**Massive Galileons and Vainshtein screening: a numerical perspective**

# Parallel Session: GRAVITY - MODIFIED GRAVITY (B)

## Location: Park 3.23

#### B5 - Wednesday 14:00-15:40 (Thomas Sotiriou)

**14:00-14:20**

**Daniela Saadeh (School of Physics and Astronomy, University of Nottingham)**

Within the landscape of modified theories of gravity, progress in understanding the behaviour of, and developing tests for, screening mechanisms has been hindered by the complexity of the field equations involved, which are nonlinear in nature and characterised by a large hierarchy of scales. This is especially true of Vainshtein screening, where the fifth force is suppressed by high-order derivative terms becoming dominant within a large Vainshtein radius.

I will present phi-enics, a numerical code based on the finite element method that can be used to overcome this problem, and apply it two case studies of interest for screening: a model containing high-order derivative operators in the equation of motion and one characterised by nonlinear self-interactions in two coupled scalar fields. I will use phi-enics to perform a theoretical test of Vainshtein screening, by comparing the behaviour of a set of massive Galileon theories exhibiting screening against their UV completion. We show that the screening does not survive the extension, casting doubt over whether Vainshtein screening can take place within the limits of validity of the theories that invoke it.

**Breaking the Vainshtein screening in clusters of galaxies**

**14:20-14:40**

**Vincenzo Salzano (Institute of Physics, University of Szczecin)**

Extended theories of gravity (ETG) with a screening mechanism have acquired much interest recently in the quest for a viable alternative to General Relativity (GR) on cosmological scales, given their intrinsic property of being able to pass Solar System scale tests and, at the same time, to possibly drive universe acceleration on much larger scales mimicking Dark Energy effects. In this talk we will focus on an ETG model characterized by an intrinsic breaking of the Vainshtein mechanism inside large astrophysical objects. We will explore the possibility that such breaking might be responsible of those gravitational effects which, in the context of GR, are generally attributed to Dark Matter, thus eventually ending with an ETG model which might unify Dark Energy and Dark Matter. Based upon works 1607.02606 and 1701.03517.

**Designing Horndeski and the effective fluid approach**

**14:40-15:00**

**Wilmar Alberto Cardona Castro (Physics , Universidad del Valle)**

We present a family of designer Horndeski models, i.e., models that have a background exactly equal to that of the ΛCDM model but perturbations given by the Horndeski theory. Then, we extend the effective fluid approach to Horndeski theories, providing simple analytic formulae for the equivalent dark energy effective fluid pressure, density and velocity. We implement the dark energy effective fluid formulae in our code EFCLASS, a modified version of the widely used Boltzmann solver CLASS, and compare the solution of the perturbation equations with those of the code hi CLASS which already includes Horndeski models. We find that our simple modifications to the vanilla code are accurate to the level of ∼ 0.1% with respect to the more complicated hi CLASS code. Furthermore, we study the kinetic braiding model (KGB) both on and off the attractor and we find

that even though the full case has a proper ΛCDM limit for large n, it is not appropriately smooth, thus causing the quasistatic approximation to break down. Finally, we focus on our designer model (HDES), which has both a smooth ΛCDM limit and well-behaved perturbations, and we use it to perform MCMC analyses to constrain its parameters with the latest cosmological data. We find that our HDES model can also alleviate the soft 2σ tension between the growth data and Planck 18 due to a degeneracy between σ_8 and one of its model parameters that indicates the deviation from the ΛCDM model.

**Covariant perturbations in scalar-tensor (ST) theory of gravitation**

**15:00-15:20**

**Joseph Ntahompagaze (Physics, University of Rwanda, College of Science and Technology)**

The 1+3 covariant perturbations in scalar-tensor (ST) theory of gravitation is applied to a multi-fluid universe. The scalar and harmonic decompositions are applied to the perturbation equations. As an application, a radiation-dust system together with a scalar fluid as a fluid component in the Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime background will be analyzed for power-law models.

**The effect of the quasi-static approximation on cosmological observables**

**15:20-15:40**

**Francesco Pace (JBCA, University of Manchester)**

A model-independent way of parameterising effects of modified gravity models is the quasi-static approximation. In this approximation, time derivatives are considered to be negligible with respect to spatial derivatives. This implies that, in the Fourier space, only terms proportional to k^2 will usually be considered. The quasi-static approximation will provide time- and scale-dependent expressions for the effective gravitational constant and the slip parameter. These two quantities are enough to fully characterise a model, but they are only approximate expressions and will, therefore, fail on certain scales. In this talk, I will present results of an ongoing study about the goodness of different flavours of the quasi-static approximation in reproducing observable spectra. I will explain how different recipes compare and are related to each other and show how well (or how bad) the modified gravity parameters reproduce the exact numerical expressions and how this translates into observable spectra

#### B6 - Wednesday 16:10-17:50 (Thomas Sotiriou)

**Linear stability analysis of hairy black holes in quadratic DHOST theories**

**16:10-16:30**

**Kazufumi Takahashi (Physics, Kobe University)**

We study static spherically symmetric black hole solutions with a linearly time-dependent scalar field and discuss their linear stability in the shift- and reflection-symmetric subclass of quadratic degenerate higher-order scalar-tensor (DHOST) theories. We present the explicit forms of the reduced system of background field equations for a generic theory within this subclass. Using the reduced equations of motion, we show that in several cases the solution is forced to be of the Schwarzschild or Schwarzschild-(anti-)de Sitter form. We consider odd-parity perturbations around general static spherically symmetric black hole solutions and derive the concise criteria for the black holes to be stable. Our analysis also covers the case with a static or constant profile of the scalar field.

**Black hole perturbations and gauge fixing in generalised kinetic braiding theories**

**16:30-16:50**

**Cecilia Gergely (Department of Theoretical Physics, University of Szeged)**

The recent direct observations of gravitational waves (GWs) have restricted the propagation speed of the tensorial modes of scalar-tensor gravitational theories. Both the study of the dispersion relations of GWs from black hole binary mergers and the coincident gamma-ray counterparts detected from the GWs emitted by the neutron star merger have established that tensorial modes propagate with the speed of light. Generalised kinetic braiding theories form the surviving subset of Horndeski theories, which are exempt from Ostrogradsky instabilities. One way to confirm or falsify such theories is to observe the evolution of the black hole perturbations, the ringdown. We have developed [1] a new 2+1+1 decomposition of space-time based on a nonorthogonal double foliation for the study of the perturbations of spherically symmetric, static black holes in scalar-tensor theories. In contrast with a previous similar attempt, our formalism enabled unambiguous gauge fixing, which resembles most closely the Regge-Wheeler gauge of general relativity. An effective field theory action in terms of metric and embedding type scalars of the decomposition has been varied to give the background equations for scalar-tensor spherically symmetric, static black holes at first order and the perturbation dynamics at the second order.

[1] C. Gergely, Z. Keresztes, L. Á. Gergely, Phys. Rev. D 99, 104071 (2019)

**Dynamic Signatures of Black Hole Binaries with Superradiant Clouds**

**16:50-17:10**

**Jun Zhang (Physics, Imperial College London)**

Superradiant cloud may develop around a rotating black hole, if there is a bosonic field with Compton wavelength comparable to the size of the black hole. In our work, we investigate the effects of the cloud on the orbits of nearby compact objects. In particular, we consider the dynamical friction and the backreaction due to level mixing. Under these interactions, the probability of a black hole dynamically capturing other compact objects, such as stellar mass black holes and neutron stars, is generally enhanced with the presence of cloud. For extreme mass ratio inspirals and binary stellar mass binary black holes, the cloud-induced orbital modulation may be detected by observing the gravitational waveform using space-borne gravitational wave detectors, such as LISA. Interestingly within a certain range of boson Compton wavelength, the enhanced capture rate of stellar mass black holes could accelerate hierarchical mergers, with higher-generation merger product being more massive than the mass threshold predicted by supernova pair instability. These observational signatures provide promising ways of searching light bosons with gravitational waves.

**Two-body Effects for Disformal Dark Energy**

**17:10-17:30**

**Scott Melville (DAMTP, University of Cambridge)**

In scalar-tensor theories of dark energy, matter can experience fifth forces mediated by the scalar field. Solar system tests for such forces provide some of the strongest constraints on these theories beyond LambdaCDM.

We have recently found that these forces can be qualitatively very different in binary orbits away from the ‘test mass’ limit (i.e. when both bodies have nonzero mass), thanks to a resummation of exchange diagrams which occurs at small separation and large relative velocity. This resummation takes place at a similar scale to the Vainshtein screening mechanism, however it is a distinct (two-body) effect which is present in theories which do not enjoy conventional Vainshtein screening. This talk will describe these recent developments in the two-body problem for disformally coupled scalars, and discuss to what extent planetary motion and other approximately binary systems can constrain dark energy.

#### B7 - Thursday 14:00-15:40 (Thomas Sotiriou)

**The Effective Field Theory of Two Interacting Spin-2 Fields**

**14:00-14:20**

**Justinas Rumbutis (Physics, Imperial College London)**

Theories of multiple spin-2 fields appear in various areas of physics. For example, an infinite number of such fields can be found in Kaluza-Klein tower of states from dimensional reduction of higher dimensional gravity as well as in the spectrum of string theory. Massive spin-2 fields are used in some models of dark matter and in cosmic acceleration models. Therefore, it is important to understand what are the possible mutual interactions of multiple massive spin-2 fields. In this talk I will describe the effective field theory (EFT) of two interacting massive spin-2 fields with the highest possible EFT cutoff and the consistency checks of this theory.

**Interacting Spin-2 Fields**

**14:20-14:40**

**Lasma Alberte (Theoretical Physics, Imperial College London)**

We consider the effective field theory of multiple interacting massive spin–2 fields. We focus on the case where the interactions are chosen so that the cutoff is the highest possible, which occurs when the interactions are of the same structure as in ghost free massive gravity. We highlight two classes of interactions.

In the first class the mass eigenstates only interact through potential operators that carry no derivatives in unitary gauge. In the second class, a specific kinetic mixing between the mass eigenstates is included non–linearly. Performing a decoupling and ADM analysis, we point out the existence of a ghost present at a low–scale both for the constrained and unconstrained formulations of the first class of interactions. For the second class of interactions where kinetic mixing is included, we derive the full $Lambda_3$–decoupling limit and confirm the absence of any ghosts.

**Positivity Bounds in Massive Gravity**

**14:40-15:00**

**Arshia Momeni (Physics, Imperial College London)**

Effective field theories of gravity are the central theoretical tool in building cosmological models of the universe. Whether such effective field theories admit a UV completion is not a question that can be answered without assumptions about their properties in the UV. The requirement that the UV completion is Lorentz invariant, unitary, local and causal puts strong constraints on the consistency of low energy effective field theories. These constraints, also known as positivity bounds, have been used to significantly restrict the parameter space of massive gravity theories. In this talk, I will present the results obtained from the application of positivity bounds on the effective field theory of multiple interacting massive spin-2 fields.

**Gauged galileons and massive gravity**

**15:00-15:20**

**Sebastian Garcia-Saenz (Physics, Imperial College)**

The interactions of a massive graviton are greatly simplified at energies far above the particle’s mass — what is known as the decoupling limit of massive gravity — when a description based on massless spin-2, spin-1 and spin-0 fields becomes applicable. The spin-0 sector is particularly interesting, being described by a galileon theory, a property that is at the origin of many of the virtues of massive gravity. This talk is about the opposite story: given a galileon theory, can one derive massive gravity as a low-energy completion? The answer turns out to be yes, and I will show how the gauging of the symmetry that defines the galileon yields all the necessary ingredients to construct theories of massive gravity.

**Cosmological Perturbations in Generalised Massive Gravity**

**15:20-15:40**

**Michael Patrick Roland Kenna-Allison (ICG)**

Generalised Massive Gravity is an extension of dRGT massive gravity which promotes the free parameters of the theory to functions, whilst maintaining Lorentz invariance. In this talk we study cosmological perturbations for the scalar, vector and tensor sectors and outline the no ghost and gradient instability conditions, which in turn put restrictions on the form of the free functions of the theory. Unlike in pure dRGT massive gravity, we find that the vectors no longer have a vanishing kinetic term .

#### B8 - Thursday 16:10-17:50 (Thomas Sotiriou)

**Cosmological implications of a non-minimally coupled scalar field as dark energy**

**16:10-16:30**

**Matteo Braglia (Physics and Astronomy, University of Bologna)**

I discuss the cosmological imprints of a non-minimally coupled scalar field. In the original Jordan frame, where matter particles follow geodesics of the metric, the coupling to gravity regulates both the late time acceleration of the Universe and the time variation of the effective Newton constant. Without resorting to any effective description, I describe the background and perturbed evolution of the Universe for different choices of the scalar field potential and coupling. I describe the linear perturbations and their impact on the CMB observables and matter power spectrum, particularly focusing on a new scalar field isocurvature mode. I then show the current cosmological constraints and forecasts on the model and Post-Newtonian parameters.

**Resolving the Hubble tension with emergent dark radiation in unitary gravity**

**16:30-16:50**

**William Barker (Cavendish Laboratory/Kavli Institute, University of Cambridge)**

We propose a one-parameter extension to LCDM, expected to strongly affect cosmological tensions. An effective dark radiation component in the early universe redshifts away as hot dark matter, then quintessence, leaving a falsifiable cosmic torsion field in the current epoch. Our modified gravity is a new Poincare gauge theory, foremost among the 33 theories recently found algorithmically to be both power-counting renormalisable and free from ghosts and tachyons. To obtain it, we systematically chart the cosmologies of these new theories, as special cases of the most general parity-preserving, Ostrogradsky-stable theory with a Yang-Mills action. As well as the massless 2+ graviton, our theory may contain a massive 0- graviton. The flat Friedmann equations are emergent for any spatial curvature (k-screening), with tension-resolving freedom at the scale-invariant epoch that reliably attracts away to modern LCDM evolution. We close with upcoming Hamiltonian analysis, COSMOMC validation and solar system tests.

**Reviving Horndeski Theory using Teleparallel Gravity after GW170817**

**16:50-17:10**

**Jackson Levi Said (Institute of Space Sciences and Astronomy)**

The binary neutron star merger events associated with the gravitational wave GW170817 and its electromagnetic counterpart GRB170817A has tremendously constrained the gravitational wave speed of propagation to the speed of light to within deviations of at most one part in $10^{15}$. This has severely limited several theories of gravity, one of which is Horndeski gravity which was regarded as a general framework to study modified gravity. By using the toolset of Teleparallel Gravity, a potential solution to the problem surrounding standard Horndeski gravity has been proposed in arXiv:1904.10791. The source of the solution comes from the naturally lower-order nature of Teleparallel Gravity. In arXiv:1907.10057, the propagation of gravitational wave modes are shown to not constraint the $G_4$ and $G_5$ standard Horndeski contributors to the same degree as standard theory. In this talk, I will introduce this new solution, describe the effect this will have on the propagation of gravitational waves as well as some potential effects of this new analogue of Horndeski gravity