This is Part 3 in a series on the age of the universe. Read Parts 1 and 2.
The FLRW metric is a model. And you know the saying, all models are wrong, but some are useful. The FLRW metric is parsimonious: it’s the simplest conception that captures the most amount of observations. And it is indeed simple. It assumes that at large enough scales the universe is HOMOGENOUS: that it’s roughly the same from place to place, and that this uniform blob of stuff is slowly getting diluted as the universe expands.
We make these assumptions because a) it’s close enough to reality, and b) it makes the math of general relativity, which is notoriously nasty, slightly less nasty.
And it’s through the language of the FLRW metric that we get our universal clock. In this metric, in these equations, there a parameter that represents the passage of time. Typically for this we use the symbol tau, which is the Greek alphabet precursor to the letter t, so that fits. And we call this the “proper time” because that seems rather fitting.
Anyway, the FLRW metric gives you a recipe for figuring out the proper time since the beginning of the universe. You just have to find yourself in a frame of reference that expands with the universe, which means you have to just be chilling, going with the flow, and not moving in any particular direction relative to everything else.
Well, how the heck do you do THAT? It just so happens that the universe gives us a way to figure out how we’re moving relative to cosmic expansion, and that’s the cosmic microwave background. The CMB was emitted all at the same time (well, within about 10,000 years, which is close enough) in all directions all throughout the universe at once. And since it’s bombarding us from all directions on the sky, then we can use it to detect our movement: if we make an all-sky map of the CMB (and we have, multiple times), then if it appears redshifted in one direction and blueshifted in the opposite direction, then we can figure out our movement that goes against the flow.
Subtract that out, and boom what do you know, you’re now in a frame of reference that’s at rest with respect to the entire universe. Pretty Zen, if you ask me. And now that you have that, you can calculate your proper time since the beginning of the universe, aka the age of the universe since the big bang.
Now we don’t NEED the CMB to do this, but it makes things WAY easier, so thank you, for once, universe, for making our jobs a little less grueling.
But HOLD ON. The FLRW metric (and no I just can’t say that enough) makes an ASSUMPTION: that the universe is super smooth. But aren’t there things like galaxies and clusters and voids? That doesn’t look super smooth to me. We’ve all gotten used to the homogenized milk of the universe, and a lumpy cosmos is a little hard to swallow.
And maybe if we’re getting this assumption wrong, then the FLRW metric isn’t as useful as we hoped, and we’re getting the age of the universe wrong, and when we finally meet the aliens they’re going to laugh at us.
This is the argument behind something called the “timescape theory”, which sounds like you’d find it printed in multicolor text in a website designed in 1997, but its creator is an actual cosmologist who was trained in Stephen Hawking’s group at the University of Cambridge. His name is David Wiltshire, and argues that the lumpiness of the universe throws off the FLRW metric.
He says that time flows faster in the empty voids than it does in the dense galaxies and clusters. And because of this, our estimates of the age of the universe are off because we’re assuming everything is pretty much the same.
Now, everything IS pretty much the same, we’ve measured this, but only at big enough scales. A chunk of universe inside a box roughly 100 megaparsecs on a side does indeed look like any other chunk of the same size. But WITHIN that box the universe is mostly void, somewhere around 70-90%, depending on who you’re asking.
The problem with timescape is that it takes a nonstandard approach to applying general relativity that doesn’t exactly give clear, consistent results. Standard cosmology says hey, look, the universe is super smooth at super big scales, and then it only gets lumpy once you zoom in a big. Following this logic, the time dilation inside voids is way small compared to the time dilation in your living room, and while it’s real, it’s really tiny, like less than a hundredth of a percent, so not something we need to worry about.
Wiltshire says this is bullocks. We’re starting with an assumption of average-ness, then adding in lumps. He argues that we should first start with the lumps, add them all together, THEN average the result. In this approach, the time dilation is HUGE, big enough to explain away the existence of dark energy and drastically alter the age of the universe depending on where you live (for galaxies, its 14.2 billion years, for voids, it’s over 18 billion years).
But that’s not the end of the story. Calculating the age of the universe isn’t the only application of the FLRW metric. We also use it in our simulations of the growth of structures in the universe. If we were doing it wrong, if our approach of assume-smooth-then-add-some-wiggles wasn’t right, then it would show up in our simulations as arrangements of galaxies that don’t conform to observations.
The simulations agree with observations. They just WORK, which while not a proof is at least a strong sign that we’re on the right track…and that timescape isn’t.
Again, not totally ruled out, but I’m not sweating bullets over here. The FLRW metric is safe and sound, and we know the age of the universe.
To be continued…
