Research teams on both sides of the Atlantic have shown that precise modeling of the universe and its contents will change the detailed understanding of the evolution of the universe and the growth of structure in it. One hundred years after Einstein introduced general relativity, it remains the best theory of gravity, the researchers say, consistently passing high-precision tests in the solar system and successfully predicting new phenomena such as gravitational waves, which were recently discovered by the Laser Interferometer Gravitational-Wave Observatory.

The equations of general relativity, unfortunately, are notoriously difficult to solve. For the past century, physicists have used a variety of assumptions and simplifications in order to apply Einstein's theory to the universe.

On Earth, that's something like averaging the music made by a symphony. The audience would hear a single average note, keeping the overall beat, growing generally louder and softer rather than the individual notes and rhythms of each of the orchestra's instruments.

Wanting details and their effects, U.S. and European teams each wrote computer codes that will eventually lead to the most accurate possible models of the universe and provide new insights into gravity and its effects.

While simulations of the universe and the structures within it have been the subject of scientific discovery for decades, these codes have made some simplifications or assumptions. These two codes are the first to use Einstein's complete theory of general relativity to account for the effects of the clumping of matter in some regions and the dearth of matter in others.

Both groups of physicists were trying to answer the question of whether small-scale structures in the universe produce effects on larger distance scales. Both confirmed that's the case, though neither has found qualitative changes in the expansion of the universe as some scientists have predicted.

"Both we and the other group examine the universe using the full theory of general relativity, and have therefore been able to create more accurate models of physical processes than have been done before," said James Mertens, a physics PhD student at Case Western Reserve University who took the lead in developing and implementing the numerical techniques for the U.S. team.