Bimetric Theory Research Articles

2D BAO vs. 3D BAO: Solving the Hubble Tension with Bimetric Cosmology

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.

Perturbations of bimetric gravity on most general spherically symmetric spacetimes

Perturbations of bimetric gravity on most general spherically symmetric spacetimes

Black holes in multimetric gravity

We construct a wide class of black hole solutions to the general theory of ghost-free multimetric gravity in arbitrary spacetime dimension, extending and generalizing the known results in four-dimensional dRGT massive gravity and bigravity. The solutions are split into three generic classes based on whether the metrics can be simultaneously diagonalized—one of which does not exist in dRGT massive gravity nor bigravity, and is only possible when one has more than two interacting metric fields. We also linearize the general multimetric theory to determine the dynamics of the massive spin-2 modes, including examples where this can be done analytically, and use the linear theory to discuss the stability of the four-dimensional multi-Schwarzschild and multi-Kerr solutions. We explain how the instabilities that plague these solutions in dRGT massive gravity and bigravity carry across to the general multimetric theory, touching upon ideas of dimensional deconstruction to make sense of the results. Published by the American Physical Society 2024

Gravitational wave oscillations in bimetric cosmology

Unlike general relativity, in bimetric gravity linear gravitational waves do not evolve as free fields. In this theory there are two types of tensor perturbations, whose interactions are inherited from non-trivial couplings between two dynamical metric tensor fields in the Hassan-Rosen action, and are responsible for the phenomenon of bigravity oscillations. In this work, we analyze the dynamics of cosmological tensor modes in bimetric gravity on sub-horizon scales and close to the general relativity limit. In this limit, the system has a characteristic length scale L that is strictly contained within the comoving Hubble radius. Thus, depending on the magnitude of the comoving wavelength λ relative to L, we identify two regimes of interest where the system can be studied analytically: (i) deep sub-horizon modes with λ ≪ L, whose dynamics can be studied using multiple scale analysis and are characterized by small and slowly evolving super-imposed perturbations; (ii) sub-horizon modes with λ ≫ L, where the dynamics is characterized by fast super-imposed oscillations that can be studied using asymptotic techniques for highly oscillatory problems. Furthermore, our analysis represents a substantial improvement compared to previous analyses based on a generalization of the WKB method, which, as we show, is ill-suited to study the system at hand.

On the absence of ghosts in quadratic bigravity

An extension of the bimetric theory of gravity is considered that includes quadratic Ricci curvature terms associated with each metric. The issue of the Boulware-Deser ghost is analyzed. The Hamiltonian constraint is derived and the existence of a secondary constraint is shown, proving that the theory is ghost-free.

Deformed Fredkin model for the ν=5/2 Moore-Read state on thin cylinders

We propose a frustration-free model for the Moore-Read quantum Hall state on sufficiently thin cylinders with circumferences ≲7 magnetic lengths. While the Moore-Read Hamiltonian involves complicated long-range interactions between triplets of electrons in a Landau level, our effective model is a simpler one-dimensional chain of qubits with deformed Fredkin gates. We show that the ground state of the Fredkin model has high overlap with the Moore-Read wave function and accurately reproduces the latter's entanglement properties. Moreover, we demonstrate that the model captures the dynamical response of the Moore-Read state to a geometric quench, induced by suddenly changing the anisotropy of the system. We elucidate the underlying mechanism of the quench dynamics and show that it coincides with the linearized bimetric field theory. The minimal model introduced here can be directly implemented as a first step towards quantum simulation of the Moore-Read state, as we demonstrate by deriving an efficient circuit approximation to the ground state and implementing it on an IBM quantum processor. Published by the American Physical Society 2024

Post-reionization 21-cm power spectrum for bimetric gravity and its detectability with SKA1-mid telescope

Post-reionization 21-cm power spectrum for bimetric gravity and its detectability with SKA1-mid telescope

BIANCHI TYPE I MAGNETIZED DARK ENERGY COSMOLOGICAL MODEL IN BIMETRIC THEORY OF GRAVITATION

We investigatedBianchitype-I magnetized dark energy cosmological model in bimetric theory of gravitation. The paper explores the geometrical and physical properties of the model inboth power law andexponential law. All the physical parameters of both the lawsare decreasing with time. It is found thatexpansion with steady speed in power law model while in exponential model, our universe has accelerating contraction. Other geometrical and physical properties are also discussed.

A stringy massive double copy

We derive a massive double copy construction within string theory. To this end, we use massive vectors of the open string spectrum that appear in compactifications to four dimensions and construct massive spin-2 tensors as closed string states, thereby mimicking the structure of the massless graviton. We then compute three-point amplitudes for the scattering of massless and massive spin-2 closed string states and reveal the double copy structure of the latter. With these results being finite in the string scale, we are further able to reproduce the cubic Lagrangian of ghost-free bimetric theory around flat spacetime for bulk massive spin-2 states originating in products of vectors of extended brane supersymmetry.

Intersections of twisted forms: New theories and double copies

Tree–level scattering amplitudes of particles have a geometrical description in terms of intersection numbers of pairs of twisted differential forms on the moduli space of Riemann spheres with punctures. We customize a catalog of twisted differential forms containing both already known and new differential forms. By pairing elements from this list intersection numbers of various theories can be furnished to compute their scattering amplitudes. Some of the latter are familiar through their CHY description, but others are unknown. Likewise, certain pairings give rise to various known and novel double–copy constructions of spin–two theories. This way we find double copy constructions for many theories, including higher derivative gravity, (partial massless) bimetric gravity and some more exotic theories. Furthermore, we present a derivation of amplitude relations in intersection theory.

Cosmological evolution in bimetric gravity: observational constraints and LSS signatures

Bimetric gravity is an interesting alternative to standard GR given its potential to provide a concrete theoretical framework for a ghost-free massive gravity theory. Here we investigate a class of Bimetric gravity models for their cosmological implications. We study the background expansion as well as the growth of matter perturbations at linear and second order. We use low-redshift observations from SnIa (Pantheon+ and SH0ES), Baryon Acoustic Oscillations (BAO), the growth (fsigma _{8}) measurements and the measurement from Megamaser Cosmology Project to constrain the Bimetric model. We find that the Bimetric models are consistent with the present data alongside the Lambda CDM model. We reconstructed the “ effective dark energy equation of state”(omega _{de}) and “Skewness”(S_{3}) parameters for the Bimetric model from the observational constraints and show that the current low-redshift data allow significant deviations in omega _{de} and S_{3} parameters with respect to the Lambda CDM behaviour. We also look at the ISW effect via galaxy-temperature correlations and find that the best fit Bimetric model behaves similarly to Lambda CDM in this regard.

Absence of gravitational polarization mechanism in the canonical bimetric theory

Absence of gravitational polarization mechanism in the canonical bimetric theory

Bimetric-affine quadratic gravity

Bimetric gravity is a theory of gravity that posits the existence of two interacting and dynamical metric tensors. The spectrum of bimetric gravity consists of a massless and a massive spin-2 particle. The form of the interactions between the two metrics ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ and ${f}_{\ensuremath{\mu}\ensuremath{\nu}}$ is constrained by requiring absence of the so-called Boulware-Deser ghost. In this work we extend the original bimetric theory to its bimetric-affine counterpart, in which the two connections, associated with the Ricci scalars, are treated as independent variables. We examine in detail the case of an additional quadratic in the Ricci scalar curvature term ${\mathcal{R}}^{2}(g,\mathrm{\ensuremath{\Gamma}})$ and we find that this theory is free of ghosts for a wide range of the interaction parameters, not excluding the possibility of a dark matter interpretation of the massive spin-2 particle.

Equations of Motion for Charged Spinning Fluid in Bi-metric Type Theories of Gravity

The General theory of relativity is one of the most successful theories ofgravity. Despite its successful applications, it has some difficulties in examiningthe behaviour of particles precisely in strong gravitational fields. Bi-metric typetheories of gravity are classified as alternative theories of gravity that describingsuch strong gravitational fields, such as the gravitational field formed at the coreof our galaxy. In order to obtain the equations of motion for spinning fluids, weuse the Weyssenhoff tensor to express the spin fluid. The equations of motion forspinning fluids are derived using Euler-Lagrange equation. We present theequations of motion for spinning fluids and their corresponding spin deviationequations in some classes of Bi-metric type theories. Also, we obtain equationsof motion for spinning fluids and their corresponding spin deviation for avariable mass. Moreover, we extend our study to examine the status of motionfor spinning charged fluids and their corresponding spin deviation equations.

Non-relativistic and ultra-relativistic scaling limits of multimetric gravity

We present a method of contraction that can be applied to re-construct the recent extended non-relativistic and ultra-relativistic algebras as well as corresponding action principles. The methodology involves the use of multiple copies of Poincaré algebra. Consequently, the contraction defines non-relativistic or ultra-relativistic limits of multimetric theories of gravity. In particular, we show that the non-relativistic scaling limit of bi-metric gravity corresponds to the recent formulation of an action principle for Newtonian gravity with a constant background mass density.

Towards modified bimetric theories within non-product spectral geometry

We discuss a class of doubled geometry models with diagonal metrics. Based on the analysis of known examples we formulate a hypothesis that supports treating them as modified bimetric gravity theories. Certain steps towards the generic case are then performed.

Non-Gaussian signatures of a thermal Big Bang

What if Big Bang was hot from its very inception? This is possible in a bimetric theory where the source of fluctuations is thermal, requiring the model to live on a critical boundary in the space of parameters and can be realized when an anti-DBI brane moves within an EAdS 2 × E 3 geometry. This setup renders the model unique, with sharp predictions for the scalar spectral index and its running. We investigate the non-Gaussian signatures of this thermal bimetric model, or “bi-thermal” for short. We adapt the standard calculation of non-Gaussianities for P(X,ϕ) models to the thermal nature of the model, emphasising how the bi-thermal peculiarities affect the calculation and alter results. This leads to precise predictions for the shape and amplitude of the three-point function of the bi-thermal model (at tree-level): f local NL = -3/2 and f equil NL = -2 + 4 √(3)π/9 ≃ 0.4. We also discover a new shape of flattened non-gaussianity ∝ (k 1 + k 2 - k 3)-3/2 + permutations, which is expected due to the excited thermal initial conditions. These results, along with our earlier predictions for the scalar power spectrum, provide sharp targets for the future generation of cosmological surveys.

Spectral interaction between universes

We derive a perturbative formula for the direct interaction between two four-dimensional geometries. Based on the spectral action principle we give an explicit potential up to the third order perturbation around the flat vacua. Wepresent the leading terms of the interaction as polynomials of the invariants of the two metrics and compare the expansionto the models of bimetric gravity.

Cosmological future singularities in massive gravity and massive bigravity

We study the future cosmological singularities in the framework of massive gravity and minimal massive bigravity theory. In this regards, we consider the possible classes of finite-time future singularities such as sudden, big rip, big freeze and big brake singularities in the massive universe. In dRGT model with an open expanding universe we obtain the sudden singularity in the future at a finite-time which generally without taking account of any particular realistic equation of state, is not avoidable and except the fluid density, all dynamical physical quantities such as pressure approach to infinity. To complete our study, we search the future cosmological singularities in the context of minimal massive bigravity theory and we find that the cosmology of this theory suffers from the sudden and big brake singularities, in which we can see that the parameters of the model approaches to zero the sudden singularity can be removed.

Low redshift constraints on scale-covariant models

The search for a physical model which explains the observed recent acceleration of the universe is a compelling task of modern fundamental cosmology. Recently Fernandes \textit{et al.} presented low redshift observational constraints on a scale invariant model by Maeder. Phenomenologically this can be interpreted as a bimetric theory with a time-dependent cosmological constant. It was shown that a matter density $\Omega_m\sim0.3$ is a poor fit to the data, and the best-fit model would require a fluid with a much smaller density and a significantly positive equation of state parameter. This model is a particular case of an earlier and broader class of models by Canuto \textit{et al.}, which we study here. Specifically, we consider it in two distinct scenarios: as a genuine alternative to $\Lambda$CDM (i.e., without any cosmological constant) and as a parametric extension thereof (where both a cosmological constant and the new mechanism can coexist, and the relative contributions of both are determined by the data). We find that the first scenario can in principle fit the low-redshift data (but a good fit would require values of model parameters, such as the matter equation of state, in conflict with other data), while in the second one the deviation from $\Lambda$CDM is constrained to be small.