Everything in the universe has gravity – and feels it too. Yet this most common of all fundamental forces is also the one that poses the greatest challenges to physicists. Albert Einstein’s general theory of relativity has been remarkably successful in describing the gravity of stars and planets, but it doesn’t seem to fit perfectly on all scales.

Tests of general relativity have withstood many years of observational testing, from Eddington’s measurement of the Sun’s deflection of starlight in 1919 to the recent discovery of gravitational waves. But gaps in our understanding begin to appear when we try to apply it to extremely small distances, where the laws of quantum mechanics operate, or when we try to describe the entire universe.

Our new study, published in Nature Astronomy, has now tested Einstein’s theory on the largest scale. We believe that our approach may one day help solve some of the biggest mysteries in cosmology, and the results suggest that the theory of general relativity may need to be adjusted on this scale.

## Wrong model?

Quantum theory predicts that empty space, the vacuum, is packed with energy. We don’t notice its presence because our devices can only measure changes in energy rather than its total amount.

But according to Einstein, vacuum energy has repulsive gravity – it pushes empty space apart. Interestingly, it was discovered in 1998 that the expansion of the universe is actually accelerating (a finding that was awarded the 2011 Nobel Prize in Physics). However, the amount of vacuum energy, or dark energy as it has been called, required to explain the acceleration is many orders of magnitude smaller than what quantum theory predicts.

Therefore, the big question, called “the old cosmological constant problem,” is whether the vacuum energy actually gravitates—exerts a gravitational force and changes the expansion of the universe.

If so, why is its gravity so much weaker than predicted? If the vacuum is not pulled at all, what causes the cosmic acceleration?

We don’t know what dark energy is, but we have to assume it exists to explain the expansion of the universe. Similarly, we must also assume the existence of a type of invisible matter presence, called dark matter, to explain how galaxies and clusters evolved to become the way we observe them today.

These assumptions are baked into the scientists’ standard cosmological theory, called the lambda model of cold dark matter (LCDM) – which suggests that there is 70% dark energy, 25% dark matter and 5% ordinary matter in the cosmos. And this model has been remarkably successful in fitting all the data collected by cosmologists over the past 20 years.

But the fact that most of the universe is made up of dark forces and matter, with odd values that don’t make sense, has led many physicists to wonder if Einstein’s theory of gravity needs to be modified to describe the entire universe.

A new twist emerged a few years ago when it became apparent that different ways of measuring the cosmic expansion rate, called the Hubble constant, give different answers—a problem known as the Hubble tension.

The disagreement, or tension, is between two values of the Hubble constant. One is the number predicted by the LCDM cosmological model, which was developed to match the light left over from the Big Bang (the cosmic microwave background radiation). The second is the rate of expansion measured by observing exploding stars called supernovae in distant galaxies.

Many theoretical ideas have been proposed for ways to modify the LCDM to explain the Hubble tension. Among them are alternative theories of gravity.

## Digging for answers

We can design tests to check if the universe follows the rules of Einstein’s theory. General relativity describes gravity as the curvature or distortion of space and time, bending the paths along which light and matter travel. Importantly, it predicts that the trajectories of light rays and matter should be bent by gravity in the same way.

Together with a team of cosmologists, we put the fundamental laws of general relativity to the test. We also investigated whether modifying Einstein’s theory could help solve some of the open problems in cosmology, such as the Hubble tension.

To find out whether general relativity is correct on a large scale, we set out for the first time to investigate three aspects of it simultaneously. These were the expansion of the universe, the effects of gravity on light, and the effects of gravity on matter.

Using a statistical method known as Bayesian inference, we reconstructed the gravity of the universe through cosmic history in a computer model based on these three parameters. We were able to estimate the parameters using cosmic microwave background data from the Planck satellite, supernova catalogs, and observations of the shapes and distribution of distant galaxies with the SDSS and DES telescopes. We then compared our reconstruction to the prediction of the LCDM model (essentially Einstein’s model).

We found interesting hints of a possible discrepancy with Einstein’s prediction, albeit with rather low statistical significance. This means that there is still a possibility that gravity works differently on a large scale, and that general relativity may need to be adjusted.

Our study also found that it is very difficult to solve the Hubble tension problem by simply changing the theory of gravity. The complete solution would probably require a new ingredient in the cosmological model, which existed before the time when protons and electrons first combined to form hydrogen shortly after the Big Bang, such as a special form of dark matter, an early type of dark energy or primordial magnetic fields. Or, perhaps, there is an as yet unknown systematic error in the data.

That said, our study has shown that it is possible to test the validity of general relativity over cosmological distances using observational data. Although we have not yet solved the Hubble problem, we will have much more data from new probes in a few years.

This means that we will be able to use these statistical methods to continue to tweak general relativity, to explore the limits of modifications, to pave the way for solving some of the open challenges in cosmology.

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