquiry, but it does nothing but harm to dissimulate.
All physical models depend on a "frame of reference". The most common one being the inertial frame of reference.
They do that because it all depends on how and from where you look at something, which is just another way of saying that the models depend on an observer.
Alternatively you could interpret that as there actually being some sort of universal truth, but then the experience of it is different for every single observer.
And then again, you are the one picking an interpretation or belief over another.
The term "frame of reference" refers to how you have to set up the equations and how you define values, for example physical coordinates of a location. It doesn't change the actual predictions of the evolution of a physical system (and if it did, that's generally a good sign that the model is missing something!).
For example, you can model gravity in Newtonian mechanics on the surface of Earth as a force that pulls all objects down at a constant 9.8m/s^2 acceleration. Or you can step off the planet, and model the entire Earth as a closed gravitational system, and measure the gravitational attraction between the mass of the Earth and the things on or near its surface using F=G * m_e * m / r_e^2.
When you get to relativity, you discover that the problem is that spacetime is defined in such a way that there is no well-defined global "ruler" or "clock" that applies independently to all observers, so that 1 meter or 1 second for me on Earth is not the same 1 meter or 1 second on a spaceship travelling at 0.2c. What is independent to all observers is the speed of light in a vacuum, and from these two facts, you can in fact derive how to map the definitions of how your rulers and clocks would be distorted if you moved to a different reference frame.
Can we prove that the laws of physics are the same for everyone? No. That's an assumption. It seems to be a reasonable one, but it's an assumption.
But we got to our current understanding of physical models from other ideas. [Edit: That is, other ideas of what the models should be.] How did we get here? By people believing other things, and them finding out experimentally that things didn't work that way, even for the people who believed that they did.
Things can, of course, include both real and actionable content, and also wordplay.
Essentially we're saying "our model is fine as long as 80% of the mass is made up of some unknown matter"...
edit: in other words - superluminal inflation is big, but that's not a bang
Some more details at my two comments above: