Brax, Philippe
Davis, Anne-Christine
Noller, Johannes

We analyse the late time cosmology and the gravitational properties of doubly coupled bigravity in the constrained vielbein formalism (equivalent to the metric formalism) when the mass of the massive graviton is of the order of the present Hubble rate. We focus on one of the two branches of background cosmology where the ratio between the scale factors of the two metrics is algebraically determined. We find that the late time physics depends on the mass of the graviton, which dictates the future asymptotic cosmological constant. The Universe evolves from a matter dominated epoch to a dark energy dominated era where the equation of state of dark energy can always be made close to -1 now by appropriately tuning the graviton mass. We also analyse the perturbative spectrum of the theory in the quasi-static approximation, well below the strong coupling scale where no instability is present, and we show that there are five scalar degrees of freedom, two vectors and two gravitons. In Minkowski space, where the four Newtonian potentials vanish, the theory manifestly reduces to one massive and one massless graviton. In a cosmological FRW background for both metrics, four of the five scalars are Newtonian potentials which lead to a modification of gravity on large scales. The fifth one gives rise to a ghost which decouples from pressure-less matter in the quasi-static approximation. In this scalar sector, gravity is modified with effects on both the growth of structure and the lensing potential. In particular, we find that the Sigma parameter governing the Poisson equation of the weak lensing potential can differ from one in the recent past of the Universe. Overall, the nature of the modification of gravity at low energy, which reveals itself in the growth of structure and the lensing potential, is intrinsically dependent on the couplings to matter and the potential term of the vielbeins. We also find that the time variation of Newton's constant in the Jordan frame can easily satisfy the bound from solar system tests of gravity. Finally we show that the two gravitons present in the spectrum have a nontrivial mass matrix whose origin follows from the potential term of bigravity. This mixing leads to gravitational birefringence.

We study a previously largely unexplored branch of homogeneous and isotropic background solutions in ghost-free massive bigravity with consistent double matter coupling. For a certain family of parameters we find 'self-inflated' FLRW cosmologies, i.e. solutions with an accelerated early-time period during the radiation-dominated era. In addition, these solutions also display an accelerated late-time period closely mimicking GR with a cosmological constant. Interestingly, within this family, the particular case of beta(1) =3D beta(3) =3D 0 gives bouncing cosmologies, where there is an infinite contracting past, a non-zero minimum value of the scale factor at the bounce, and an infinite expanding future.

In this paper we consider how the strong-coupling scale, or perturbative cutoff, in a multi-gravity theory depends upon the presence and structure of interactions between the different fields. This can elegantly be rephrased in terms of the size and structure of the 'theory graph' which depicts the interactions in a given theory. We show that the question can be answered in terms of the properties of various graph-theoretical matrices, affording an efficient way to estimate and place bounds on the strong-coupling scale of a given theory. In light of this we also consider the problem of relating a given theory graph to a discretised higher dimensional theory, a la dimensional deconstruction.

In this paper we construct a family of ways in Inch matter can couple to one or more metrics'/spin-2 fields in the vielbein formulation. We do so subject to requiring the weak equivalence principle and the absence of ghosts from pure spin-2 interactions generated by the matter action. Results are presented for Massive, and Multi-Gravity theories and we give explicit expressions for the effective matter metric in all of these cases.

In this paper we construct a family of ways in Inch matter can couple to one or more metrics'/spin-2 fields in the vielbein formulation. We do so subject to requiring the weak equivalence principle and the absence of ghosts from pure spin-2 interactions generated by the matter action. Results are presented for Massive, and Multi-Gravity theories and we give explicit expressions for the effective matter metric in all of these cases.

In this paper we investigate the decoupling limit of a particular class of multi-gravity theories, i.e. of theories of interacting spin-2 fields. We explicitly compute the interactions of helicity-0 modes in this limit, showing that they take on the form of multi- Galileons and dual forms. In the process we extend the recently discovered Galileon dualities, deriving a set of new multi-Galileon dualities. These are also intrinsically connected to healthy, but higher-derivative, multi-scalar field theories akin to ‘beyond Horndeski’ models.

Scargill, James H. C.
Noller, Johannes
Ferreira, Pedro G.

In this paper we study multi-gravity (multi-metric and multi-vielbein) theories in the presence of cycles of interactions (cycles in the so-called 'theory graph'). It has been conjectured that in multi-metric theories such cycles lead to the introduction of a ghost-like instability, which, however, is absent in the multi-vielbein version of such theories. In this paper we answer this question in the affirmative by explicitly demonstrating the presence of the ghost in such multi-metric theories in the form of dangerous higher derivative terms in the decoupling limit Lagrangian; we also investigate the structure of interactions in the vielbein version of these theories and argue why the same ghost does not appear there. Finally we discuss the ramifications of our result on the dimensional deconstruction paradigm, which would seek an equivalence between such theories and a truncated Kaluza-Klein theory, and find that the impediment to taking the continuum limit due to a low strong-coupling scale is exacerbated by the presence of the ghost, when these theories are constructed using metrics.

Mulryne, David J.
Noller, Johannes
Nunes, Nelson J.

We calculate the perturbed action, at second and third order, for a massive three-form field minimally coupled to gravity, and use it to explore the observational predictions of three-form inflation. One intriguing result is that the value of the spectral index is nearly independent of the three-form potential, being fixed solely by the number of e-folds of inflation, with n(s) = 0.97 for the canonical number of 60. Considering the bispectrum, we employ standard techniques to give explicit results for two models, one of which produces a large non-Gaussianity. Finally, we confirm our results by employing a duality relating the three-form theory to a non-canonical scalar field theory and explicitly re-computing results in this dual picture.

We consider generalized chameleon models where the conformal coupling between matter and gravitational geometries is not only a function of the chameleon field phi, but also of its derivatives via higher order co-ordinate invariants (such as partial derivative(mu)phi partial derivative(mu)phi; square phi, ....). Specifically we consider the first such non-trivial conformal factor A(phi; partial derivative(mu)phi partial derivative(mu)phi). The associated phenomenology is investigated and we show that such theories have a new generic massaltering mechanism, potentially assisting the generation of a sufficiently large chameleon mass in dense environments. The most general effective potential is derived for such derivative chameleon setups and explicit examples are given. Interestingly this points us to the existence of a purely derivative chameleon protected by a shift symmetry for phi -> phi + c. We also discuss potential ghost-like instabilities associated with mass-lifting mechanisms and find another, mass-lowering and instability-free, branch of solutions. This suggests that, barring fine-tuning, stable derivative models are in fact typically anti-chameleons that suppress the field's mass in dense environments. Furthermore we investigate modifications to the thin-shell regime and prove a no-go theorem for chameleon effects in non-conformal geometries of the disformal type.

We investigate non-Gaussianity in general single field models without assuming slow-roll conditions or the exact scale invariance of the scalar power spectrum. The models considered include general single field inflation (e.g. Dirac-Born-Infeld and canonical inflation) as well as bimetric models. We compute the full non-Gaussian amplitude A, its size f NL, its shape, and the running with scale n NG. In doing so we show that observational constraints allow significant violations of slow-roll conditions and we derive explicit bounds on slow-roll parameters for fast-roll single field scenarios. A variety of new observational signatures is found for models respecting these bounds. We also explicitly construct concrete model implementations giving rise to this new phenomenology.

We consider general mixtures of isocurvature and adiabatic cosmological perturbations. With a minimal assumption set consisting of the linearized Einstein equations and a primordial perfect fluid we derive the second-order action and its curvature variables. We also allow for varying equation of state and speed of sound profiles. The derivation is therefore carried out at the same level of generality that has been achieved for adiabatic modes before. As a result we find a new conserved super-horizon quantity and relate it to the adiabatically conserved curvature perturbation. Finally we demonstrate how the formalism can be applied by considering a Chaplygin gas-like primordial matter model, finding two scale-invariant solutions for structure formation.

Lagos, Macarena
Baker, Tessa
Ferreira, Pedro G.
Noller, Johannes

We present a method for parametrizing linear cosmological perturbations of theories of gravity, around homogeneous and isotropic backgrounds. The method is sufficiently general and systematic that it can be applied to theories with any degrees of freedom (DoFs) and arbitrary gauge symmetries. In this paper, we focus on scalar tensor and vector-tensor theories, invariant under linear coordinate transformations. In the case of scalar-tensor theories, we use our framework to recover the simple parametrizations of linearized Horndeski and "Beyond Horndeski" theories, and also find higher-derivative corrections. In the case of vector-tensor theories, we first construct the most general quadratic action for perturbations that leads to second-order equations of motion, which propagates two scalar IDoFs. Then we specialize to the case in which the vector field is time-like (a la Einstein-Aether gravity), where the theory only propagates one scalar DoE. As a result, we identify the complete forms of the quadratic actions for perturbations, and the number of free parameters that need to be defined, to cosmologically characterize these two broad classes of theories.

Lagos, Macarena
Bellini, Emilio
Noller, Johannes
Ferreira, Pedro G.
Baker, Tessa

We analyse cosmological perturbations around a homogeneous and isotropic background for scalar-tensor, vector-tensor and bimetric theories of gravity. Building on previous results, we propose a unified view of the effective parameters of all these theories. Based on this structure, we explore the viable space of parameters for each family of models by imposing the absence of ghosts and gradient instabilities. We then focus on the quasistatic regime and confirm that all these theories can be approximated by the phenomenological two-parameter model described by an effective Newton's constant and the gravitational slip. Within the quasistatic regime we pinpoint signatures which can distinguish between the broad classes of models (scalar-tensor, vector-tensor or bimetric). Finally, we present the equations of motion for our unified approach in such a way that they can be implemented in Einstein-Boltzmann solvers.