Before the Big Bang, time and space may have switched places
The Black Hole Big Bang theory says our universe fell into a black hole at the same time.
If you’ve read my story on the Big Bang Black Hole Hypothesis, you know that the universe may have begun as a black hole that formed in another universe. Given the amount of matter in this universe, this black hole must have been a monster in the parent universe, perhaps swallowing up all the matter and radiation in that universe before finally evaporating.
One of the amazing features of this transition from mother to daughter universe is the flipping of time and space which not only resets entropy to effectively zero but allows all the matter that ever fell into that black hole to appear in the new universe at the moment of its beginning.
The reason why this makes sense is because black hole singularities and Big Bang singularities are not like points in space but portals that stretch across space and/or time, allowing matter to transition from one region of spacetime to another. One theory is that our universe’s Big Bang was such a portal connecting to a black hole singularity (a region of infinite density and spacetime curvature) in another universe.
From the perspective of the mother universe, the black hole singularity is a point in space. Matter impacts it at different times, but, from the perspective of the daughter universe, the singularity is in time and matter emerges at different places.
This leads to the startling conclusion that the Big Bang was not compressed in space and time, but rather had an initial spatial extent in the same way that a black hole has a temporal extent (exists at different points in time in the mother universe).
This theory derives from connecting what is called a de Sitter universe representing our universe to a black hole so that instead of all matter simply ending at the black hole’s singularity, it emerges into a new universe.
The way to visualize this is with something called a conformal or Penrose diagram. Here is an example of one for an ordinary, flat, non-expanding (i.e., Minkowski) region of space and time:
Penrose diagrams for fun and profit
The Penrose diagram is simply a trick of perspective that is useful for visualizing how things move in curved spacetimes, including crossing black hole event horizons, wormholes, entering and leaving universes, and all the interesting features of General Relativity.
It works like this. Suppose I want to understand everything that happens on a large field like a soccer field, but I am most interested in what is happening at a particular point in the field. This field represents space and time, say, with cross field being space and down field being time. To see the whole field, but keep the action in the center of my view, I might want to set up a special kind of fisheye camera lens. This lens compresses things that are distant and expands things that are close to its boresight.
This view looks a lot like a perspective view, but warped so that parallel lines appear to merge together to a point at infinite distance in both downfield and cross field directions. This creates a kind of diamond shaped view with the goal posts being tiny dots at the top and bottom of the view and the left and right boundaries of the field likewise being compressed and connected to the goal posts at 45 degree angles. These boundaries represent the horizon.
A true fisheye lens shows the horizon as a circle surrounding the image while the action below is magnified. The Penrose diagram is similar but the horizon represents the path of a beam of light from infinite distance to infinite future and from infinite past to infinite distance. Thus, the four horizons are straight lines (past to East, past to West, West to future, and East to future) that form a diamond. (We are of course ignoring two spatial dimensions in the hopes that we can understand better with just one!)
Now, in the Penrose diagram light travels at 45 degree angles always, no matter what kind of gravitational influences there are. This is one of the nice features because in an ordinary spacetime diagram light can travel in all kinds of ways. Light cones, those “cones” that tell us from where light could have reached us and where it can go, can bend and rotate in curved spacetimes so it is really confusing what is in a person’s past or future light cone. In a Penrose diagram it is very clear. Anything more than the 45 degree line (0 is north) is “spacelike” so it doesn’t influence us and we can’t influence it. Anything less than 45 degrees is “timelike” so we can influence it and vice versa.
In Penrose diagrams black holes look like this:
In this animation, we see an astronaut given by the blue dot falling into a black hole. They see the black hole as light arriving along the red squiggly line which comes from the anti-horizon. This is the after image of the collapsing star that formed the black hole, exponentially redshifting to infinity. (Sometimes it is called a false horizon. This is what you see in pictures of black holes.) Once they are through the horizon, they observe light falling into the black hole through the true horizon, which is only visible from inside the black hole (light blue squiggly line). (The reason is because the horizon itself is inescapable and no light can reach the outside from it.)
The important point here is that the singularity at the center of the black hole does not appear to be just a point in the Penrose diagram. Rather, it is a line stretching in the spacelike dimension from infinite West to infinite East. If you think about it, this makes sense as a representation of the lifetime of the black hole. As matter and light fall into the black hole during its lifetime, they strike the singularity further and further to the East in our diagram. For example, a beam of light at some time t will enter the horizon at a 45 degree angle and strike the singularity at a particular point x. A second beam at some later t+T will strike it further East at a point y>x. You can draw this yourself. Just keep drawing 45 degree lines perpendicular to the horizon starting further and further in the future, i.e., north. This will continue for the lifetime of the black hole with each beam of light hitting the singularity further and further East.
Of course, inside the black hole, East and West don’t mean the same thing as outside. Outside they mean infinite spacelike distances. Inside, they are all part of the singularity. The singularity is like an infinitely large universe with a past but no future.
Or is it?
What if it does have a future and that future is another universe?
If that is true, how do we deal with the fact that it has spatial extent, potentially of lightyears?
The De Sitter Universe
To answer that question, we need to know something about the universe that we would need to be living in for this to be true. This is the de Sitter universe. A de Sitter universe is, quite simply, a universe that exists on the hypersurface (surface with dimension greater than 2) of a higher dimensional equivalent to a hyperbola. Space is on an expanding hypersphere (a higher dimensional sphere with a 3D surface).
The de Sitter universe has long been a way of explaining dark energy as simply a feature of the de Sitter topology. The cosmological constant, which represents dark energy in the most accepted cosmological models such as the Lambda-Cold Dark Matter model, is related to the rate of expansion of the hypersphere. When connected to a black hole singularity, the de Sitter universe requires a cosmological constant that generates a flat universe (one where Euclidean rather than curved geometry prevails on average). This is precisely what we observe in our universe.
Another feature of the de Sitter universe is that its Penrose diagram is a square rather than a diamond. This means that the de Sitter universe has spacelike extent in the distant past and future. While the standard Penrose diagram of a non-expanding Minkowski spacetime assumes that all beams of light converge in infinite past and future, in the de Sitter universe, they do not. Points can remain spacelike separated indefinitely because of the expansion of the de Sitter universe itself. Thus even over infinite time an observer can not access all of the universe.
What this means is that when you connect a de Sitter universe to a black hole singularity, the matter that falls into the black hole emerges in the Big Bang of the de Sitter universe at different points that are spacelike separated. Moreover, the place where matter emerges is correlated to the time in the mother universe when it fell in. Because the de Sitter universe starts expanding from its Big Bang, those points can remain spacelike separated for a long time. Thus, while the Big Bang appears to have been a point in space and time, that is an illusion of the spacelike separation followed by rapid expansion of space itself.
You can think of it like a balloon with many dots on its surface each representing matter that fell into the black hole at a different time. At the Big Bang these points were spacelike separated so that when the expansion began, they began to interact over time rather than initially.
This leads us to the amazing conclusion that the universe is likely to be vastly larger than what we can observe and that all the matter we can see is simply matter that fell into the black hole at around the same time in the mother universe. (That is a lot of matter and I cannot even suppose how a universe size black hole would form all at once. There is a lot we don’t know about black hole formation.)
It also suggests that the distribution of matter in this universe beyond what is observable would be correlated with the rate at which matter entered the black hole in the mother universe. We could have the lion’s share of it in our observable neighborhood or there could be even vaster and more densely packed regions outside of what we can observe. Here is a Penrose diagram of the two universes connecting:
Solving the Horizon Problem
This theory solves the horizon problem. The horizon problem is the problem that all regions of the sky seem to be correlated with one another. This would not be true with any standard Big Bang model. Only regions that were close together at the Big Bang should be correlated, and those would be close together in the sky when the Cosmic Microwave Background (CMB) was emitted only 300 kYrs after the Big Bang. Inflationary theory is like saying that the universe was put in a big quantum blender initially and that was enough to correlate everything.
The black hole Big Bang cosmology both explains inflation without a quantum explanation and solves the horizon problem without an inflationary cause. Rather, the matter that makes up the observable universe, including the CMB, all fell into the black hole around the same time. Therefore, it all became correlated as it fell in. Matter outside the observable universe, meanwhile, may not be correlated with matter inside it because that matter fell into the black hole at different times. We will never be able to see it unfortunately to confirm this hypothesis.
Looking Ahead
Right now, unfortunately, there isn’t a good experimentum crucis to perform that would distinguish the Black Hole Big Bang theory from inflationary theory that does not include a black hole origin. Inflationary theory, for now, is considered almost settled science despite a lack of a particle theory explanation. A de Sitter universe, on the other hand, only makes sense in the context of inflationary theory. While it may be tempting to look for remnants of the mother universe in the matter of today’s universe, it is unlikely that any clear signatures other than correlations would remain from the matter’s state before falling into the black hole because tidal forces become effectively infinite at the region connecting the black hole topology to the de Sitter. Therefore, all matter would be reduced to quantum mush before it could emerge into a new universe.
Nevertheless, it seems clear that this theory is a strong contender for an alternative theory of cosmology that removes the final end and beginning of the universe and suggests that there are many universes connected by black holes. Moreover, it makes a prediction that the observable universe is not all there is in this universe. On the other hand, since black holes do not last an infinite amount of time, the initial big bang is likely not infinite in spatial size either. Instead, it would have to be correlated to the lifespan of the initial black hole. The lifetime of this universe, however, has no such constraint. It may eventually recycle its matter into another universe. Given that the universe appears to be flat rather than heading towards a Big Crunch, it is unclear how that would happen.
Easson, Damien A., and Robert H. Brandenberger. “Universe generation from black hole interiors.” Journal of High Energy Physics 2001.06 (2001): 024.
Penrose diagrams
A Penrose diagram is a kind of spacetime diagram arranged to make clear the complete causal structure of any given…jila.colorado.edu
Picturing Black Holes
HPS 0410 Einstein for Everyone Back to main course page John D. Norton Department of History and Philosophy of Science…www.pitt.edu