The inconstant constant

Georges Lemaître

In a previous post, The Hubble-Lemaître Law, I explained how Georges Lemaître discovered in 1927 the expansion of the universe, but as he published in a French-language journal, it didn't make a great impact, and for almost a century the discovery was attributed to Edwin Hubble, who published in 1929 in a much more widely circulated English-language journal. This injustice was corrected on October 29, 2018, by the International Astronomical Union, and I echoed the renaming of the law in my post, published three days later in this blog.

The Hubble-Lemaître Law says this: The farther away a galaxy is, the faster it is receding from us. Its recessional velocity is proportional to its distance. The constant of proportionality is called the Hubble constant, which has the dimension of 1/time. In the International System of Units, this dimension would be expressed as seconds⁻¹ or 1/second, but in practice, its definition (speed/distance) is used, with the following units: km/s/Mpc, which means: the increase in the recessional velocity of a galaxy (in km/s) as its distance from us increases (measured in Megaparsecs). One Megaparsec (Mpc) is one million parsecs, and one parsec is equal to 3.2616 light-years.

In fact, this constant is not constant. Along the history of the universe, its value has changed. Initially, it decreased, but starting about 5 billion years ago, it began to increase when the expansion of the universe accelerated. Its current value is represented by the symbol H₀, where the subscript 0 means now.

The current value of the Hubble constant has been refined over time. The first value Hubble obtained was 500 km/s/Mpc, which was too high because he used incorrect Cepheid variable stars to calculate the distance to galaxies. The values ​​currently calculated are an order of magnitude lower. The problem is that, depending on the method used to calculate them, different values ​​are obtained, as I explained in the post titled The problem with the Hubble constant. I will repeat the problem here:

• When Cepheid variable stars or supernovae are used to estimate the distance to a galaxy, and the redshift of that galaxy is used to estimate the speed at which it is moving away from us (i.e. the speed of expansion of space), a value of 74±1.4 km/s/Mpc is obtained.
• When calculated from the standard cosmological model, which in turn is based on data provided by the cosmic microwave background radiation, the result is 67.4±0.5 km/s/Mpc.

It is clear that the two values ​​are incompatible, because their maximum probability margins do not overlap.

Grvitational lens

A new method, independent of the two mentioned above, has been recently used to measure the distance to galaxies, from which the value of H₀ is calculated. This method consists of detecting gravitational lensing. What is that?

According to the general theory of relativity, objects of very high mass bend the direction of light rays that pass near them. When supernovae located in very distant galaxies are observed, their light must go through intermediate regions where there may be clusters of galaxies, alternating with voids, until the light reaches us. This journey can lead to changes in the direction of the light ray (gravitational lensing effects) which, upon reaching us, cause optical illusions: distortions of the shape of the very distant galaxy, and even its decomposition into two apparently different objects, which turn out to be the same.

By comparing these images, it is possible to measure the differences in the time it takes for the light from these objects to reach Earth via different paths. By combining these data with estimates of the mass distribution of the galactic lens that produced the distortion, H₀ can be calculated. The value obtained was 71.6±3.3 km/s/Mpc.

I asked Gemini to generate an image that would allow me to compare the three intervals, but the response from the associated image generator (NanoBanana) was unusable. A few days later, Google released a new image generator (NanoBanana 2), which correctly resolved the issue and generated this image:

This is the image I generated using Paint:

It is clear that the new approximation (although more uncertain) fits the higher value better than the lower. The authors intend to improve the accuracy of their measurements with new observations. Perhaps it's time to consider that the standard cosmological model should be modified, as I suggested in the post mentioned above. All the more so, since the acceleration of cosmic expansion that led to the standard cosmological model is now in question.

The same post in Spanish

Thematic Thread about Standard Cosmology: Previous Next

Manuel Alfonseca