A thousand years ago, Vikings took Iceland spar to sea. The translucent crystal split light into two rays. By their brightness, they could find the sun even in fog. Birefringence — the physical term for this phenomenon — now helps hunt for the most elusive force in the cosmos.
A century after Einstein, ripples in spacetime, gravitational waves opened a new window. LIGO and Virgo laser antennas catch the tremors from mergers of black holes and neutron stars in close pairs. Identical travel for left and right polarizations is what standard theory predicts. But astrophysical puzzles hint at more. As early as 1933, Fritz Zwicky noticed hidden mass in galaxy clusters. Later, Vera Rubin confirmed this for individual galaxies. And in 1998, Adam Riess and colleagues discovered the accelerated expansion of the Universe, attributed to dark energy. Data from the cosmic microwave background and large-scale structure point to a global asymmetry — perhaps left and right are not equal in space.
Modified gravity offers a way out. One theory is f(R) gravity with a Chern–Simons term. To the Einstein action, they add a function of curvature R and a parity-violating term. It turns spacetime into a giant Iceland spar: left and right gravitational waves feel the cosmos differently. The authors calculated the effect in two formulations: metric and Palatini. In the latter, metric and connection are independent, like notes and an instrument. Here birefringence occurs: both amplitude and speed change. The equation resembles a damped pendulum, but friction and frequency depend on polarization. Formally: h''_{L,R} + $Ξ_{L,R}$ h'_{L,R} + ω²_{L,R} $h_{L,R}$ = 0, where indices L and R denote left and right waves.
Comparison of three f(R) models with cosmological data yielded tangible numbers. In the Palatini formalism, birefringence is enhanced by a few to tens of percent; in the metric formalism, up to a factor of two. Current observations already draw boundaries. From the speed of waves from the merger of two neutron stars — the event GW170817 — the coupling parameter is constrained at the level of 10⁻⁷. That is like measuring the Earth–Moon distance with an error of a hair's thickness. Phase distortions in the GWTC-3 catalog tighten it further: 10⁻¹⁴. The effect grows with redshift not linearly but polynomially. At cosmic distances where dark energy dominates, the signal becomes more noticeable. Next-generation gravitational observatories — LISA, Einstein Telescope — will listen to the Universe at such depths.
The ancient "sunstone" finds a second life. Through polarization distortions, physicists hope to glimpse the nature of dark energy and test whether the cosmos is indifferent to the difference between right and left. If detectors pick up birefringence, it would be a breakthrough no less than the discovery of accelerated expansion. For now, the spacetime crystal keeps its secrets. It awaits the next observer.
Icelandic spar, known to Vikings as a ‘sunstone’, helped find the sun in cloudy weather. Today, its physical analogue in cosmology may help ‘see’ dark energy through the polarization of gravitational waves.