Geometry is Destiny…or is it?

4–7 minutes

Cosmologists used to think that gravity alone determined the shape of the universe, and that shape, in turn, determined its future. But that raised a lot of problems.

Gravity works by curving space-time, so it can also force the fabric of space to contract. It would then slow the universe’s expansion from an originally faster rate.

The universe would have reached its current scale in less time than the current rate of expansion implies — less than 14 billion years, perhaps significantly so.

But some globular star clusters are around 13 billion years old — and stars didn’t begin forming immediately after the Big Bang. The universe must be older than that.

Dark energy solves this problem, and more…

First, let’s backtrack a bit — to the Hubble time.

Near the beginning of our cosmology unit, we estimated how long ago the Big Bang occurred — that is, how old the universe is.

We can do this by measuring the present-day separation between galaxies.

We know the galaxies’ positions now; we know that they started scrunched together. We can find their speed from their cosmological redshifts based on the Hubble Law. From there, it’s a simple matter of finding the time they took to move from Point A to Point B.

Now, I don’t know about you, but it seems like a royal pain in the behind to do this calculation for every galaxy in the whole dang sky. Instead, we can use the Hubble constant, H0, which summarizes the separation between all galaxies.

The Hubble constant has units of km/s/Mpc, which is a speed divided by a distance.

Flip the Hubble constant over (take the reciprocal), and you now have a distance divided by a speed — which is the equation for time.

We then convert the megaparsecs to kilometers so that all the distance units are the same and cancel out, leaving us with a time in seconds. And for convenience’s sake, we convert seconds to years — because the number of seconds since the universe’s beginning is going to be an absurdly massive number.

That gives us the Hubble time:

Now we can plug in any value for H0. That will give us the estimated time since the Big Bang for any given rate of galaxy recession.

The current best estimate for the Hubble constant is just under 70 km/s, which puts the Big Bang at roughly 14 billion years ago.

But that is not necessarily accurate.

The above graphic represents the Hubble time as 1/H0 (remember, it’s literally just a reciprocal of H0).

The Hubble time is the time since galaxies were all compressed together in one spot…if their recessional velocity has remained constant.

That would, it would seem, require a universe without gravity. Because even as expanding space carries galaxies apart from one another, gravity would counteract that, pulling them back together.

The expansion would slow.

A universe whose age is actually equal to the Hubble time would need to be totally empty — no energy, and no matter, dark or otherwise. Certainly no life, no people. It would be “empty,” as the graphic above puts it.

…or would it?

If there is a force that can counteract gravity, then the universe’s past and future is no longer dependent on gravity.

Also, think about what acceleration literally means. The universe is expanding faster now than it was in the past.

Flip that statement around: the universe was expanding slower in the past than it is now.

In the past, the expansion rate was slower. The current separation between galaxies would have taken longer to reach.

The universe can be older.

Remember what we were saying before, about some globular star clusters being around 13 billion years old?

In particular, Messier 92 here is about 13.8 billion years old. It’s one of the oldest globular clusters known.

As one astronomer once said, “You can’t be older than your mother.” The universe must be older than its oldest “occupants.” So it’s got to be older than 13.8 billion years.

And globular clusters are hardly the oldest known objects in the universe. The earliest newborn galaxies can be observed even farther back, and the first quasars — erupting supermassive black holes — are even older, as you can see below.

Acceleration allows for this.

If the expansion of the universe is currently accelerating, then it would have been expanding more slowly in the past — and it would have taken longer to reach its current scale.

Long enough to place the Big Bang before the formation of the earliest quasars, galaxies, and globular clusters.

Now, notice that in the graphic above, the lines for the “empty” and “accelerating” universes begin in close to the same place. This is purely coincidental. The Hubble time, calculated for a universe with no matter or energy, just happens to roughly equal the actual age of our accelerating universe: about 14 billion years.

And just as acceleration accounts for the universe’s past, so too does it determine its future.

For decades, cosmologists said that “geometry is destiny.” That is, the shape of space determines its fate. There are three possible types of curvature that space could have: positive, negative, and flat.

In a reality where only gravity dominates, the flat and negatively curved models must expand forever; there is not enough matter present for gravitation to stop the expansion. On the other hand, a positively curved universe must eventually rebound and contract under the influence of gravity.

But gravity does not dominate.

Dark energy — whatever the heck it is — acts as an antigravity force. And that means that even a positively curved universe may expand forever.

Our universe’s future depends not on its geometry, but on the nature of dark energy.

And that is the biggest question left in cosmology.

What the heck is dark energy? Is it vacuum energy? Quintessence? Something else entirely? How does it work? Is it constant? Is it changing? How has it worked in the past…and how will it work in the future? Will there be a “big rip”? A “big crunch”? A “big freeze”?

We don’t know.

But there’s a lot that we do know — enough that we’ve since modified the original big bang theory. And that’s what we’ll explore next up.


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4 responses to “Geometry is Destiny…or is it?”

  1. Ross Avatar
    Ross

    Is our universe be evolving within another universe? A motherverse!

    Liked by 1 person

    1. Emma Avatar

      Hi Ross! It could be 😉 I’ve read of a concept that the singularity at the heart of a black hole is physically similar to the conditions of the big bang as we understand them. So in theory, every black hole could spawn a “child” universe, and we could exist within the black hole of a “motherverse.” However, I’ve read nothing to indicate this is a prevalent theory. As far as I know, it’s just an idea, a possibility–but a pretty cool one, at that!

      Like

  2. disperser Avatar

    Nice post explaining the current state of things (as we understand them).

    And yet, from a layman’s perspective, some of the underlying reasoning behind this understanding sounds circular.

    We assume something and predict something, but observations contradict our prediction, so we modify the predictions based on our observation by tweaking our assumption to make it fit. But we don’t change the initial premise.

    For instance, as mentioned above, some observed cosmic objects are as old as the Universe, a physical impossibility. Rather than say we are limited in what we can see (we can’t see past roughly 14 billion years), me modify our assumption by introducing theoretical concepts that can’t be tested to fit both our initial assumption (Big Bang) and predictions (current observations), and we then say, “See? It fits!” (I’m being a bit snarky … maybe a lot snarky).

    That is perhaps best exemplified by the graph showing the timeline. How unfortunate of us that we are at the graph’s inflection point . . . or maybe it’s fortunate because we can predict almost anything (backward and forward) and it might be correct (hence the various models that all converge at our current point in time).

    Again, I’m not disputing the assumptions or underlying models (I can’t because I don’t remember any of my advanced math course), but it reminds me a bit of the Texas Sharpshooter fallacy.

    Anyway, nice read, and someday we’ll . . . well, not we, but someone, will know it all.

    Meanwhile:

    Big Bang – Wikipedia

    Liked by 1 person

    1. Emma Avatar

      I do love how willing you are to question everything. A few months back, I got an email from a reader who mentioned, among other things, that my blog was now their primary source of information. After a split second of glowing with pride, my heart sank quite a bit. I’m not qualified to be anyone’s primary source, and I hope that people will seek out resources beyond my blog and be willing to question anything I say here!

      That said…I’m not qualified to fully answer you, but there’s a few things I can say here at this point in my studies:
      1) You’re not alone. Even scientists–even cosmologists themselves–can get uncomfortable with the type of data analysis and reasoning necessary to piece together cosmology.
      2) In just a few posts from now, we’ll cover the single most solid source of evidence we have for our current understanding of cosmology. In short, the post coming up will make predictions that are testable using the data from the CMB. We’ll cover the CMB data once we’ve got a bit more requisite knowledge down.
      3) Even the general scientific method is a cyclical process. We almost never start out with a perfect model of nature. But when contradictory evidence arises, we don’t necessarily throw out the old model; we often just need to modify the old one in order to better fit the data. That’s true for branches of science that fit the “general” scientific method and it’s just as true for astronomy.
      4) The Big Bang theory and the accelerating expanding universe are fairly solid theories at this point, but there is a ton of scientific debate over the exact details. When everything ultimately depends on the nature of something that makes up over 80% of the mass/energy in the universe and that is completely unknown to us, there are bound to be massive gaps in our understanding. There are contradictory data sets. There’s an ongoing effort to make more and more accurate observations and measurements to rule out uncertainty and try to reconcile the data. And while scientists are ultimately human, I don’t know of a single cosmologist who wouldn’t be thrilled to make some totally new observation that completely upends our understanding!
      5) The current theories as I’ve been describing them thus far are solidly grounded in available evidence to the best of my knowledge. But this is the final frontier of astronomy, and it’s a rapidly and actively evolving field. For all I know, a discovery will be published tomorrow that will cast doubt on something I’ve recently explained. And that’s okay! If that happens, I’ll do my best to revise my post to indicate as much–but I will likely be unqualified to explain the new understanding.

      Liked by 1 person

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