# Hubble Tension

Introduction

On April 26, 1290, there was a great debate between Harlow Shapley and Herber Curtis about the scale of the universe. Shapley took the position that the Milky Way was the extent of the universe. Curtis took the position that there was something beyond the Milky Way. Shapley thought that other large star clusters were “spiral nebulas” buried within our galaxy, while Curtis claimed they were galaxies of their own.

There was no definitive outcome to the debate. However, the answer came from astronomer Edwin Hubble, who later in the 1920s used the Mt. Wilson Telescope in California, measured the distance between the early stars, and found the distance between the earth and a Cepheid star V1 in the Andromeda formation. “The distance turned out to be about 1 million light years, about three times the size Shapley estimated.

This discovery opened Pandora’s box. Hubble created a number that would become the root of one of the biggest unsolved problems in cosmology. Hubble discovered that galaxies in space were moving away from us, and the further they were away, the faster they seemed to be receding. His original approach was that the velocity of the object receding was the distance. This became the “Hubble constant, H0.” The physical meaning of H0 is simple; it tells us how fast a galaxy is receding from us.

The problem became, “How do you find the distance to a star?” Astronomers turned to cephied variables, stars that pulsate in a very regular way.

A Solution

In the 1900s, Henrietta Swan Leavitt studied many Cepheid variables in the Magellanic cloud and discovered a crucial relationship between their periods and luminosities: the slower it pulses, the brighter its luminosity.

This new characteristic led to a new way to calculate the distance to a galaxy. These steps are:

1. Find the pulsation period, then calculate how bright the star is from the pulsation period. This is known as the “absolute magnitude.”

2. Compare the star’s apparent brightness or signal amplitude.

3. Calculate the distance using the brightness distance relationship. Here is the equation:

m – M = 5 log(d/10)

Where:

M = Absolute Magnitude (true brightness)

m= Apparent Magnitude (how bright it appears)

d = Distance to that object

It turns out that cepheids are useful to a value of a few tens of megaparsecs. It was found that the 1a supernovae are helpful on a scale of a few hundred megaparsecs. Sometimes, astronomers use the two methods to confirm the distance measurement.

With advanced technology, astronomers have now settled on a value for H0 of about 73.4 km/sec megaparsec using Cepheid variables. Astronomers were not sure of this number and wanted cosmological models to verify it. If the values matched, that would verify the H0 number. If not, it would indicate a flaw in the understanding of the Cosmos. The comparison method involved the cosmic microwave background (CMB) signal, which is thought to be the oldest light in the universe—the faint glow left over from the “Big Bang” permeating the entire cosmos. It allegedly provided a snapshot of the universe just 390,000 years after the Big Bang, before stars and galaxies formed.

Measurements from the CMB are not directly reliant on the cosmic distance ladder. Astronomers use the WMAP and Planck spacecraft to map the CMB’s tiny temperature fluctuations across the expanse of the visible universe. These fluctuations reflect the density variations in the early universe and relate to various cosmological parameters, including the rate of the universe’s expansion.

When astronomers calculated the Hubble constant using these two methods, they expected the same value. However, they encountered a dichotomy. The value using the CMB method turned out to be 67 km/sec, less than using cepheids and supernovae. This discrepancy is significant. This discrepancy is what is referred to as the Hubble tension. There is a conflict between the universe’s expansion rate observed directly in our local neighborhood and the expansion rate inferred from the conditions of the early universe.

Astronomers thought this discrepancy could be due to the limited resolution of the Hubble and other giant telescopes. They waited for the results from JWST, hoping the infrared observatory would resolve the crisis. However, the results only confirmed their fears. The increasing resolution seen in the Hubble and then the JWST reduced the error of the measurements. Follow-on measurements using even more data points confirmed the Hubble tension.

Based on this, astronomers confidently ruled out measurement error as the cause of Hubble tension. Observations of the JWST have validated the value of H0, confirming the crisis in cosmology. This means that Hubble exposes a gap in our fundamental understanding of the universe.

Now that we have confirmed the value of the H0, we do not know exactly what we are missing. We may be making a mistake in the distance measurements, or there is something wrong with your understanding of the CMB. There is even a possibility that both values are flawed and an unknown factor is at play.

There are three reasons why resolving this is critical:

1. Testing the Standard Model of Cosmology: H02 = (8πG/3)/p – kc2/a2 + Δc2/3

Where:

The first term is the expansion rate

The second term is Curvature of Space

Third term is Dark Energy

2. Understanding Dark energy, the alleged mysterious force driving the expansion of the universe, which is calculated to be up to 68% of the observable universe. The Hubble constant is directly related to the rate of this expansion. So, discrepancies in this measurement could offer new insights into the nature of dark energy.

3. Understanding the rate of expansion is key to predicting the universe’s fate. Different rates imply different scenarios, from endless expansion in which galaxies become increasingly isolated to a big crunch where the universe collapses into itself and a big rip in which the fabric of space-time is torn apart.

Resolving this “Hubble tension” is a step toward understanding our cosmic destiny. Now, astronomers are exploring different approaches to measuring the universe’s expansion rate. A new method involves studying gravitational sources such as merging black holes or compact objects, accompanied by some optical light waves. Another approach involves measuring the distance between red stars by observing their helium flash, which offers a precise cutoff point for their intrinsic brightness. However, astronomers still need to determine which of these is more accurate.