First predicted by Albert Einstein in 1916 as a consequence of general relativity, gravitational waves were conclusively detected on September 14, 2015, by the LIGO collaboration during the merger of two black holes (1). These ripples in spacetime not only affirm Einstein's predictions but also offer unparalleled insights into the universe's most extreme events.
In a study published on September 12, 2017, in Physical Review Letters (2), physicists Juri Smirnov and Moritz Platscher from the Max Planck Institute, alongside Kevin Max from the Scuola Normale Superiore in Pisa, analyzed LIGO data (1). They propose that gravitational waves could oscillate within the framework of bigravity—a modified gravity theory distinct from the bimetric universe models by Andrei Sakharov and Jean-Pierre Petit.
This hypothesis stems from cosmology's biggest puzzles: ordinary matter accounts for just 5% of the universe's density, with dark matter and dark energy dominating the remaining 95%. While many theories invoke exotic particles, LHC experiments have yet to find them. As Smirnov notes, "This prompts us to consider modifying gravity itself."
Smirnov adds, "In our work, we explore the signals a gravity modification would produce. Bigravity predicts a unique signature that sets it apart from other theories."
Bigravity describes the universe's structure and dynamics using two metric tensors—mathematical frameworks for spacetime geometry. General relativity relies on one; bigravity introduces a second.
The metrics, denoted g and f, behave differently: metric g couples to matter, while f remains sterile, interacting solely through gravity. This duality yields two gravitons: the massless one from general relativity and a massive counterpart.
The concept of a massive graviton, traveling slower than light, dates to the 1930s with Wolfgang Pauli. A rigorous framework emerged in 2010 from Claudia de Rham, Gregory Gabadadze, and Andrew Tolley (3). Bigravity builds on this by incorporating the second metric.
Each graviton arises from a unique mix of the two metrics: one massless, the other massive.
This mirrors neutrino oscillations. With three flavors—electron, muon, and tau—electron neutrinos (most commonly produced) are superpositions of mass eigenstates, as Platscher explains: "Their mass isn't fixed but a blend of the three." Bigravity's gravitons follow suit, enabling oscillations.
Gravitons blend g and f metrics, allowing transitions during propagation. Detectors like LIGO sense only g-type waves, produced in events like black hole mergers, as they couple to matter.
En route, g-waves could oscillate into undetectable f-waves. Platscher states, "If bigravity holds, this oscillation imprints a distinct signature on the signal we can measure."
Can LIGO verify bigravity? Smirnov cautions, "As a young theory, bigravity requires further development. Our study lays groundwork, but much exploration lies ahead."
