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Starts With A Bang

This Is How Astronomers Know The Age Of The Universe (And You Can, Too)

Our entire cosmic history is theoretically well-understood, but only because we understand the theory of gravitation that underlies it, and because we know the Universe’s present expansion rate and energy composition. Light will always continue to propagate through this expanding Universe, and we will continue to receive that light arbitrarily far into the future, but it will be limited in time as far as what reaches us. We still have unanswered questions about our cosmic origins, but the age of the Universe is known. (NICOLE RAGER FULLER / NATIONAL SCIENCE FOUNDATION)

The hot Big Bang occurred 13.8 billion years ago, and there’s no other possible answer consistent with what we know today.

Conceptually, it might seem like the simplest idea in existence to determine the age of the Universe. Once you figure out that the Universe is expanding, all you need to do is measure the expansion rate today and use the laws of physics to determine how the expansion rate must have changed over time. Instead of extrapolating forward to determine the fate of the Universe, you do the calculating backwards instead, and go all the way back until you achieve the conditions of the hot Big Bang itself.

This obvious method not only works, but it remains the best way we have to calculate the Universe’s age even today. Yet it’s very easy to go awry, as there are many simplifying assumptions you can make that will give you an easy answer that isn’t necessarily correct, including errors that even a Nobel Laureate made earlier this year. Here’s how you, too, can figure out the age of the Universe.

Standard candles (L) and standard rulers (R) are two different techniques astronomers use to measure the expansion of space at various times/distances in the past. Based on how quantities like luminosity or angular size change with distance, we can infer the expansion history of the Universe. Using the candle method is part of the distance ladder, yielding 73 km/s/Mpc. Using the ruler is part of the early signal method, yielding 67 km/s/Mpc. (NASA / JPL-CALTECH)

The first place to start is with the expanding Universe itself and the one parameter we’ve strived to measure longer than any other: the Hubble constant. On the largest scales, the galaxies we find in the Universe obey a very simple relation between the two observable quantities of distance and redshift, where the farther away an object is from us, the greater its measured redshift will be.

Remarkably, the law that relates them is extremely straightforward: the recession speed that you would infer from a galaxy’s redshift equals the distance to that galaxy multiplied by the Hubble constant. Even more remarkably, that constant has the same value for pretty much every galaxy we measure, particularly for galaxies within a few billion light-years of us. Even though there are additional cosmic motions inherent to each galaxy induced by gravitational effects, this law remains true when you average over all the galaxies you can find.

The redshift-distance relationship for distant galaxies. The points that don’t fall exactly on the line owe the slight mismatch to the differences in peculiar velocities, which offer only slight deviations from the overall observed expansion. The original data from Edwin Hubble, first used to show the Universe was expanding, all fit in the small red box at the lower-left. (ROBERT KIRSHNER, PNAS, 101, 1, 8–13 (2004))

So what do we measure the Hubble constant to be? It depends on how you measure it, since:

  • if you measure it by using signals that were imprinted all the way back in the earliest stages of the Big Bang, you get a value for the Hubble constant of 67 km/s/Mpc, with an uncertainty of 1–2%,
  • but if you measure it by measuring individual light sources that don’t arrive until the Universe is already billions of years old, you obtain a value for the Hubble constant of 73 km/s/Mpc, with an uncertainty of just 2–3%.
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Why these two values don’t match — and why they give such different, mutually inconsistent answers — is one of the major conundrums of modern cosmology.

A series of different groups seeking to measure the expansion rate of the Universe, along with their color-coded results. Note how there’s a large discrepancy between early-time (top two) and late-time (other) results, with the error bars being much larger on each of the late-time options. The only value to come under fire is the CCHP one, which was reanalyzed and found to have a value closer to 72 km/s/Mpc than 69.8. (L. VERDE, T. TREU, AND A.G. RIESS (2019), ARXIV:1907.10625)

However, the very astute among you will notice something about the Hubble constant itself: it comes in units that are a speed (km/s) per unit distance (Mpc, where 1 megaparsec is about 3.26 million light-years). If you look at a galaxy that’s 100 Mpc away, you’d expect it to recede away ten times faster than one only 10 Mpc away, but only one-tenth as fast as a galaxy 1,000 Mpc away. That’s the simple power of the redshift-distance relation.

But there’s another way to manipulate the Hubble constant: to recognize that a speed (distance-per-time) per (divided by) unit distance (distance) is the same as units of inverse time. What could the physical meaning of that “inverse time” correspond to? Perhaps, you might reasonably imagine, it could correspond to the age of the Universe.

The different possible fates of the Universe, with our actual, accelerating fate shown at the right. The specifics of the Universe’s composition affect the age of the Universe, as you can see by looking at the ‘start point’ occurring at different values in the past for different cosmologies, even with the exact same expansion rate today. (NASA & ESA)

There are approximately 3.1 × 10¹⁹ kilometers in one megaparsec, which means that if you turn the Hubble constant into an inverse time, you find some fascinating things.

  • The “time” that a value of 67 km/s/Mpc corresponds to is equivalent to 14.6 billion years.
  • The “time” that a value of 73 km/s/Mpc corresponds to is equivalent to 13.4 billion years.

These are both almost equal to the accepted age of the Universe, but not quite. In addition, they’re both almost equal to one another, but differ by approximately the same amount that the two estimates for the Hubble constant differ by: 9% or so.

However, you cannot simply change the age of the Universe by changing the Hubble constant, and there’s a subtle but vital reason why this is so.

A photo of me at the American Astronomical Society’s hyperwall in 2017, along with the first Friedmann equation at right. The first Friedmann equation details the Hubble expansion rate squared on the left hand side, which governs the evolution of spacetime. The right side includes all the different forms of matter and energy, along with spatial curvature (in the final term), which determines how the Universe evolves in the future. This has been called the most important equation in all of cosmology, and was derived by Friedmann in essentially its modern form back in 1922. (PERIMETER INSTITUTE / HARLEY THRONSON)

The value of the Hubble constant today isn’t simply the inverse of the value of the age of the Universe, even though the units work out to give you a measure of time. Instead, the expansion rate that you measure — the Hubble constant today — must balance the sum total of every form of energy that contributes to the Universe’s composition, including:

  • normal matter,
  • dark matter,
  • neutrinos,
  • radiation,
  • dark energy,
  • spatial curvature,
  • and anything else you can cook up.

The equation that governs the expanding Universe (shown above) can be solved exactly in some simple cases.

The scale of the Universe, on the y-axis, is plotted as a function of time, on the x-axis. Whether the Universe is made of matter (red), radiation (blue), or energy inherent to space itself (yellow), it decreases towards a size/scale of 0 as you extrapolate backwards in time. The age of the Universe multiplied by the Hubble constant will equal different values for Universes made up of different compositions. (E. SIEGEL)

If your Universe is exclusively made up of radiation, you find that the Hubble constant multiplied by the age of the Universe since the Big Bang equals ½, exactly. If your Universe is exclusively made up of matter (normal and/or dark), you find that the Hubble constant multipled by the age of the Universe equals ⅔, exactly. And if your Universe is entirely made of dark energy, you’ll find that there is no exact answer; the value of the Hubble constant multiplied by the age of the Universe always continues to increase (towards infinity) as time goes on.

This means that if we want to accurately calculate the age of the Universe, we can do it, but the Hubble constant alone isn’t enough. In addition, we also need to know what the Universe is made out of. Two imagined Universes with the same expansion rate today but made out of different forms of energy will have different expansion histories and, therefore, different ages from one another.

Measuring back in time and distance (to the left of “today”) can inform how the Universe will evolve and accelerate/decelerate far into the future. We can learn that acceleration turned on about 7.8 billion years ago with the current data, but also learn that the models of the Universe without dark energy have either Hubble constants that are too low or ages that are too young to match with observations. If dark energy evolves with time, either strengthening or weakening, we will have to revise our present picture. This relationship enables us to determine what’s in the Universe by measuring its expansion history. (SAUL PERLMUTTER OF BERKELEY)

So, to find out how old the Universe actually is since the onset of the hot Big Bang, all we have to do is determine the expansion rate of the Universe and what the Universe is made out of. There are a variety of methods that we can use to make this determination, but there’s one vital thing we have to remember: many of the ways we have of measuring one parameter (like the expansion rate) are dependent on our assumptions about what the Universe is made out of.

In other words, we cannot assume that the Universe is made out of a certain amount of matter, a certain amount of radiation, and a certain amount of dark energy in a way that’s independent of the expansion rate itself. Perhaps the most powerful way to illustrate this is to look at the leftover glow from the Big Bang itself: the Cosmic Microwave Background.

The leftover glow from the Big Bang, the CMB, isn’t uniform, but has tiny imperfections and temperature fluctuations on the scale of a few hundred microkelvin. While this plays a big role at late times, after gravitational growth, it’s important to remember that the early Universe, and the large-scale Universe today, is only non-uniform at a level that’s less than 0.01%. Planck has detected and measured these fluctuations to better precision than ever before, and can use the fluctuation patterns that arise to place constraints on the Universe’s expansion rate and composition. (ESA AND THE PLANCK COLLABORATION)

This, above, is a map of the fluctuations in the Cosmic Microwave Background. Overall, every direction in the Universe displays the same average temperature as every other direction: approximately 2.725 K. When you subtract that mean value out, you get the pattern that you see above: the fluctuations, or departures from the average temperature.

Where you see dark blue or dark red spots, those are regions where the temperature fluctuations are largest: approximately 200 microkelvin colder (for blue) or hotter (for red) than the mean value. These fluctuations exhibit particular patterns in their magnitude on a variety of angular scales, with the fluctuations rising in magnitude down to some particular angular scale of about 1 degree, then decreasing and increasing in an oscillatory fashion. Those oscillations tell us some vital statistics about the Universe.

Four different cosmologies lead to the same fluctuation patterns in the CMB, but an independent cross-check can accurately measure one of these parameters independently, breaking the degeneracy. By measuring a single parameter independently (like H_0), we can better constrain what the Universe we live in has for its fundamental compositional properties. However, even with some significant wiggle-room remaining, the age of the Universe isn’t in doubt. (MELCHIORRI, A. & GRIFFITHS, L.M., 2001, NEWAR, 45, 321)

What’s most important to realize is that there are many possible combinations of values that can fit any particular graph. For example, given the fluctuations we see, we can have a Universe with:

  • 4% normal matter, 21% dark matter, 75% dark energy and a Hubble constant of 72,
  • 5% normal matter, 30% dark matter, 65% dark energy and a Hubble constant of 65,
  • or 8% normal matter, 47% dark matter, 49% dark energy, -4% curvature and a Hubble constant of 51.

You will notice a pattern here: you can have a larger Hubble constant if you have less matter and more dark energy, or a smaller Hubble constant if you have more matter and less dark energy. What’s remarkable about these combinations, however, is that they all lead to almost exactly the same age for the Universe since the Big Bang.

There are many possible ways to fit the data that tells us what the Universe is made of and how quickly it’s expanding, but these combinations all have one thing in common: they all lead to a Universe that’s the same age, as a faster-expanding Universe must have more dark energy and less matter, while a slower-expanding Universe requires less dark energy and greater amounts of matter. (PLANCK COLLABORATION (MAPS AND GRAPHS), E. SIEGEL (ANNOTATIONS))

The reason that we can claim the Universe is 13.8 billion years old to such enormous precision is driven by the full suite of data that we have. A Universe that expands more quickly needs to have less matter and more dark energy, and its Hubble constant multiplied by the age of the Universe will have a larger value. A slower-expanding Universe requires more matter and less dark energy, and its Hubble constant multiplied by the age of the Universe gets a smaller value.

However, in order to be consistent with what we observe, the Universe can be no younger than 13.6 billion years and no older than 14.0 billion years, to more than 95% confidence. There are many properties of the Universe that are indeed in doubt, but its age isn’t one of them. Just make sure you take the Universe’s composition into account, or you’ll wind up with a naive — and incorrect — answer.

Ethan Siegel is the author of Beyond the Galaxy and Treknology. You can pre-order his third book, currently in development: the Encyclopaedia Cosmologica.


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