Everything in the Universe has gravity – and feels it too. However, this most common of all fundamental forces is also the one that presents the greatest challenges to physicists.

Albert Einstein’s theory of general relativity was extremely successful in describing the gravity of stars and planets, but it does not seem to apply perfectly on all scales.

General Relativity has undergone many years of observational testing, from Eddington’s measurement of the deflection of starlight by the Sun in 1919 to the recent detection of gravitational waves.

However, 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 *Astronomy of Nature*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 general relativity may need to be modified on this scale.

## Defective model?

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

However, according to Einstein, vacuum energy has repulsive gravity – it pushes empty space away. Interestingly, in 1998 it was discovered 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, necessary to explain the acceleration is many orders of magnitude smaller than what quantum theory predicts.

Hence, the big question, dubbed “the old cosmological constant problem,” is whether vacuum energy actually attracts—exerting a gravitational force and changing the expansion of the universe.

If so, then why is its gravity so much weaker than predicted? If the vacuum does not attract 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 also need to assume that there is a type of invisible matter present, called dark matter, to explain how galaxies and clusters evolved into the way we see them today.

These assumptions are built into scientists’ standard cosmological theory, called the lambda cold dark matter model (LCDM) – suggesting that there is 70 percent dark energy, 25 percent dark matter and 5 percent ordinary matter in the universe. 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, taking on strange values that don’t make sense, has prompted many physicists to wonder if Einstein’s theory of gravity needs modification to describe the entire universe.

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

The disagreement, or intensity, is between two values of the Hubble constant.

One is the number predicted by the LCDM cosmological model, which has been developed to match the light left over from the Big Bang (the cosmic microwave background radiation).

The other is the rate of expansion measured by observing exploding stars known as supernovae in distant galaxies.

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

## Looking for answers

We can design tests to test whether the universe obeys 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 tested the basic laws of general relativity. We also explored whether modifying Einstein’s theory could help solve some of the open problems in cosmology, such as the Hubble intensity.

To find out whether general relativity is correct on large scales, we set out, for the first time, to simultaneously investigate three aspects of it. 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 could estimate the parameters using cosmic microwave background data from the Planck satellite, supernova catalogs as well as observations of the shapes and distribution of distant galaxies from 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 mismatch with Einstein’s prediction, albeit with rather low statistical significance.

This means that there is still a possibility that gravity works differently on large scales and that the theory of general relativity may need to be modified.

Our study also found that it is very difficult to solve the Hubble voltage problem by only changing the theory of gravity.

The full solution would probably require a new component in the cosmological model, which would have existed before the time protons and electrons combined to form hydrogen just 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 yet another unknown systematic error in the data.

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

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

*Kazuya Koyama, Professor of Cosmology, University of Portsmouth and Levon Pogosian, Professor of Physics, Simon Fraser University*

**This article is republished from The Conversation under a Creative Commons license. Read the original article.**

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