A Simple Cosmological Model
This is a summary of the trip I did to the begining of the universe. Sure, there are other places to visit, but for sure there is not other place in the universe like the begining of it. The thing is that to understand the begining of the universe you need to understand cosmology and the knowledge we have of it is derived from General Relativity (GR).
This was a trip I had to do on my own and based only in what it is currently known about the universe. In summary what we know is:
- Universe looks the same everywhere we look at (this is called homogeneous and isotropic)
- Universe is expanding, here you can imagine dots in a balloon, and how they get away from each other as the balloon grows (in fact I used that analogy for a spherical 2 spacially dimensional universe)
Additionally I wanted to derive my road map to the big bang based on thought experiments and not relying on GR. So here are the path I followed on every branch to that begining of universe.
- The first branch I took was wether to decide if the universe is finite or infinite. Looks like everyone agrees that the universe is finite in terms of “time”, there was a begining of time — Universe might have existed without the linear, allways forward time, we are familiar with, but since we can not express (yet) or measure (yet) such state I will agree that the universe is finite on term of “time”. Now, question is, is it finite in terms of space? AFIK there is no answer to that question yet, but well, I had to go to the big bang so I decided that it would be easier (it is) if it is spacially finite. Here goes the circumference (1D spacially), and the balloon(2D spacially) to help me imaging the universe. In fact, I mostly agree that we can use the concept of infinite if that leads to finite answers, but answering “infinite” to a physical question really means: “that question is meaningless, and why know why” or “we dont know, so we throw infinite which allows anything”
- The second branch I took was the rate at which the universe was expanding. It might follow some complex law, for example blowing into a balloon makes it grow at jumps, or starting very slowly the going faster, or starting faster and the going slower. See GR has something to say here, based on matter density and some arbritary constant (dark energy), universe will grow then collapse or will grow forever accelerating (Einstein worked on it to fit so it was not expanding at all). Well I said I was not going to use GR, and since expansion can initially be aproximated by linear (non accelerating) expansion I will use that.
You might argue that those decisions I took were totally arbritary and in fact against the latest information we have (yes looks that the rate of expansion is increasing, so that dark enery has an increasing role). But keep in mind that this is my own trip to the big bang, my purpose is not to get there but to travel there, learn and enjoy the trip, In the meanwhile I learn what others did on their trip, and know what my roadmap lacks of.
This cosmological model (my roadmap) is what would have come if Hubble expansion had been detected before GR. You can take a look at the details here: https://github.com/f-alonso-vendrell/SimpleCosmologicalModel/blob/master/SimpleCosmologicalModel2.pdf
In this summary I will work on an universe that has only one spacial dimension and time. You might say, how can that be? Well imagine you can only see in one direction and the opposite, when you look further you also see things as they were in the past (as light and information took time to get to you).
If the universe is finite, and rate of expasion is constant and so is the speed of light, the “light rays” trace keeps allways the same “angle”, like the orange line in the following picture (light rays received by us), we notice here time lapse but not expansion:

But keeping that angle in a spacially finite linearlly expanding universe, leads to logarithmic spirals:

The angle of our particular spiral depends on the ratio of universe expansion and speed of light.
One thing you note is that if you use those lines in oposite directions they cross an infinite number of times, and from an observer it will look as an infinite number of big bangs.

Of course, the model I present can be twisted to fit better observational data, but that was not the purpose, since taking into account GR leads to better models. Purpose was having fun.
While I was writting this model the following conjectures came to my mind:
- That certain standard model constants could have values due to cosmological constrains, e.g. size of the universe, ratio speed of light/expansion rate at the moment of simetry break.
- That, different fields might have been more relevant in the past (now hidden due to the high energies needed) and in the future others fields will be (e.g. the dark energy might lead to particles which will interact and that future universe observers will see us as a caotic epoc where electromagnetism and gravity didnt allow their particles to interact), seeing us as their big bang.
- If we rescale space time, what happened in a matter of 0.000000000001 seconds might be an entire epoc with their particles/fields interactions, maybe complex, maybe self-aware, with a growing entropy now hidden in the inner structure of our universe, and what will happen in 1000 Billion years will be an instant for the future particles/fields interactions, maybe complex, maybe self-aware… and our entropy (our legacy) hidden in their universe structure.
