Abstract
Based on preliminary results from the Causal Fermion Systems framework regarding the matter-antimatter asymmetry in the universe, I propose a novel story line for the universe that would, if correct, resolve a number of problems in cosmology. First and foremost, the here-presented arguments suggest to identify cold dark matter as third generation (anti-)neutrino mass-eigenstates ν 3. Furthermore, the proposal suggests a new look at the problem of initial conditions. Last but not least, the proposal also provides a new angle on the cosmological constant.
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Notes
- 1.
- 2.
Such analogies are of course always to be taken with the necessary grain of salt. They are intended to help the reader gain a rough intuition on the role different objects play in the framework.
- 3.
The weak theoretical motivation mentioned here comes from my limited understanding of the CFS framework and how the objects therein might be interpreted. In Sect. 3.2 I will discuss a different point of view which is superficially equivalent but not so commonly considered. This point of view might be more readily compatible with the CFS framework and seems to be favorable with respect to conceptional issues as well.
- 4.
I consider this to be a sensible notation as for any two times t a and t b the hypersurfaces can be mapped into each other isometrically hence there is no change that could be observed by an outside observer. In the absence of matter or other perturbations the notion that de-Sitter space is exponentially expanding is absolutely meaning less. It only acquires meaning once you put test matter (or any group of test bodies for that matter) there, tracing out a geodesic foliation with their proper time functions.
- 5.
In fact for the considerations later on the only thing we need is for the modification to allow for de-Sitter space as a solution and for the instability mechanism to arise in the right form, all without modifying the late time behaviour too much. The choice made here is simply to demonstrate that such modifications in fact exist and [38] shows that the compatibility with observations can be arranged.
- 6.
This claim has not been checked beyond the rough sketch of arguments that I will present here.
- 7.
This by itself is of course no feat as introducing an additional functional degree of freedom allows one to fit almost anything.
- 8.
Note, that this suggests, that for the evolution of the universe only the ratio of the Λ and \(L_P^2\) is relevant. This in a sense resolves the problem that there are two fundamental energy scales in the universe, as this ratio is dynamical in both scenarios. Hence only one of them sets a fundamental scale.
- 9.
This leaves the effective masses of the quarks and charged leptons to be explained. Except for the tau, the effective masses of the quarks and their charged leptonic counterparts are within an order of magnitude. Recent calculations show that the binding energy in the strong force can account for almost all the mass in the neutrons and protons, see for example [40]. In that light I consider it plausible that the difference in effective masses within a generation can be accounted for by self-interaction effects.
- 10.
Here I would like to emphasize that it is the mass-eigenstates that matter for the particle creation and not the eigenstates of the weak interaction.
- 11.
“Time” here has to be considered a place holder for an appropriate parameter that tracks the history of the universe.
- 12.
One way to motivate this is to look at the stationary holographic equipartition in [28]. Where an equality between the gravitational degrees of freedom in the bulk and the boundary is stated for stationary spacetimes, hence N bulk = N boundary. With (26) this leaves N bulk ∝ Λ−1. Together with Eq. (21) this leaved the density of degrees of freedom in a spacelike hypersurface to be \(N/V\propto \sqrt {\Lambda }\) which decreases with decreasing Λ. It is conceivable that this could reduce the rate of particles created. However for the present work we will just impose this reduction as a condition.
- 13.
Remember that in Sect. 4 I discussed the fact that the newly created particles fill the kinetic states starting from the one with the least momentum.
- 14.
If we take \(\rho _M(t_{rh }) \propto \left (1p + 1n + 1 e +\alpha \nu _3\right ) + \rho _{\nu _\mu , \nu _e}\) the ratio \( \frac {\rho _R(t_{rh})}{\rho _M(t_{rh})}\approx 10^2\) drops significantly. Adding binding energy to the third generation fermions prior to reheating would increase that ratio on the other hand.
- 15.
A more precise formulation would be that this scenario is compatible with a universe where third generation (anti-)neutrino mass-eigenstates make up Cold Dark Matter. If other observations would in fact rule out third generation (anti-)neutrino mass-eigenstates this would unfortunately not suffice to kill the narrative presented here as we can—at present—simply adjust α to the bounds given by those experiments. In that case however the scenario presented here would of course fail to account for Cold Dark Matter, which would weaken its case. We hope to be able to constrain α from fundamental considerations in future research.
- 16.
Note that for example such an abundance would render the total matter content in the universe having a strong chirality asymmetry.
- 17.
If this picture is true and the universe was created by some sort of god, she certainly must have a good sense of humor.
- 18.
This might actually have consequences for the initial evolution of supermassive black holes. However this has to be left to future work.
- 19.
It is important to realize that this period can in principle go on forever back in time. In fact if one considers time to be an emergent phenomenon describing a rate of change, such as was advocated by many discussants at the workshop “Progress and Visions in Quantum Theory in View of Gravity” at the Max Planck for Mathematics in Science in Leipzig in October 2018, then in this phase the concept of time ceases to make sense, because there is no such thing as change. Note that “past incompleteness” results such as [6] typically rely on geodesics, which implies the existence of a test particle. What I suggest here is that everything, all matter, radiation and even vacuum fluctuations have a creation time, i.e. their past directed trajectory is de facto incomplete. For radiation it is the reheating time, for particles the creation time and for fluctuations the point when they shrink below the Planck length. Let us extrapolate back in time. Let us consider the last fluctuation outgrowing the interacting region before creation time. We can trace that back to when it was smaller than Planck scale, hence when it disappeared. Nothing that happened before that moment plays any role for our universe today. One can therefore consider the pure, empty de Sitter space as an idealized past boundary condition. With the spacetime completely void of any structure an external observer could not tell the passage of time for the physical system she is looking at. On the level of the physical system any result that depends on a notion of test particles, i.e. geodesics, has no meaning if we assume the spacetime to be truly empty de Sitter space.
- 20.
The future asymptotic behaviour is content of Conjecture 1.
- 21.
It would be interesting to see whether the set of idea developed by Padmanabhan [23,24,25,26,27,28,29,30,31] can be linked in to the discussion presented here. That would allow to interpret I c as a sort of conservation law for the transition. For this to be possible however a necessary requirement would be that I c = 4π is true in the limit where the difference between the two energy levels goes to zero i.e. Λhigh = Λlow, hence de Sitter space.
- 22.
It seems to me that this would ultimately be the highest possible value for Λ that makes any physical sense.
- 23.
At the moment this is in fact my best guess for how the instability mechanism could work in this scenario.
- 24.
It is unclear how rigid the framework is with that respect. For example, it is unclear whether one could accommodate for axions, by adding additional fermionic sectors.
- 25.
I will discuss some of the consequences for some of these experiments in more detail in an upcoming paper.
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Acknowledgements
I would like to thank Felix Finster, Todd Oliynyk, Emmanuel Saridakis, Erik Curiel, Calum Robertson, Markus Strehlau, Mark Bugden, Marius Oancea and Isha Kotecha for listening patiently to my clumsy explanations in the early stage of the development of these ideas. I would like to thank Alice Di Tucci for explaining to me the debate surrounding the initial singularity and pointing me to relevant sources.
I would like to thank Thanu Padmanabhan and Hamsa Padmanabhan for helpful discussions during my visit in Zurich.
This work was supported by the Australian Research Council grant DP170100630.
I am indebted to Ann Nelson, who brought the problem with the Gunn-Tremaine bound to my attention.
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Paganini, C.F. (2020). Proposal 42: A New Storyline for the Universe Based on the Causal Fermion Systems Framework. In: Finster, F., Giulini, D., Kleiner, J., Tolksdorf, J. (eds) Progress and Visions in Quantum Theory in View of Gravity. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-38941-3_4
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