High-precision laboratory experiments with neutrons and atoms are converging to a verdict on 'chameleon fields' as a possible explanation of dark energy, explains Tobias Jenke.
The spatial distance between two points in the Universe increases with time, a discovery attributed to Lemaître. Independently of Friedmann, he derived the basic equations for a dynamic Universe, linking the solutions to Slipher's observation of redshift and Hubble's distance measurements of far-away galaxies. Seventy years later, observations of Type-Ia supernovae led by Perlmutter, Schmidt and Riess resulted in the surprising discovery that the expansion of the Universe is accelerating1,2.
The driving force of the Universe's accelerating expansion is referred to as dark energy, a time-dependant generalization of the cosmological constant. Astronomical observations reveal that dark energy accounts for roughly 70% of the total energy density of our Universe. Its origin, however, is completely unknown.
One approach for explaining the source of dark energy involves a scalar field. The discovery of the Higgs boson confirmed the existence of fundamental scalar fields in nature, and many string-theory or supergravity models introduce scalar fields, which are massless on solar-system scales. However, as they generally couple to matter with gravitational strength, the resulting long-range force would violate precision tests of the equivalence principle (EP) of inertial and heavy mass — hence the search for a mechanism effectively screening contributions violating EP.
Khoury and Weltman suggested just such a screening mechanism in 20043. They introduced a scalar field evolving cosmologically and coupling to matter, and called it the 'chameleon field', “since its physical properties, such as its mass, depend sensitively on the environment”3. The theory has two free parameters: a dimensionless coupling strength β, and an exponent n known as the Ratra–Peebles index. The scalar field acquires an effective mass that depends on the local matter density. In high-density regions (like on Earth), this mass is large and the range of the force mediated by the particle is tiny — the EP-violating force is therefore exponentially suppressed. Consequently, chameleon fields seem to be untestable using macroscopic bodies. On cosmological scales, however, the ambient mass density is very low, and the effective mass of the field is comparable to the present Hubble constant. This results in an interaction range of the mediated force of up to several thousands of parsecs. While the Universe expands, its mass density decreases, leading to amplification of the field, which drives the observed accelerated expansion of the Universe.
In 2011, Brax and Pignol discovered that chameleon theories could nevertheless be tested by means of tabletop experiments4. They suggested using quantum states of ultracold neutrons (UCNs) in the Earth's gravitational field. UCNs move very slowly, with velocities of a few metres per second. They are produced in sources like the PF2 neutron turbine at the Institut Laue–Langevin in Grenoble, France. On horizontal, flat surfaces, UCNs form bound quantum states in the linear gravity potential of the Earth. The typical spatial extent of the associated wavefunctions is a few tens of micrometres. Hence, the mass density of UCNs is too low for the screening mechanism of the chameleon field to be significant. The states have energy eigenvalues in the pico-eV range with unique energy differences. Therefore, any two states can be treated as an effective two-level system, enabling resonance spectroscopy techniques to be employed. These techniques were first used in 2009 and were immediately deployed to search for chameleon fields5: the existence of such fields would produce characteristic shifts in the transition frequencies measured. The experiment found no deviation from Newtonian gravity. As a conclusion, chameleon fields with a coupling strength β larger than 5.8 × 108 were excluded, improving previous limits from atomic spectra by a factor of ten million.
Several communities have joined the search for chameleon fields. Today, the best experimental constraints come from an atom interferometry experiment6 examining whether gravitational acceleration depends on local matter density. The testing of the total parameter space for chameleon fields is likely to be completed in the near future. As a result, chameleon fields may have to be ruled out as sources of dark energy. But, more excitingly, any positive result could explain the origin of one of the biggest mysteries in modern physics.