Two mathematicians have, rather bravely, proposed a unified theory of dark matter and dark energy that alters Einstein’s equations describing the fundamentals of gravity.

Shouhong Wang of Indiana University and Tian Ma of Sichuan University suggest that the law of energy and momentum conservation in spacetime is valid only when normal matter, dark matter and dark energy are all taken into account.

For normal matter alone, energy and momentum are no longer conserved, they say.

The two aren’t arguing with the concept of curved spacetime that Einstein used in his field equations. But, they suggest, the presence of dark matter and dark energy requires a new set of gravitational field equations that take into account a new type of energy caused by the non-uniform distribution of matter in the universe.

This new energy can be both positive and negative, and the total over spacetime is conserved, they say.

The new gravitational field equations are based on curved spacetime, along with a new scalar potential field representing the new energy density, and the interactions between the two.

“Many people have come up with different theories for dark energy,” says Wang. “Unfortunately, the mystery remains, and in fact, the nature of dark energy is now perhaps the most profound mystery in cosmology and astrophysics. It is considered the most outstanding problem in theoretical physics.”

The researchers suggest that the energy-momentum tensor of normal matter is no longer conserved, and that new gravitational field equations follow from Einstein’s principles of equivalence and general relativity, and the principle of Lagrangian dynamics.

“The difference between the new field equations and Einstein’s equations is the addition of a second-order covariant derivative of a scalar potential field,” says Wang.

“Most importantly, this new energy and the new field equations offer a unified theory for both dark energy and dark matter, which until now have been considered as two totally different beasts sharing only ‘dark’ in name. Both dark matter and dark energy can now be represented by the sum of the new scalar potential energy density and the coupling energy between the energy-momentum tensor and the scalar potential field.”

Kevin Zumbrun, chair of the Department of Mathematics at IU Bloomington, says the new unified theory appear sound in principle.

“It is speculative at the cosmological level, since one must match with experiment, but the math is solid,” he said. “It’s a new and elegant angle on things, and if this does match experiment, it is a huge discovery. Quite exciting!”