What is wrong with the expansion of our universe?

How will our universe end? How did it evolve? How much dark matter it contains, and how much dark energy? To answer these questions, we need to know about the Hubble constant.

The Hubble constant isn’t something we encounter in our everyday lives, yet this little number could destroy our way of thinking about our universe.

The Hubble constant is a number, which indicates the expansion rate of our universe, in correlation with the distance to us. It is named after Edward Hubble who discovered a linear correlation between the redshift¹ of stars and their distance to Earth. Together with George Lemaître, he described a law, which connects redshift, distance, and escape velocity with the Hubble constant.

Hubble’s law: v=z×c=H₀D

V = escape velocity

Z = redshift

C = speed of light

H₀= Hubble constant

D = distance

The Hubble constant is estimated to be 70km/s×Mps, one megaparsec (Mps) being around 3,26 light years. This weird unit must be interpreted like this: If the Hubble constant is 70km/s×Mps, a galaxy is moving away from us with 70km/s, when it is one megaparsec away.

But if everything moves away from us, are we the centre of the universe? This assumption is obvious, but too easy to make. It also violates the cosmological principle, which states that the universe looks the same from every angle. So, everything moves away from everything. How could that be?

The answer is simple but hard to understand at the same time: space expands. It is the same as blowing up a balloon. You can try it at home: if you mark points on the balloon and blow it up, the points will move away from each other.

There is no real escape velocity, the other galaxies aren’t actually moving. The space in between just gets bigger. The observed redshift doesn’t come from the moving galaxy but the “stretched” space.

Later, it was discovered that the Hubble constant, in fact, isn’t constant at all. It changes constantly in time and since the expansion rate is accelerating, it gets higher with the distance to us. For this discovery, the physicists Saul Perlmutter, Brian Schmidt, and Adam Riess received the Nobel Prize in 2011.

But there comes the trouble. Depending on how the Hubble constant is measured, there are different results between 65 and 75. While this is significantly more precise than early measurements, which gave a number between 50 and 100, it is still mysterious, since we are also getting a lot better at taking good measurements.

To calculate the Hubble constant, you must know the distance and the apparent escape velocity of two galaxies. Since velocity is the changing distance over time, the main task is to measure distance. The different numbers come from two main ways of measuring the Hubble constant. One is mathematically out of the observation of the cosmic microwave background (CMD), and the other is through the observation of distance from stars, so-called “standard candles”.

The cosmic microwave background is radiation that originated from the early universe. It contains important information from which the cosmological standard model was calculated. This model describes the evolution of the universe as we know it – with a big bang at the beginning, as well as the known and unknown matter that it contains. These calculations result in a Hubble constant of 67km/s×Mps (Planck results, 2018).

Standard candles are a way of measuring distance through the observation of light. Stars with the same luminosity seem darker when they are further away. This phenomenon can also be observed with streetlights. If the true luminosity is known as well as the observed luminosity, the distance to the observer can be calculated. The most common standard candles are Cepheid variables, a kind of star that pulsates in its brightness. With the period-luminosity relation, developed by Henrietta Leavitt in 1912, the luminosity can be calculated out of the pulsation.

Besides Cepheids, a special kind of supernova (supernova type 1a) can be used as a standard candle. This supernova occurs when a white dwarf (a sort of star) explodes. The luminosity of this explosion is always the same and well-known, which is why it can be used as a standard candle.

A third option was developed mainly by Wendy Freedman. It is the tip of the red giant branch (TRGB). For this method, the helium fusion of red giants (another kind of star) is observed. The fusion has again always the same luminosity, so it fits as a standard candle. The funny name comes from the position of these stars on a Hertzsprung-Russell-Diagram, a diagram that shows all the different kinds of stars depending on their current state in their life circle.

It is important to mention that these different standard candles cannot be used isolated, the calculation is always a mixture of at least two methods. Nevertheless, the Cepheids and the Supernovae give us a Hubble constant of 74kmsMps (Freedman et al, 2021), much higher than the Hubble constant of 67km/s×Mps, calculated out of the CMB. Only the TRGB method gives us a Hubble constant that lies in between the others: 69kmsMps (Freedman et al, 2021).

Until today, the discrepancy between these Hubble constants is unknown.

But what does it matter? As stated in the beginning, the expansion rate is crucial to determine not only how much matter there is in the universe, but also how it will end eventually. The expansion is a balance between one force that pushes, described through the Hubble constant and one force that contracts, which is gravitation. If we know how high the expansion rate is, we can derive how much matter there is. On the same note, we can determine how the balance will shift in the end. If the expansion overtakes, the universe will expand forever. If the gravitation is stronger, it will collapse. Or the two forces will be perfectly balanced, and the expansion will stagnate. This last option is assumed in the cosmological standard model. But only if the Hubble trouble is solved, we can be sure if it describes our universe as it is or if we need new physics after all.

Johanna Krautkrämer

¹Redshift occurs when light moves away from the observer. The light waves get “stretched” through the movement and appear redder than the source of light actually is.

Sources:

Youtube.com – Urknall, weltall und das Leben: 

Leifiphysik.de – Hubble Gesetz

Heise.de – Expansion des Universums, Diskrepanz bei Hubble Konstante doch vor dem Ende 

Youtube.com – Increasing Accuracy in the Hubble Constant: Consistency with LCDM

Wikipedia.org – Tip of the Red Giant Branch

Spektrum.de – Wie groß ist die Expansion des Universums?

Iopscience.iop.org – Wendy Freedman – Measurements of the Hubble Constant: Tensions in Perspective (Freedman et al, 2021)

Aanda.org – Planck 2018 results – VI. Cosmological parameters (Plank results 2018, Plank Collaboration 2020)