We explore spacetime symmetries and topologies of the two metric sectors in Hassan-Rosen bimetric theory. We show that, in vacuum, the two sectors can either share or have separate spacetime symmetries. If stress-energy tensors are present, a third case can arise, with different spacetime symmetries within the same sector. This raises the question of the best definition of spacetime symmetry in Hassan-Rosen bimetric theory. We emphasize the possibility of imposing ansatzes and looking for solutions having different Killing vector fields or different isometries in the two sectors, which has gained little attention so far. We also point out that the topology of spacetime imposes a constraint on possible metric combinations.

Bimetric gravity can reproduce the accelerated expansion of the Universe, without a cosmological constant. However, the stability of these solutions to linear perturbations has been questioned, suggesting exponential growth of structure in this approximation. We present a simple model of structure formation, for which an analytical solution is derived. The solution is well-behaved, showing that there is no physical instability with respect to these perturbations. The model can yield a growth of structure exhibiting measurable differences from ACDM.

Ghost-free bimetric gravity is an extension of general relativity, featuring a massive spin-2 field coupled to gravity. We parameterize the theory with a set of observables having specific physical interpretations. For the background cosmology and the static, spherically symmetric solutions (for example approximating the gravitational potential of the solar system), there are four directions in the parameter space in which general relativity is approached. Requiring that there is a working screening mechanism and a nonsingular evolution of the Universe, we place analytical constraints on the parameter space which rule out many of the models studied in the literature. Cosmological solutions where the accelerated expansion of the Universe is explained by the dynamical interaction of the massive spin-2 field rather than by a cosmological constant, are still viable.

Ghost-free bimetric gravity is a theory of two interacting spin-2 fields, one massless and one massive, in addition to the standard matter particles and fields, thereby generalizing Einstein's theory of general relativity. To parameterize the theory, we use five observables with specific physical interpretations. We present, for the first time, observational constraints on these parameters that: (i) apply to the full theory, (ii) are consistent with a working screening mechanism (i.e., restoring general relativity locally), (iii) exhibit a continuous, real-valued background cosmology (without the Higuchi ghost). For the cosmological constraints, we use data sets from the cosmic microwave background, baryon acoustic oscillations, and type Ia supernovae. Bimetric cosmology provides a good fit to data even for large values of the mixing angle between the massless and massive gravitons. Interestingly, the best-fit model is a self-accelerating solution where the accelerated expansion is due to the dynamical massive spin-2 field, without a cosmological constant. Due to the screening mechanism, the models are consistent with local tests of gravity such as solar system tests and gravitational lensing by galaxies. We also comment on the possibility of alleviating the Hubble tension with this theory.

Bimetric gravity is a ghost-free and observationally viable extension of general relativity, exhibiting both a massless and a massive graviton. The observed abundances of light elements can be used to constrain the expansion history of the Universe at the period of Big Bang nucleosynthesis. Applied to bimetric gravity, we readily obtain constraints on the theory parameters which are complementary to other observational probes. For example, the mixing angle between the two gravitons must satisfy θ≲ 18^∘ in the graviton mass range ≳ 10-16 eV/c2, representing a factor of two improvement compared with other cosmological probes.

In general relativity, the endpoint of spherically symmetric gravitational collapse is a Schwarzschild-[(A)dS] black hole. In bimetric gravity, it has been speculated that a static end state must also be Schwarzschild-[(A)dS]. To this end, we present a set of exact solutions, including collapsing massless dust particles. For these, the speculation is confirmed.

We present a method for solving the constraint equations in the Hassan-Rosen bimetric theory to determine the initial data for the gravitational collapse of spherically symmetric dust. The setup leads to equations similar to those for a polytropic fluid in general relativity, here called Lane-Emden-like equations. Using a numerical code which solves the evolution equations in the standard 3 + 1 form, we also obtain a short-term development of the initial data for these bimetric spherical clouds. The evolution highlights some important features of the bimetric theory such as the interwoven and oscillating null cones representing the essential nonbidiagonality in the dynamics of the two metrics. The simulations are in the strong-field regime and show that, at least at an early stage, if the bimetric initial data are close to those for general relativity, the bimetric evolution stays close to the evolution in general relativity as well, and with no instabilities, albeit with small oscillations in the metric fields. In addition, we determine initial data and first evolution for vacuum bimetric spherically symmetric nonstationary solutions, providing generic counterexamples to a statement analog to Jebsen-Birkhoff theorem in bimetric relativity.