A physicist in the US has calculated that dark matter — the unknown entity that makes up the vast majority of matter in the universe — could arise in a simple generalized quantum theory of gravity.

One of the most enduring problems of modern physics is that the theories of gravity and quantum mechanics do not readily mix. For over 90 years Einstein’s general theory of relativity has done a good job of describing gravity at large lengths scales, but it runs into trouble for all things very small, where quantum mechanics prevails. The trouble is in part due to the fact that quantum mechanics predicts the existence of fleeting “virtual” particles, which in Einstein’s equations cause awkward values of infinity.

Most physicists therefore believe we need a quantum theory of gravity. A basic way to explore this idea is by looking at an “effective field theory”, which describes the gravitational force as a well-defined series. In Einstein gravity the series would have just one term: a linear function of R, the curvature of space--time. However, to address quantum issues other terms can be added to the series, such as an R2 function. These higher-order terms contain other parameters, and for R2 one of those parameters is m2, where m is the mass of a new scalar particle or field.

Keep it heavy

A possible side-effect of introducing new terms is that the theory can create gravitational effects that experiments would have shown up already. Consequently theorists usually keep m heavy so that all new effects are hidden until below the so-called Planck length (roughly 10-35 m), where Einstein’s theory of gravity breaks down. Now, however, Jose Cembranos of the University of Minnesota in the US, has found that when he makes m much lighter, the particle can account for dark matter. The particle can be identified as a new graviton, and would operate at lengths of about 0.1 mm or less.

No-one yet knows what dark matter is, although explanations for it are frequently given as hypothetical particles or within modified versions of gravity. Cembranos told physicsworld.com his study is important because “it helps to get a general idea of what can be signals or observations if dark matter is related to the quantum completion of the gravitational interaction.”

“I think the R + R2 model is another interesting example of the similarity and difference of modified gravity versus ‘real’ dark matter,” says HongSheng Zhao at the University of St. Andrews in the UK. “I quite agree that it could be casted as a scalar field, which could clump. Such clumps could bend the orbits of stars like real dark matter, but it is not clear if they will bend the light as real dark matter.”

No need to mention gravity

However, Nemanja Kaloper, a physicist at the Univerity of California at Davis who studies alternative gravity theories says he is not excited about Cembranos’s study. He considers the type of effective field theory approach taken by Cembranos to be normal Einstein gravity with an extra scalar field that explains dark matter only by being fine tuned. “All this can be done without ever mentioning f(R) gravity,” he adds. “None is needed, and actually introducing it is making the story less predictive because the parameter that determines the scalar mass is not uniquely calculable but is very sensitive to the ultraviolet completion of the theory.”

The research is published in Physical Review Letters