The homogeneous birth hypothesis

Imagine an observer at a fixed spatial coordinate in the universe’s comoving coordinates. Let’s label his time coordinate as $t$. Let the three-dimensional spacetime “surfaces” of constant $t$ represent the hypersurfaces of the homogeneity of the universe. In other words, let’s consider an observer for whom the microwave background radiation appears isotropic. Then, as we move backward in time to investigate our observer’s circumstances in the early universe, the CMB remains isotropic for him. Suppose that before space became transparent, other isotropic phenomena could fix the observer’s spatial coordinates. For simplicity, let us also use the observer’s proper time as the coordinate $t$ and ignore local inhomogeneities.

Now, let us go as far back in time as we can. Some theories predict that we should end up in the Big Bang singularity. Could the singularity be avoided? Numerous proposals have been put forward. Some suggest that the universe is in an endless cycle of expansions and contractions. Others suggest that the universe was eternal before a quantum event triggered the expansions. And there is also the Hartle-Hawking “no-boundary” proposal. I would like to put forward yet another hypothesis.

What if the universe started as an infinite flat space filled with homogeneous “matter” (or whatever the quantum fields were at that early stage) of a certain constant and finite energy density ${\rho }_0$? In other words, there may exist a time coordinate $t_0$ at which the hypersurface of homogeneity is perfectly flat, perfectly homogenous, and has a certain finite and constant energy density ${\rho }_0$. Before $t_0$ the universe did not exist, and after $t_0$ the laws of general relativity force its expansion in agreement with the Friedmann equation

Let me spend some time justifying this setup.

Question 1. Why is the initial universe flat?

The easy answer is that it is flat because this is what our observational evidence indicates.

Question 2. Why is the initial universe infinite?

This should not be controversial; I am just using the cosmological principle here. It is now, so it always was.

Question 3. Why was it created with this particular density ${\rho }_0$?

I hypothesize that the value of ${\rho }_0$ is not arbitrary, but can be physically derived, for example, as the maximum possible energy density. This can be Planck density or some other theoretically derived value.

Question 4. Why is the density perfectly homogeneous?

Here again, I hypothesize that this could be derived theoretically; for example, the relevant quantum fields have a maximum “saturation” value, which was maxed out everywhere, thus making the universe perfectly homogeneous.

Question 5. Where did the later inhomogeneities come from?

From the probabilistic nature of quantum mechanics.

Question 6. Why can’t we extrapolate the universe further to the events before $t_0$?

Even if there is no upper limit on energy density, the reason we cannot extrapolate the universe’s history further back in time is that the universe did not exist, that is the spacetime manifold ends (or rather, begins) at $t_0$.

Question 7. Why would the universe just pop into existence ready with all this structure?

This is not really a lot of structure, in my opinion—a perfectly homogeneous flat space. There is only one thing that would make it simpler: if it were empty. And why would such a space just pop into existence? I don’t know. But why would a singularity come about and later explode? This, I don’t know either. Actually, the idea of flat, infinite space, homogeneously filled with matter, just popping into existence seems quite appealing compared to the alternatives.

Question 8. Doesn’t spacetime having a boundary violate the equivalence principle?

It does. So does a singularity. But I am not sure if the boundary actually exists, that is if the hypersurface at $t_0$ is real or just a mathematical construct. Perhaps it is more like an open interval – the universe has existed only for all $t>t_0$. Then, the equivalence principle is not violated. Maybe there are physical reasons for that too, like the uncertainty principle. But this seems too speculative to make a judgment call at this time.

Question 9. Doesn’t this violate singularity theorems?

It does not. In the homogeneous birth hypothesis, spacetime is incomplete as a presupposition rather than as a result of a theorem.

Question 10. How does your theory accommodate dark energy?

It does not. I just wanted to convey the basic idea. It doesn’t make sense to try to accommodate all astronomical data at this stage of theory development.

Question 11. Doesn’t this imply a preferred global reference frame?

It does. The initial hypersurface at $t_0$ can be treated as a beginning of “global” time. This does not seem to be a problem, though. We have been observing a global reference frame for a long time, as the universe’s comoving frame, i.e., the frame in which the CMB is isotropic.

Question 12. But again, why are you ruling out curvature of the universe?

I know the arguments – our patch of the universe may be too small to see its true curvature. But the concept of global space curvature feels unnatural to me. This notion was invented by mathematicians a few centuries ago, motivated not by real three-dimensional phenomena but carried over as an analogy from the analysis of curved two-dimensional surfaces. And although general relativity later proved that three-dimensional space can also be curved, all tests so far confirmed only local curvature. People like global curvature nonetheless, often for very arbitrary reasons (Hawking and Wheeler preferred a closed universe, while Penrose hoped for an open one – I recommend comparing their arguments). In other words, it seems to me that it is humans who advance the notion of global curvature, with typically human motivations behind them. Meanwhile, nature tries to tell us that nothing like this exists. When I see statements like “out of all possible values, why curvature of the universe should be exactly 0?” my reaction is: “out of all possible values why parameter $\beta$ in the Newton’s second law $F=\beta +ma$ should be exactly 0?” People came up with this curvature parameter that relates to nothing real and are now trying to figure out why its measured value is so close to zero. Facepalm.

Obviously, this theory comes at a cost, and there are several questions that do not yet have good answers. But let us investigate now what we get in return.

1. There is no singularity. Singularity is the bane of general relativity. If spacetime has no singularities, then we have no problem with breaking the known laws of physics. I strongly hope that, in the end, it turns out that singularities do not exist and that the existing physical laws are sufficient.
2. The flatness problem is solved. Yes, the universe was just born flat. There is no need to explain it. Let’s turn this into a presupposition (like the one that the speed of light is constant).
3. The horizon problem is solved. The universe is homogeneous because it was born this way. No inflation is needed to describe its evolution. There is no inflation-induced multiverse. Things are pure and simple.

This is a very rough draft, so all feedback is very welcome. Please write me at black.holes.dont.exist@gmail.com.