“Deep into that darkness peering, long I stood there, wondering, fearing, doubting, dreaming dreams no mortal ever dared to dream before.” -Edgar Allen Poe
Earlier this week, the Nobel Prize in Physics was announced for the discovery that the Universe is not only expanding,
but that this expansion is accelerating!
What does an accelerated expansion physically mean?
If all you had in the Universe was some initial expansion and the mutual gravitational attraction of everything in it, you’d expect that as an object got farther and farther away from you, over time, its apparent motion away from you would slow down.
If there was enough matter, you’d expect that the expansion would eventually lose out to gravity, and that the objects moving away from you today would someday reverse course and wind up moving towards you.
If there weren’t enough, the expansion would win out, and that the objects moving away from you today would slow down some, but would keep on moving away from you for all eternity.
But if the expansion is accelerating, there’s something more to it.
Unlike the three decelerating cases above (with Ω > 0, where the recession speed of any particular galaxy slows down over time), or even the case of an empty Universe (with Ω = 0, where the recession speed of a galaxy remains constant), a Universe with an accelerated expansion will actually have a particular galaxy recede away from you faster and faster as time goes on!
(For some more details, check out Sean Carroll’s dark energy FAQ.)
Until the 1990s, it was pretty much assumed that the Universe would be decelerating, and it was thought that in order to understand both the history and fate of the Universe, there would be two important measurements we’d have to make.
The first would be Ho, the Hubble parameter today. If a galaxy is a certain distance away from us, we expect to find it moving away from us at a certain rate, where the apparent recessional speed is given, very simply, by Hubble’s Law. For relatively nearby objects (i.e., galaxies “only” about a billion light-years or less away from us), accelerating, decelerating and empty Universes all look the same.
But the second important measurement (known as qo, which is traditionally called the deceleration parameter) tells us whether the Universe is accelerating or decelerating, and it is very sensitive to the motions of faraway objects! In the figure above, the lowest line has a deceleration parameter of qo = +½, the middle line has qo ≈ +0.1, and the top line — the best fit to the cosmological data from our actual Universe — has qo ≈ -0.6. (I don’t normally like to talk numbers, but these are going to be important later, so remember it; the best fit to our Universe’s data has a deceleration parameter of qo ≈ -0.6.)
That negative value tells that the Universe is not decelerating at all, but is in fact accelerating in its expansion! And we learned this, of course, from looking at those very bright, well-known objects that are so visible at such large distances: supernovae!
You see, Hubble’s Law — the nearby relationship between an object’s apparent recessional speed and its distance — is true on average, but it is not a good predictor of any individual object’s speed.
You see, in addition to getting swept up in the expansion of the Universe, every object is subject to local gravitational forces, that gives it an extra motion on top of the Hubble expansion, known as a peculiar velocity. It should come as no surprise that not only do we observe this, but simulations predict it as well!
In fact, it’s well-measured that, relative to the uniform temperature surface of the cosmic microwave background, our galaxy has a substantial peculiar velocity of about 627 km/s, which is actually huge: about 1.4 million miles per hour!
Now, this dipole is not exactly indicative of our peculiar velocity. They ought to be related, of course, but because the Earth orbits the Sun, the Sun is orbiting the galaxy, and our galaxy is constantly being tugged on by all the others in the Universe, this peculiar motion will actually change somewhat over time!
We have, in fact, mapped out the peculiar velocities of a great many objects in our neighborhood. What we’ve found is that not only do many of these objects cluster together in small groups which move together, but that there is an unexpectedly large overall dark flow on scales hundreds of million of light years in size!
Now, here’s where Tsagas’ idea comes in, and it’s very clever. He finds that if you’re moving relative to the CMB rest frame, this relative motion will cause your local region of space to have a different expansion rate from the overall Universe!
This should have the largest effect in the nearby Universe, because as you move to larger and larger scales, your peculiar velocity, even if it’s thousands of km/s, will eventually become negligibly small compared to the overall Hubble expansion.
Now remember, far above, we said that the best fit of our models to the data show that the deceleration parameter, qo ≈ -0.6, although at very much earlier times — when dark energy was unimportant — the Universe was, in fact, dominated by matter, and decelerating with an approximate deceleration parameter of qo ≈ +½.
Now, the big question, of course, is whether Tsagas’ model can explain the same cosmological data in the supernovae that dark energy does. And to Tsagas’ great credit, he is honest about what his results give, and how they compare to our concordance cosmology.
The answer is no. His model can give apparent deceleration parameters as negative as about qo ≈ -0.3, but no more than that. And that deceleration parameter goes approximately towards zero very quickly, and becomes small and positive (but much less than the qo ≈ +½ predicted by the standard Lambda-CDM model) by z = 0.3 at the latest. Now, I worried that this would become very problematic at the intermediate redshifts, where the support for the dark energy model is strongest.
So, I took the best available supernova data, along with the fits for models such as the dark energy model, an empty Universe, and a few others (from Ned Wright’s site), and I put in a line to try to fit my best calculations for Tsagas’ model.
Now, I do give Tsagas’ model a ton of credit for being able to produce a significant (if not quite sufficient) early rise in that curve, because it does so without invoking any dark energy or negative-pressure fields! But the low-density nature of Tsagas’ toy Universe winds up producing predictions that are too close to the “empty Universe” model that are inconsistent with the intermediate-redshift supernovae.
So it’s a neat little toy, and it’s very impressive that it produces any sort of positive acceleration, but it doesn’t look like it can replace dark energy. Still, it’s always worth exploring alternatives, and every time I do, I find myself a little more convinced of how impressively dark energy actually works!