# Focus: Photon Mass Gets a Boost

Published August 16, 2002  |  Phys. Rev. Focus 10, 9 (2002)  |  DOI: 10.1103/PhysRevFocus.10.9

#### Photon Mass from Inflation

Tomislav Prokopec, Ola Törnkvist, and Richard Woodard

Published August 15, 2002

Simple physics principles might explain the mysterious magnetic fields that seem to permeate the cosmos. Researchers have suggested that the magnetism might have arisen if normally massless photons possessed mass during the Universe’s early moments of expansion. Now in the 2 September print issue of PRL, they finally show that massive photons could have existed.

The average compass would miss it, but galaxies give off microgauss strength magnetic fields, a millionth as strong as Earth’s own field. Astrophysicists think a “seed” field of at least ${10}^{-30}$ gauss in the era when galaxies began forming could have been amplified to the current value, but even that tiny primordial magnetism seems too large to have been generated so early. When confronted with cosmological anomalies, researchers often turn to a theory of ultra-rapid expansion of space before the big bang called inflation.

Cosmologist Tomislav Prokopec of Germany’s Heidelberg University and colleagues proposed that inflation could plant the seed [1]. In quantum field theory, every particle has a corresponding field extending across space. Inflation pulls those fields like taffy. Most particles, such as the photon, don’t notice this pull. But a few do, including particles called light charged scalars, which appear in several theories. As a result, pairs of virtual charged scalar particles are separated before they can annihilate one another, and they become real particles emerging from the vacuum. The vacuum becomes “polarized,” as particle physicists say.

This polarization affects photons. It takes more energy to produce a photon amidst the sea of scalars, and photons can only propagate a limited distance through them. Effectively, the photon acquires mass. In today’s Universe, other particles probably acquire mass by a similar mechanism: according to theory, they appear massive only because they are surrounded by a cloud of virtual Higgs particles. “It’s like moving through water,” says Prokopec. When inflation ends, photons lose their mass, but some of the extra energy of the electromagnetic field is left behind in the form of a small magnetic field.

Critics have charged that subtleties of the vacuum polarization would ruin the effect, says co-author Richard Woodard of the University of Florida in Gainesville, who wasn’t originally part of the team. But he was always convinced: “I could just see it in my mind.” Now, he’s helped them calculate the vacuum polarization in a mathematically correct way. He offers one caveat, though. The scalar must have a low mass, whereas the hypothetical particle driving inflation has a huge mass (perhaps ${10}^{13}$ GeV). Particle physicists find such disparities “unnatural,” although they’re actively looking for candidate scalars.

Others have looked at generating seed fields from inflation, says Tanmay Vachaspati of Case Western Reserve University in Cleveland, but they had to invoke new physics or got fields that might not be strong enough. “The generality of this result is its great strength,” he says, and should trigger lots of investigation into such massive photons. But there are non-inflationary proposals for generating seed fields as well, he adds.

Prokopec hopes the work will stimulate people to look for other interesting sparks from rubbing quantum field theory and inflation together. For Woodard the effect is “intrinsically neat” because it’s one of a few examples where quantum effects show up on cosmological scales instead of microscopic ones. “If you think about it for a minute, that’s kind of awesome.”

–JR Minkel

JR Minkel is a freelance science writer in New York City.

### References

1. A. C. Davis, K. Dimopoulos, T. Prokopec, and O. Törnkvist, Phys. Lett. B 501, 165 (2001)..