What If The Universe DID NOT Start With The Big Bang?

Thank you to Brilliant for supporting PBS. Here’s the story we like to tell about the  beginning of the universe. Space is expanding evenly everywhere, but if you rewind that  expansion you find that all of space was once compacted in an infinitesimal point of infinite  density—the singularity at the beginning of time.

The expansion of the universe from this point  is called the Big Bang. We like to tell this story because it's the correct conclusion from  the description of an expanding universe that followed Einstein's general theory of relativity  back in the 1910's. But since then we've learned so much more.

Does our modern  understanding of the universe still insist on a point-like Big Bang? Recent work actually  gives us a way to avoid the beginning of time. The key to understanding whether the universe had  a beginning is to decide whether there exists what we call a past singularity—whether all points  in space were at the same point at time t=0.

And from the earliest models of the expanding  universe, the answer seemed yes. When people like Alexander Friedmann and Georges Lemaitre solved  the equations of Einstein’s general relativity back in 19-teens and twenties, they found that,  if you rewind the expansion indeed all points converged on one point at the start of time.  But these guys made some big assumptions—for example that the universe is perfectly smooth  everywhere.

It’s not—it’s at least a little lumpy or we wouldn’t have galaxies. Could  this non-perfect-smoothness prevent our rewound universe converging on a single point? We’ll  come back to that—it’ll be important later.

The fact that the universe is mostly perfectly  smooth hints at something else that may change our prediction of a beginning of time. To explain  the general sameness of our modern vast universe, we needed to add something called cosmic inflation  to stretch out tiny smooth patches in the early universe into a smooth giant universe. At first  inflation was described as a period of extreme exponential expansion that lasted for a tiny  fraction of a second after the Big Bang.

But then we realized that this inflationary period didn’t  have to stop everywhere—perhaps it stops in spots, creating bubble universes like ours, in which  case there’d be a greater inflating spacetime that continues growing everywhere. But if this  “eternal inflation” lasts forever into the future, could it last forever into the past? If  so, perhaps the universe had no beginning.

So, our description of the universe has  gotten a little complicated over the past 100 years. We’re going to need to carefully  track our path backwards in time to see if we find a beginning. So we choose a  coordinate system for space and time, and we trace those coordinates into the past  they and see if they reach a point where we cannot trace them any further.

This can happen  if some aspect of the coordinate system “blows up”--becomes infinite. We call such points  singularities. In standard big bang cosmology there’s a singulartiy in the past where all paths  in space overlap and can’t be traced further.

This is interpreted as the time before which there  was no space. But there’s at least one example that you’ve heard of where a singularity  doesn’t mean the end of spacetime. Consider the black hole.

The simplest type of  black hole is described by the Schwarzschild metric. If we trace the Schwarzschild coordinates  from outside the black hole in, we find they blow up in two places. One is expected—at the center  of the black hole we find a proper curvature singularity—infinite spacetime warping.

But  there’s also a singularity at the event horizon. There, it appears that the coordinate of time  blows up. It’s as though we can’t trace time past that horizon.

We might be tempted to interpret  this as an uncrossable boundary, but we’d be wrong. Just because Schwarzschild coordinates  can’t cross this boundary doesn’t mean space and time end there. Sorry, you don’t bounce off  the event horizon, you fall straight through it.

We only need a simple-ish  coordinate shift to create a map across the event horizon  that is free from infinities—from singularities. For example, Eddington-Finklestein  coordinates combine space and time in a way that allows this continuous mapping all the way down to  the central singularity—where we do find an infinity that does not go away. The event horizon is what  we call a coordinate singularity—it's similar to how spherical coordinates have a singularity at  the poles where lines of latitude converge.

We say that spacetime is extendable  beyond the event horizon because a coordinate shift reveals the space beyond.  In fact, if we switch to a Penrose diagram we reveal new spaces that look like a mirror  universe and a past white hole—these are the fully extended coordinates… because we can, in  principle, trace light rays to these places. But the central singularity of the black  hole remains a physical singularity.

No light ray can be traced through this  to the other side. It’s reasonable to state that spacetime ends at the  center of a black hole. There’s no coordinate shift that extends our  map beyond the central singularity.

So what about the beginning of the  universe? Is there a singularity there, and if so is it a real physical end-of-spacetime  singularity AKA the beginning of the universe? Or is it a coordinate singularity like the event  horizon, with something on the other side.

To figure this out, we need another tool. It’s something we’ve discussed  before: geodesic incompleteness. So, a geodesic is the shortest  path through spacetime in general relativity.

It describes the curved  path travelled in a gravitational field, or the straight path traveled out of one.  Light travels something called a null geodesic, which is a path on which time itself  does not pass for the traveller. Geodesics are normally thought of as  continuing forever into the past and future, in that you can keep tracing these spacetime  lines even beyond the segment travelled by a particle.

But sometimes a geodesic will reach a  dead end where you can’t trace it any further. These are points of geodesic incompleteness,  and they are interpreted as the literal end of spacetime—like the end of the map. The singularity  at the center of a black hole is an example of such a point.

Geodesic incompleteness is how Roger  Penrose proved that black holes contain physical singularities with his black hole singularity  theorem—something we have of course covered. Geodesic incompleteness by itself is pretty  convincing, but we’re always left with a nagging worry that we plotted our geodesics in  the wrong coordinate system, like with the black hole event horizon. Another sure sign of the  end of spacetime in the black hole singularity is that the curvature blows up— the strength  of the gravitational field becomes infinite.

If we can find such a curvature singularity in a  way that’s independent of the coordinate system, we can pretty much guarantee that the fabric  of spacetime meets a bad end at that point. OK, so now that we have some sharper tools  to pry open the beginning of the universe, let’s see what we can find. Well, for geodesic incompleteness the  answer appears to be that the universe did have a beginning.

All geodesics—from  the arc followed by a thrown ball to the Earth’s orbit around the Sun—can be  extended back in time and wind up in the same infinitesimal point. And that’s even  true if you include cosmic inflation—even eternal inflation. Demonstrating this past geodesic  incompleteness has typically required certain assumptions.

For example, many arguments  have depended on the weak energy condition, which is a sort of add-on to the main equation  of general relativity that says you can’t have negative mass densities. But things probably get  pretty weird when you approach the past singularity, so it would be nice if we didn’t even  have to depend on this particular condition. More recently in 2003, Borde, Guth and Vilenkin  made a stronger argument for geodesic past incompleteness that didn’t require an energy  condition.

Instead, they only needed to assume that the average expansion rate was always  positive. This led to the Borde–Guth–Vilenkin (BGV) theorem, which states that any universe  that has, on average, been expanding throughout its history can’t have been expanding  forever—it must have a past boundary. OK, great.

But can we be sure that this  past boundary is really an end … or a beginning to spacetime? What if  spacetime is really extendible, like it was through the black hole event horizon?  Let’s look at the other criteria that we used for black holes—whether curvature becomes infinite. 

If so then our universe surely must contain a physical singularity in its past. If it  doesn’t contain curvature singularity then this doesn’t guarantee that we can extend our spacetime, but we’d need to  do a bit more investigating to be sure. This is what Geshnizjani, Ling, and  Quintin do in their paper published last year.

They applied a curvature  test to the beginnings of a range of different universes to check  the nature of any singularities. The results depend on the expansion  history of the universe. Remember that the BGV theorem tells us that  universes that have, on average, only expanded over their history must have  a past boundary, which might be interpreted as a beginning.

This new study finds that  universes with different expansion histories don’t have to begin with a singularity, and  so, perhaps, don’t have to begin. For example, a universe that expanded after a prior phase  of contraction or from a prior static phase don’t have to have past singularities. At the  same time these expansion histories also seem to violate certain energy conditions of general  relativity, and so may not be possible at all.

This isn’t really an entirely new  finding—more a confirmation that you need to break some aspect  of general relativity to avoid a beginning to the universe. Otherwise  they mostly agree with the BGV theorem. Universe that have only ever expanded, do have a beginning.

But in the researchers do find one unusual case  in which the BGV theorem may be challenged. Remember that an inflating universe has  exponential expansion. A pure exponential function with no vertical offset looks like  this: it grows rapidly into the future, but also plateaus approaching but never reaching  zero size in the past.

The BGV theorem tells us that even this ever-expanding universe should  suffer geodesic incompleteness into the past. There should be some sort of past boundary  that we’re tempted to identify as the beginning. That boundary can be depicted  as the lower diagonal edges on a Penrose diagram.

These represent past boundaries of the universe if there’s no way to  extend a null geodesic beyond them. Except, as it turns out there is a way.  This new study found that there’s a type of spacetime that could extend to  this region beyond the past boundary.

Our universe is pretty well  described with something called the Friedmann-Lemaitre-Robertson-Walker metric.  It’s that perfectly smooth, flat, expanding universe that I mentioned earlier this episode.  If you add exponential expansion to that—whether as cosmic inflation or as dark energy—then  FLRW metric can be considered to be a subset of something called de Sitter space.

In fact, as  these researchers showed, it’s possible to think of our universe—our patch of FLRW space—as  just a segment of a larger de Sitter space. The details of this are a bit much  for now, but long-story-short: the BGV theorem insists that our universe  has a past boundary. If there’s no way to map a null geodesic across that boundary then we  should interpret the boundary as a beginning of time.

But the new work shows there may be a  place for those null geodesics to travel to, or have traveled from—the larger de Sitter  space that extends beyond our FLRW universe. If our universe is extendable in this way,  that might just turn the past boundary of our universe into a coordinate singularity rather than  a real, physical one with infinite curvature etc. Now this extended spacetime may be - probably is - as illusory as the white hole and mirror universe of the  Penrose diagram.

But it’s intriguing that we have here a case where it’s not  just blatantly obvious that the universe rewinds into a non-traversable curvature  singularity at least in this one case. A word of caution though. In order to make  this work, our section of the universe—the FLRW section—has to transition smoothly  into the de Sitter space.

The only way for it to do that is for the exponentially  accelerating component—often described as the cosmological constant—to dominate over any  density fluctuations at the beginning of “our” universe. If those density fluctuations are  very small then spacetime is extendable past the past boundary of our universe and we  may not have a physical past boundary. But any significant density fluctuations would  actually close off the boundary and should turn this transition into a hard curvature  singularity—eliminating the possibility that there’s anything “before” it.

And our universe  definitely had density fluctuations at very, very early times—otherwise we would  not have galaxies and planets and YouTubers today. It’s interesting that  the same lumpiness that Friedman et al glossed over when they predicted the big  bang may make the big bang more likely. OK, that bodes poorly for an infinite past for  the universe.

There probably was a beginning of time. But the resolution of this is buried in the  unknowns of inflationary cosmology. It also awaits our theory of quantum gravity, because, even  if the universe approaches a point of infinite density in the past, our current understanding of  physics breaks down before we reach that point.

The most stunning thing about this sort  of work isn’t even the answer—whether or not there was a beginning to  the universe. And by the way, the current answer is still probably yes. To me  the most incredible thing is that we can even hope to answer questions that seem like they  should be far beyond our grasp.

That through pure reason we can learn one way or another  whether there was a beginning to spacetime. Thank you to Brilliant for supporting PBS.  Brilliant is where you learn by doing, with thousands of interactive lessons  in physics, math, programming, and AI.

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With this course you’ll learn the basics of vector operations, including scaling, transformations, polar coordinates, and the dot product. You can enhance your ability to visualize and solve complex problems in multidimensional spaces. And you’ll apply your newly developed skills to program a game, and design a logo to gain insights into how the physics of motion translate to a digital environment.

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Hey Everyone. On September 26th, 1905  Albert Einstein published his theory of special relativity and altered the course of  physics history. To celebrate the over 100 years of relativity, we have two new items at the merch  store.

First up is our universal speed limited embroidered patch. And next up is our 2D Light  Cone enamel pin with holofoil backing. With both pin and the patch, you have everything you need to derive both special relativity all on your own in case you ever get time traveled back to 1904.

This limited edition pre-sale will  run through October 7th and items will ship at the end of November. Just go to PBSspacetime. com/shop  or click the link the description.