Ordinary 3D Baryon Acoustic Oscillations (BAO) data are model-dependent, requiring the assumption of a cosmological model to calculate comoving distances during data reduction. Throughout the present-day literature, the assumed model is ΛCDM. However, it has been pointed out in several recent works that this assumption can be inadequate when analyzing alternative cosmologies, potentially biasing the Hubble constant (𝐻₀) low, thus contributing to the Hubble tension. To address this issue, 3D BAO data can be replaced with 2D BAO data, which are only weakly model-dependent. The impact of using 2D BAO data, in combination with alternative cosmological models beyond ΛCDM, has been explored for several phenomenological models, showing a promising reduction in the Hubble tension. In this work, we accommodate these models in the theoretically robust framework of bimetric gravity. This is a modified theory of gravity that exhibits a transition from a (possibly) negative cosmological constant in the early universe to a positive one in the late universe. By combining 2D BAO data with cosmic microwave background and type Ia supernovae data, we find that the inverse distance ladder in this theory yields a Hubble constant of 𝐻₀ = (71.0 ± 0.9) km /s/ Mpc, consistent with the SH0ES local distance ladder measurement of 𝐻₀ = (73.0 ± 1.0) km /s/ Mpc. Replacing 2D BAO with 3D BAO results in 𝐻₀ = (68.6 ± 0.5) km /s/ Mpc from the inverse distance ladder. We conclude that the choice of BAO data significantly impacts the Hubble tension, with ordinary 3D BAO data exacerbating the tension, while 2D BAO data provide results consistent with the local distance ladder.

Fifth forces are ubiquitous in modified theories of gravity. In this paper, we analyze their effect on the Cepheid-calibrated cosmic distance ladder, specifically with respect to the inferred value of the Hubble constant (H₀). We consider a variety of effective models where the strength, or amount of screening, of the fifth force is estimated using proxy fields related to the large-scale structure of the Universe. To quantify the level of tension between the local distance ladder and the Planck value for H₀, we calculate the probability of obtaining a test result at least as extreme as the observed one, assuming that the model is correct (the p-value). For all models considered, the level of agreement is ≳20%, relieving the tension compared to the concordance model, exhibiting an agreement of only 1%. The alleviated discrepancy comes partially at the cost of an increased tension between distance estimates from Cepheids and the tip of the red-giant branch (TRGB). Demanding also that the consistency between Cepheid and TRGB distance estimates is not impaired, some fifth force models can still accommodate the data with a probability ≳20%. This provides incentive for more detailed investigations of fundamental theories on which the effective models are based and their effect on the Hubble tension.

Fifth forces are ubiquitous in modified theories of gravity. To be compatible with observations, such a force must be screened on Solar System scales but may still give a significant contribution on galactic scales. If this is the case, the fifth force can influence the calibration of the cosmic distance ladder, hence changing the inferred value of the Hubble constant H₀. In this paper, we analyze symmetron screening and show that it generally increases the Hubble tension. On the other hand, by doing a full statistical analysis, we show that cosmic distance ladder data are able to constrain the theory to a level competitive with Solar System tests—currently the most constraining tests of the theory. For the standard coupling case, the constraint on the symmetron Compton wavelength is λ_C≲2.5  Mpc. Thus, distance ladder data constitutes a novel and powerful way of testing this, and similar, types of theories.

A potential solution to the Hubble tension is the hypothesis that the Milky Way is located near the center of a matter underdensity. We model this scenario through the Lemaître-Tolman-Bondi formalism with the inclusion of a cosmological constant (ΛLTB) and consider a generalized Gaussian parametrization for the matter density profile. We constrain the underdensity and the background cosmology with a combination of data sets: the Pantheon Sample of type Ia supernovae (both the full catalogue and a redshift-binned version of it), a collection of baryon acoustic oscillations data points and the distance priors extracted from the latest Planck data release. The analysis with the binned supernovae suggests a preference for a -13 % density drop with a size of approximately 300 Mpc, interestingly matching the prediction for the so-called KBC void already identified on the basis of independent analyses using galaxy distributions. The constraints obtained with the full Pantheon Sample are instead compatible with a homogeneous cosmology and we interpret this radically different result as a cautionary tale about the potential bias introduced by employing a binned supernova data set. We quantify the level of improvement on the Hubble tension by analyzing the constraints on the B-band absolute magnitude of the supernovae, which provides the calibration for the local measurements of H₀. Since no significant difference is observed with respect to an analogous fit performed with a standard ΛCDM cosmology, we conclude that the potential presence of a local underdensity does not resolve the tension and does not significantly degrade current supernova constraints on H₀.

For more than a century, Einstein's theory of general relativity has described gravitational phenomena with astonishing precision. However, for the theory to fit observations we need to add two elusive substances: dark energy and dark matter. Together they add up to 95% of the energy budget of the Universe. Yet, we do not know what these substances are. Another question mark is the expansion rate of the Universe; two incompatible values are obtained depending on the measuring method. These problems (dark energy, dark matter, and the expansion rate) belong to the big questions within gravity today and they may be interpreted as signs that general relativity is not the final theory for gravity. As an alternative, in this thesis we analyze an extended theory of gravity called bimetric gravity. 

In general relativity (GR), gravity is massless which means that gravitational waves propagate at the speed of light. Hence, a natural extension is to consider theories where gravity has a mass. This is precisely what bimetric gravity achieves. The theoretical consistency of this theory is firmly established but it is also crucial to test if the theory agrees with observations. In fact, in this theory there are two types of gravitational waves/fields, one massless as in GR but also one massive. When observing gravitational phenomena, we observe a mix of the two. Depending on the mixing and on the mass of the massive field, observational signatures appear for example on cosmological scales, in gravitational wave events or on solar-system scales. Until recently the phenomenology of the full theory was still uncharted, and an important question was if all observational tests could be satisfied at the same time. To address this, we devised a unified framework that enables straightforward comparison between constraints from different probes, without being restricted to a particular region of the parameter space. The result is that bimetric gravity is compatible with observations and even fit data slightly better than GR. Together with the fact that the dark energy can be explained by the interaction between the two gravitational fields, we have shown that the theory is a viable dark energy candidate. At the same time, the observational data provides a substantial restriction on the parameter space that excludes many of the popular models in the literature – an important result in and of itself.

A longstanding issue within this theory has been to predict the growth of structure while avoiding exponential instabilities. Here, we propose a simple model which solves the full, nonlinear equations of motion, which can be used to calculate the growth of structure, without any instabilities. We also describe our work towards a framework for calculating the process of gravitational collapse in this theory where we manage to solve the equations numerically for a short time interval. The results indicate that the gravitational collapse proceeds as in general relativity, assuming that the initial conditions are similar.

Future work is needed to decide whether bimetric gravity can solve any of the other big questions within gravity today, such as the discrepant expansion rate of the Universe. In this thesis, we show that it is an observationally viable dark energy candidate that exhibits novel gravitational features. In short, gravity can be massive.

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.

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.

Numerical integration of the field equations in bimetric relativity is necessary to obtain solutions describing realistic systems. Thus, it is crucial to recast the equations  as a well-posed problem. In general relativity, under certain assumptions, the covariant BSSN formulation is a strongly hyperbolic formulation of the Einstein equations, hence its Cauchy problem is well-posed. In this paper, we establish the covariant BSSN formulation of the bimetric field equations. It shares many features with the corresponding formulation in general relativity, but there are a few fundamental differences between them. Some of these differences depend on the gauge choice and alter the hyperbolic structure of the system of partial differential equations compared to general relativity. Accordingly, the strong hyperbolicity of the system cannot be claimed yet, under the same assumptions as in general relativity. In the paper, we stress the differences compared with general relativity and state the main issues that should be tackled next, to draw a roadmap towards numerical bimetric relativity.

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.