How do we know our universe is expanding?

Let’s start with a small experiment that will give us a picture of an “expanding universe”. This universe will be an inflatable ball.

We mark with a pen any point on the surface and draw a small circle around it and mark two points on the circle. The balloon is gradually inflated.

As the circle grows, the distance to the center grows, as does the distance between the two points on the circle. This applies regardless of the starting point chosen. To get a picture of an expanding universe, it is sufficient to generalize the case of a surface to the case of a volume. Each point “sees” the other points move away from it as if it were the center of expansion.

Seen from any point on the surface, all other points recede as if it were the center of expansion – Jacques Treiner (via The Conversation)

​Expansion on a large scale, but not necessarily locally

Now we need to explain how scientists came to this conclusion in terms of the observable universe, and not just an inflatable balloon.

For this we need to observe the universe on a large scale. Neither the Moon nor the Sun moves away from the Earth, and neither do other objects in the Solar System. The stars in our galaxy, the Milky Way, are not moving away from us. And even the Andromeda galaxy, more than two million light-years (AL) away, is not moving away from us. On the contrary, it is approaching us at a speed of 500 km per second.

Is the universe really expanding? Yes, but on scales from tens, hundreds of millions and billions of AL. On average, the galaxies are moving away from each other, but that doesn’t stop some from getting closer locally, and even colliding.

Example of a collision of galaxies: The Mus galaxy, located 301 million AU from our galaxy
Example of a collision of galaxies: The Mouse Galaxy, located 301 million AL from our galaxy – William Ostling / NASA

We have known about the expansion of the universe since the 1920s, when astronomers (Americans, in this case) observed that distant celestial bodies were moving away from us, and that their rate of removal was greater the farther apart they were. To do this, we needed to be able to measure, for each object, its distance from us and its speed.

Speed ​​measurement

The turning point came when physicists analyzed the light coming from stars, starting with the Sun. Newton understood that white light consisted of a continuum of wavelengths, but it was not until the beginning of the 19th century that Frauenhoffer, a German physicist, noticed the presence of dark lines in the solar spectrum.

These “absent” wavelengths are due to their absorption by elements on the star’s surface, which then scatter them in all directions, resulting in a darker line of sight. A set of characteristic dark lines indicates the presence of a chemical element.

Dark lines on a continuous solar spectrum
Dark lines on a continuous solar spectrum – Jacques Treiner (via The Conversation)

Still a century later, astronomers noticed, in the spectra of stars belonging to distant galaxies, that these sets of dark lines all had, on average, a shift towards long wavelengths compared to what we observe in the laboratory, hence a shift “towards the red”.

They interpreted these shifts as a light Doppler effect, a phenomenon that occurs when a wave (acoustic or light) is emitted by a moving source relative to a receiver.

The perceived wavelength shifts toward short wavelengths as the source approaches the receiver and toward long wavelengths as it moves away from it. The power increases as the speed of the emitting source increases. We can observe this phenomenon when an ambulance passes in front of us, where the siren is louder or lower depending on whether the ambulance is approaching or moving away from us.

These shifts “toward the red” therefore indicated that the emitting stars belonged to galaxies moving away from ours. It was still necessary to determine whether these displacements were correlated to the distances between the emitting sources. It was not until the beginning of the 20th century that astronomers had the tools to measure these distances.

Distance measurement

For stars a few light years away, the orbital parallax method is used. If we look at a star every six months, its position changes in relation to the background of the sky. We call the parallax the angle at which we see the Earth-Sun distance from the star. This angle is equal to half the change in line of sight to the star every six months.

Determining the parallax of a star
Determining the parallax of a star – Jacques Treiner (via The Conversation)

But this method is not suitable for distant stars or galaxies because the parallax is too small to be measured and the distance between the Earth and the Sun is relatively too small.

The solution was found in 1908 at Harvard, where a young astronomer, Henrietta Swan Leavitt, measured the brightness of stars belonging to a nebula visible in the southern hemisphere, the Small Magellanic Cloud (M). At the turn of the century, advances in instrumentation—telescopes and photography—made it possible to compile the first large catalogs of stars.

At Harvard, images taken by astronomers (mostly men) were analyzed by a team of half a dozen women, and Henrietta Leavitt was interested in variable stars, the Cepheids, so called because the first was discovered (in 1784) in the constellation Cepheus. These are giant stars whose brightness varies with a periodicity ranging from the order of a day to a few months.

Leavitt discovered a relationship between a star’s period and its brightness. The brighter it is, the longer the period. Since they all belong to the same group of stars, they can all be considered to be roughly the same distance from Earth, d(M), so that the differences in luminosity reflect their differences in intrinsic luminosity.

Then imagine that we see a Cepheid in another galaxy. We measure its period P and compare it to the Cepheids in the Magellanic Cloud. This makes it possible to determine the luminosity L (M) that it would have if it were at the distance d (M). However, the apparent brightness Lap decreases as the square of the distance: Lap = L (M)〖d (M)〗2/d2. Knowing the distance to the Magellanic Cloud, we derive the distance d of the Cepheid.

We can also calibrate the period-distance relationship by measuring the period of Cepheids in our galaxy, whose distance we know by parallax measurement, and use that to determine the distance from the Small Magellanic Cloud.

In any case, the desired tool was there. From the measurement of the period of a Cepheid one could deduce its distance.

The universe is expanding

At the beginning of the 20th century, the question of whether all visible celestial bodies belong to our galaxy or whether there are other galaxies separate from ours was debated. It was the measurement of the distances described above that decided the debate, the Milky Way became a galaxy among others.

But it is also the method that enabled the American astronomer Edwin Hubble to highlight the expansion of the universe. He noticed that there was a correlation between the speed at which a galaxy is moving away and its distance. The further away a galaxy is, the greater its rate of removal.

This expansion is characterized by the “Hubble constant H0”, which indicates how much the velocity increases as the distance increases by one million parsecs (Mpc), a distance equal to 3.2 million AL. Currently, when moving away from a megaparsec, the speed of celestial bodies increases by 74 km/s.

Immediate consequence: If we go back in time, the universe contracts, its density increases. How far ? Good question, but that’s another topic, Big-Bang!

This analysis was written by Jacques Treiner, theoretical physicist at the University of Paris Cité.
The original article was published on the website of The conversation.

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