50 Years of Horndeski Gravity: Exploring Modified Gravity

Jul 15, 2024, 8:00 a.m. → Jul 19, 2024, 5:00 p.m. America/Toronto

PI/1-100 - Theatre (Perimeter Institute for Theoretical Physics)

Recent years have seen a flood of new data, from gravitational wave observations of merging black holes and neutron stars to precision probes of cosmology, which allow for unprecedented tests of our understanding of gravity. Going hand-in-hand with this, there has been significant recent progress on the theoretical side in terms of formulating modified theories of gravity, and using them to make detailed predictions, including in the nonlinear and dynamical regime, which can be confronted with the observations. 

We are excited to announce a landmark conference that plans to delve into the forefront of research on modified theories of gravity and brings together leading experts from different disciplines including observational astrophysicists, numerical relativists, cosmologists and mathematical physicists to explore the present status of modified theories of gravity and envision their future theoretical development and implications for observations.

This conference is also timed to coincide with the 50th anniversary of pioneering work in this area carried out by Gregory Horndeski in the Waterloo Mathematical Physics Community. Hosted jointly by Perimeter Institute and the University of Waterloo, this conference will serve as a forum for researchers from different disciplines to exchange ideas at the cutting
edge of gravitational physics.
 

Presented by:


 

Sponsored in part by Gravity Theory Trust

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Topics:
• Modified Gravity Theories: Theoretical Framework and Models
• Tests of modified Gravity with Gravitational Waves (LIGO/LISA/PTA)
• Astrophysical/cosmological tests of gravity
• Mathematical structure of Modified gravity
• Observational tests of quantum gravity
• Modified gravity in the early universe

Conference Structure:
The conference will feature a balanced blend of plenary sessions (invited Speakers), contributed talks, panel discussions and poster presentations for students.
• Keynote presentations by renowned physicists in the field, discussing the impact of Horndeski theories and other modified theories of gravity on cosmology, dark energy, and black hole physics.
• Contributed talks: prioritizing early-career researchers
• Panel discussions on emerging research directions, unresolved questions, and potential applications of Horndeski theories.
• Poster sessions for early-career researchers and graduate students to showcase their work and receive feedback from senior scientists.

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Scientific Organizers:

• Ghazal Geshnizjani (Perimeter Institute, SOC Chair)
• William East (Perimeter Institute)
• Levon Pogosian (Simon Fraser University, Perimeter Institute Affiliate)
• Niayesh Afshordi (Perimeter Institute, U Waterloo, LOC Chair)
• Will Percival (Perimeter Institute, U Waterloo)
• Florian Girelli (U Waterloo, Perimeter Institute Affiliate)
• Jerome Quintin (U Waterloo, Perimeter Institute)
• Alex Krolewski (U Waterloo, Perimeter Institute, CITA)

 

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Monday, July 15

8:30 a.m. Registration

Federation Hall
200 University Avenue West
Waterloo, ON, Canada N2L 3G1

1 Welcome Remarks

2 Opening Talk

3 Horndeski Gravity in Cosmology

In this talk I will review how Horndeski gravity made its way in Cosmology and why it became a very popular framework for tests of gravity on cosmological scales.

Speaker: Alessandra Silvestri (Leiden University)

10:15 a.m. Break

4 How we rediscovered Horndeski gravity

I will review the steps that led to the rediscovery and the wide use of Horndeski theories as well as stress some left over open questions and ideas.

Speaker: Cédric Deffayet (École Normale Supérieure)

5 Black holes in Horndeski theories

We will discuss black hole solutions in Horndeski and beyond Horndeski theories. Starting from the no hair paradigm in GR we will elaborate on one of the first black hole solutions with secondary hair. We will then start by introducing stealth solutions, in other words GR metrics endowed with a non trivial scalar field, their regularity properties, shortcomings etc. We will then go on to construct black holes with primary scalar hair which can be regular black holes and modify usual GR static metrics. We will discuss their properties and the status of explicit stationary metrics to conclude.

Speaker: Christos Charmousis (IJCLAB CNRS)

12:30 p.m. Lunch

1:30 p.m. Free Time

6 Hi-COLA: Horndeski Goes Non-linear

Simulating non-linear scales of structure formation is essential to make use of frontier data from Stage IV galaxy surveys. Performing these simulations in modified gravity theories introduces additional challenges, and further forces us to make choices about which theories we deem ‘worth’ the computational investment. Horndeski Gravity is very helpful in this regard, as it encompasses a large swathe of models of major interest.

I’ll introduce Hi-COLA, a software suite which simulates large-scale structure formation in the class of luminal Horndeski theories. Hi-COLA was designed to be:

i) flexible — it avoids hard-coded models and instead receives a user-specified Lagrangian;

ii) consistent — the background expansion history, linear growth and nonlinear screening are solved consistently with one another;

iii) efficient — using the COLA method, large sets of simulations can be generated at low cost.

I’ll explain how Hi-COLA can be used to make robust predictions for scalar-tensor theories on nonlinear scales. If time permits, we’ll also dip a toe into constraining the Horndeski framework with gravitational waves.

Speaker: Tessa Baker (University of Portsmouth)

3:15 p.m. Break

Contributed Talks: Contributed Talks (Session 1)

7 Photon Rings and Shadow Size for General Axi-Symmetric and Stationary Integrable spacetimes

There are now multiple direct probes of the region near black hole horizons, including direct imaging with the Event Horizon Telescope (EHT). As a result, it is now of considerable interest to identify what aspects of the underlying spacetime are constrained by these observations. For this purpose, we present a new formulation of an existing broad class of integrable, axisymmetric, stationary spinning black hole spacetimes, specified by four free radial functions, that makes manifest which functions are responsible for setting the location and morphology of the event horizon and ergosphere. We explore the size of the black hole shadow and high-order photon rings for polar observers, approximately appropriate for the EHT observations of M87*, finding analogous expressions to those for general spherical spacetimes. Of particular interest, we find that these are independent of the properties of the ergosphere, but does directly probe on the free function that defines the event horizon. Based on these, we extend the nonperturbative, nonparametric characterization of the gravitational implications of various near-horizon measurements to spinning spacetimes. Finally, we demonstrate this characterization for a handful of explicit alternative spacetimes.

Speaker: Kiana Salehi (Perimeter Institute/University of Waterloo)

8 Modified gravity getting to the one-point clustering statistics

Gravitational collapse shaped the cosmic large-scale structure and created a plethora of different density environments. For optimally probing gravity with galaxy surveys like Euclid and Rubin LSST, we need to dissect different density environments that are lumped together in traditional two-point statistics. I will explain how the one-point probability distribution of dark matter densities can be predicted analytically including signatures of modified gravity that match with cosmological simulations for nDGP and f(R) gravity. I will provide an outlook on how those predictions can be translated to galaxy clustering and weak lensing and observables.

Speaker: Cora Uhlemann (Universität Bielefeld)

9 Generalized disformal Horndeski theories: consistency of matter coupling and cosmological perturbations

Invertible disformal transformations are a useful tool to investigate ghost-free scalar-tensor theories. By performing a higher-derivative generalization of the invertible disformal transformation on Horndeski theories, we construct a novel class of ghost-free scalar-tensor theories, which we dub generalized disformal Horndeski theories. In the talk, I will clarify the basic idea for constructing the invertible disformal transformation with higher derivatives. I will also discuss some aspects of the generalized disformal Horndeski theories, including the consistency of matter coupling and cosmological perturbations.

Speaker: Dr Kazufumi Takahashi (Yukawa Institute for Theoretical Physics, Kyoto University)

10 Quantum Energy Conditions and Bouncing Cosmologies

Classical energy conditions are used to provide restrictions on the matter fields present in the stress-energy tensor to avoid possible unphysical spacetimes. These classical energy conditions are imperative to the singularity theorems of Hawking and Penrose. However, we know that spacetime breaks down near said singularities and a quantum theory of gravity is needed. One insight into this area is semi-classical gravity where the spacetime is kept “classical” and the stress-energy tensor is quantized. In this regime one may ask what reasonable restrictions should be imposed on the quantum expectation of the stress-energy tensor? One such possibility is the smeared null energy conditions (SNEC). We will review motivation for the SNEC and explore its consequences in cosmological spacetimes that would otherwise violate the classical null energy condition, such as bouncing cosmologies.

Speaker: Brayden Hull (UWaterloo & PI)

11 Spontaneous scalarization in scalar-Gauss-Bonnet gravity and beyond

In my talk I will discuss the black hole spontaneous scalarization in scalar-Gauss-Bonnet gravity. Some of the basic ideas, results and astrophysical consequences will be presented.
I will also discuss a new fully non-linear dynamical mechanism for the formation of scalarized black holes which is different from the spontaneous scalarization.

Speaker: Prof. Stoytcho Yazadjiev (Sofia University)

Poster Session

Tuesday, July 16

12 Do Neutron stars k-mouflage?

Scalar-tensor theories with a screening mechanism can serve as a viable model of cosmic acceleration, while still passing existing local tests of gravity. The validity of different screening mechanisms, such as kinetic screening (or k-mouflage) has been studied extensively in static and weak field regimes. However, only recently have works started to focus on determining whether these would work as expected near extremely compact objects. In this talk I will discuss some recent efforts to characterise kinetic screening mechanisms in these highly dynamical and non-linear regimes using numerical relativity in the case of a single oscillating neutron star, as well as how this picture may change for a binary neutron star configuration in a quasi-equilibrium state.

Speaker: Dina Traykova (Max Planck Institute for Gravitational Physics)

13 Scalarized black holes - from equilibrium models to nonlinear dynamics

Black holes in Horndeski theories of gravity are a perfect playground for exploring possible deviations from General Relativity in a theory-specific manner and studying their astrophysical manifestation. I will review the recent advances in constructing stationary hairy black hole models in Gauss-Bonnet theories. Special attention will be paid to their nonlinear dynamics when isolated or put in a binary, and the resulting astrophysical implications. The potential loss of hyperbolicity will also be discussed.

Speaker: Daniela Doneva (University of Tuebingen)

10:30 a.m. Break

14 Nonlinear dynamics of compact object mergers in Einstein-scalar-Gauss-Bonnet gravity

In recent years, gravitational wave observations of compact objects have provided new opportunities to test our understanding of gravity in the strong-field, highly dynamical regime. To perform model-dependent tests of General Relativity with these observations, one needs accurate inspiral-merger-ringdown waveforms in alternative theories of gravity. In this talk, we will discuss the nonlinear dynamics of compact object mergers in a class of modified theories of gravity, as well as the challenges in numerically obtaining those solutions. The theory we focus on is Einstein-scalar-Gauss-Bonnet gravity, which is a representative example of a Horndeski gravity theory and is interesting because it admits scalar hairy black hole solutions.

Speaker: Maxence Corman

15 Black hole binaries in Einstein-scalar-Gauss-Bonnet gravity and their effective-one-body description

I will show how to derive libraries of semi-analytic gravitational waveforms for coalescing “hairy” black hole binaries, focusing on the example of Einstein-scalar-Gauss-Bonnet gravity (ESGB). To do so, I will start from the state-of-the-art, effective-one-body waveform model “SEOBNRv5PHM” in general relativity, and deform it with ESGB corrections to infer inspiral-merger-ringdown waveform estimates.

Speaker: Félix-Louis Julié (Max Planck Institute for Gravitational Physics)

12:30 p.m. Lunch

Poster Session

Contributed Talks: Contributed Talks (Session 2)

16 Constructing rotating black holes in Horndeski gravity

Exploring the structure of compact objects in modified theories of gravity is mandatory to parametrize the possible deviations w.r.t general relativity and confront these theories to the current and future observations. While important efforts have been devoted to understand the phenomenology of stars and black holes, it is still a challenging task to provide new exact analytical solutions describing rotating black hole in such theories. In this talk, I propose to recent efforts to construct such solutions. Concretely, I will review how one can mix the disformal field redefinitions affect the Petrov type of a given gravitational field and how this can be used to constrain the derivation of rotating black hole. Then, I will review the main properties of a new solution of a subset of Horndeski theories called the disformal Kerr black hole and comment on the most promising directions to derive exact rotating black hole solutions in scalar-tensor theories.
This talk will be based on the two articles: https://inspirehep.net/literature/1800972, https://inspirehep.net/literature/1877661

Speaker: Jibril BEN ACHOUR (Arnold Sommerfeld Center (Germany) / ENS de Lyon (France))

17 Assessing observational constraints on dark energy

Observational constraints on time-varying dark energy are commonly presented in terms of the two CPL parameters $w_0$ and $w_a$. Recent observations favor a sector of this parameter space in which $w_0 > -1$ and $w_0 + w_a < -1$, suggesting that the equation of state underwent a transition from violating the null energy condition (NEC) at early times to obeying it at late times. In this talk, I will demonstrate that this initial impression is misleading, by showing that simple quintessence models satisfying the NEC at all times predict an observational preference for the same sector. The upshot is that the CPL parameterization is simultaneously useful for detecting deviations from cosmological-constant dynamics ($w = -1$) but unreliable for predicting the true behavior of $w(z)$.

Speaker: David Shlivko (Princeton University)

18 Quasinormal modes and non-linear behaviour

Gravitational waves from black hole binary mergers can tell us a lot about the physics of the system. At the late part of the graviational wave signal, GR predicts the presence of characteristic frequencies (called quasinormal modes) in the signal. Measuring multiple quasinormal modes is a strong consistency test for GR.

Here we probe the regime where a signal can be described entirely by quasinormal modes. We consider a higher order effect, where the remnant black hole is absorbing some radiation and so has a changing mass and spin. We test the contribution of this effect to the signal in a physically relevant scenario. We find evidence that this effect causes other mode excitations as well as a changing frequency contribution.

Speaker: Taillte May (Perimeter Institute)

19 Non-linear gravitational waves in Horndeski gravity

The non-linear dynamics of gravitational wave propagation in spacetime can contain drastic new phenomenology that is absent from the linearised theory. In this talk, I will probe the non-linear radiative regime of Horndeski gravity by making use of disformal field redefinition. I will discuss how disformal transformations alter the properties of congruences of geodesics and in particular how they can generate disformal gravitational waves at the fully non-linear level. I will illustrate this effect by presenting a new exact radiative solution in Horndeski gravity describing a scalar pulse. Analysing the non-linear dynamics of this new radiative solution will show that it contains tensorial gravitational waves generated by a purely time-dependent scalar monopole. This intriguing result is made possible by the higher-order nature of Horndeski gravity.

Speaker: Dr Hugo Roussille (École Normale Supérieure de Lyon)

20 Formulating the complete initial boundary value problem in numerical relativity to model black hole echoes

Recently, there has been much interest in black hole echoes, based on the idea that there may be some mechanism (e.g., from quantum gravity) that waves/fields falling into a black hole could partially reflect off of an interface before reaching the horizon. There does not seem to be a good understanding of how to properly model a reflecting surface in numerical relativity, as the vast majority of the literature avoids the implementation of artificial boundaries, or applies transmitting boundary conditions. Here, we present a framework for reflecting a scalar field in a fully dynamical spherically symmetric spacetime, and implement it numerically. We study the evolution of a wave packet in this situation and its numerical convergence, including when the location of a reflecting boundary is very close to the horizon of a black hole. This opens the door to model exotic near-horizon physics within full numerical relativity.

Speaker: Conner Dailey (UWaterloo & PI)

3:30 p.m. Break - Presenters should remove posters

21 Town Hall - Modified gravity strong field regime

Lead: Will East

Speakers: Enrico Barausse, Laura Bernard, Maxence Corman, Suvendu Giri

Wednesday, July 17

22 Gravitational wave generation in effective field theories of dark energy

I will present the class of effective field theories of dark energy, which aim to reproduce a dark energy-like phenomenology by modifying general relativity with the addition of a scalar graviton. I will review how non-linearities can "screen" local scales from scalar effects, therefore allowing these theories to pass existing solar-system experimental tests. I will then present fully relativistic simulations of gravitational wave generation in these theories in 1+1 dimensions (stellar oscillations and collapse) and 3+1 dimensions (binary neutron stars). I will show that screening tends to suppress the (subdominant) dipole scalar emission in binary neutron star systems, but it fails to quench monopole scalar emission in gravitational collapse, and quadrupole scalar emission in binaries. This opens the way to the exciting possibility of testing dark energy with gravitational wave data.

Speaker: Enrico Barausse (International School for Advanced Studies (SISSA))

23 Beyond Horndeski theories

This talk will introduce scalar-tensor theories of gravity that contain a single scalar degree of freedom in addition to the usual tensor modes. These theories constitute the very broad family of Degenerate Higher-Order Scalar-Tensor (DHOST) theories, which include and extend Horndeski theories. Cosmological aspects of these theories will then be discussed. Finally, I will also present some results concerning black hole perturbations in the context of these models of modified gravity.

Speaker: David Langlois (APC/Université Paris Cité, CNRS)

10:30 a.m. Break

24 Non-linear dark energy simulations

The coming years will see an amazing increase in data on the large-scale structure of the Universe, ushering in a new phase for "precision cosmology". One of the major questions in fundamental physics concerns the nature of the dark energy, and the new data may help to shed light on this issue. But in order to unlock the full power of the future data to test alternative models like Horndeski Gravity, we need theoretical predictions that are as accurate as the new observations on all scales, including non-linear scales. In my presentation I will introduce our relativistic N-body code for cosmological simulations, gevolution, and how we are using it to look at non-linear effects in the Universe. In particular I will discuss our k-essence simulations, how to use them for cosmology, and what can happen when dark energy clustering becomes non-linear in models with low speed of sound.

Speaker: Martin Kunz (University of Geneva)

25 Testing screened modified gravity models

Since the discovery of the accelerated expansion of the universe, significant progress has been made to develop modified gravity theories as alternatives to dark energy and these have been developed into tests of General Relativity itself via cosmological observations. These models share common properties such as screening mechanisms they use to evade the stringent Solar System tests. In this talk, I will review recent status of observational tests of screened modified gravity models and discuss the prospect of cosmological tests of gravity from ongoing surveys such as Euclid.

Speaker: Kazuya Koyama (University of Portsmouth)

12:30 p.m. Lunch

1:30 p.m. // Free Time

Contributed Talks: Contributed Talks (Session 3)

26 Constraining modified gravity models using galaxy cluster masses

We present a comprehensive joint analysis of two distinct methodologies for measuring the masses of galaxy clusters: hydrostatic measurements and caustic techniques. We show that by including cluster-specific assumptions obtained from hydrostatic measurements in the caustic method, the potential mass bias between these approaches can be significantly reduced. While this may appear to diminish the caustic method as a technique independent of the dynamical state of a cluster, it provides a means to refine mass constraints and offers an avenue for scrutinizing modifications to gravity. Applying this approach to two well-observed massive galaxy clusters A2029 and A2142, we find no discernible mass bias, affirming the method's validity. We draw a similar conclusion when applying this approach to modified gravity models. Specifically, our implementation allows us to investigate Chameleon and Vainshtein screening mechanisms, enhancing our understanding of these modified gravity scenarios.
Furthermore, we explore the prospect of achieving more precise constraints with fewer systematic errors by exclusively employing the caustic method to constrain screening mechanisms on a larger scale, encompassing several hundred stacked galaxy clusters.

Speaker: Ms Minahil Adil Butt (SISSA)

27 mochi_class: A tool to streamline cosmological analyses of Horndeski's gravity

I will introduce mochi_class, a refined version of the popular Einstein-Boltzmann solver hi_class optimised for calculations within Horndeski's gravity framework. Thanks to (i) a re-parametrisation of Horndeski functions, (ii) a numerically stable quasi-static approximation, and (iii) support for time-dependent inputs, mochi_class enhances hi_class capabilities and nicely complements other public Einstein-Boltzmann solvers. Additionally, I will present a non-parametric approach that, when integrated with Principal Component Analysis, can effectively reconstruct Horndeski functions from well-studied modified gravity models, extending the exploration of scalar-tensor theories beyond conventional parametrisations. I will conclude by highlighting practical applications where mochi_class can prove instrumental in analysing current and forthcoming large-scale structure data.

Speaker: Dr Matteo Cataneo (University of Bonn)

28 Testing gravity with the Dark Energy Survey

Measurements of the large-scale distribution of matter in the Universe are one of our primary tools for testing the predictions of general relativity on cosmological scales. I will describe how we pursue this using data from galaxy imaging surveys, focusing on Dark Energy Survey galaxy clustering and weak lensing analyses as an example. I will highlight results from the DES Year 3 analysis that are relevant for testing gravity, some practical aspects of extending survey analyses beyond ΛCDM, as well as ongoing work to address these challenges to prepare for future surveys.

Speaker: Jessica Muir (Perimeter Institute)

29 A Cosmic Glitch in Gravity

We present a model that modifies general relativity on cosmological scales, specifically by having a 'glitch' in the gravitational constant between the cosmological (super-horizon) and Newtonian (sub-horizon) regimes. This gives a single-parameter extension to the standard ΛCDM model, which is equivalent to adding a dark energy component, but where the energy density of this component can have either sign. Fitting to data from the Planck satellite, we find that negative contributions are, in fact, preferred. Additionally, we find that roughly one percent weaker superhorizon gravity can somewhat ease the Hubble and clustering tensions in a range of cosmological observations. Therefore, the extra parametric freedom offered by our model deserves further exploration, and we discuss how future observations may elucidate this potential cosmic glitch in gravity, through a four-fold reduction in statistical uncertainties.

Speaker: Mr Yunfei Wen (California Institute of Technology)

30 Cosmological implications from DESI Y1 BAO and Future Forecasts

We present key cosmological findings from the Dark Energy Spectroscopic Instrument (DESI)’s first year baryon acoustic oscillations (BAO) measurements. DESI's BAO provide robust measurements of the transverse comoving distance and Hubble rate across seven redshift bins, spanning a redshift range of 0.1 < z < 4.2. DESI BAO data alone align well with the flat ΛCDM model with Ωm=0.295±0.015. Paired with a baryon density prior from Big Bang Nucleosynthesis and the acoustic angular scale from the cosmic microwave background (CMB) data, we find H0=68.52±0.62 km/s/Mpc. Combined analyses with CMB anisotropies and lensing from Planck and ACT yield Ωm=0.307±0.005 and H0=67.97±0.38 km/s/Mpc. Extending the baseline model with a constant dark energy equation of state parameter, w, results in w=−0.99+0.15−0.13. In a dark energy model with time-varying equation of state parametrized by w0 and wa, combined with various supernovae data, indicate deviations from ΛCDM at significance levels up to 3.9σ. For flat ΛCDM with the sum of neutrino mass free, DESI and CMB establish an upper limit of ∑ mν <0.072 (0.113) at 95% confidence for a ∑mν>0 (0.059) eV prior. We will also show forecasts for Y3 and Y5 results as well as prospects with DESI II.

Speaker: Hanyu Zhang

3:30 p.m. Break

31 Town Hall - New generation of LSS surveys and modified gravity/dark energy

Lead: Alex Krowlewski

Speakers: Hanyu Zhang, Jessie Muir, Kazuya Koyama, Martin Kunz

5:00 p.m. // Free Time

6:00 p.m. Banquet

Thursday, July 18

32 Post-Newtonian limit of Lorentz-violating scalar-tensor theories

We study the weak-gravity regime of higher-order scalar-tensor theories that are degenerate in the unitary gauge. In a certain subset of theories analogous to Lorentz-violating scalar-tensor theories, we show that the Vainshtein mechanism due to nonlinear derivative interactions does not work. For this family of theories we determine all the PPN parameters in terms of the EFT of dark energy parameters and discuss the experimental bounds.

Speaker: Tsutomo Kobayashi (Rikkyo University)

33 Galileon Duality and its Generalizations

Speaker: Andrew Tolley

10:30 a.m. Break

34 Extending EFT of inflation/dark energy to arbitrary background with timelike scalar profile

I extend EFT of inflation/dark energy to arbitrary background with timelike scalar profile. In this framework a set of consistency relations among EFT coefficients ensures the spatial diffeo invariance. Some applications to will also be discussed.

Speaker: Shinji Mukohyama (Kyoto University)

240718mukohyama.pdf

35 Against Horndeski

The Horndeski program is motivated by arguing that scalar-tensor modifications to gravity should have two properties: effective interactions that are at most second-order in time derivatives and only a single scalar. I will argue against both of these criteria. First I argue why the low-energy limit of known well-behaved theories can have more than two-derivative field equations. Second I argue why the scalar-tensor interactions most likely to be found competing with gravity at very low energies typically are those with two derivatives, at least when semiclassical methods are justified, and this suggests exploring multiple-scalar models.

Speaker: Cliff Burgess

12:30 p.m. Group Photo

12:40 p.m. Lunch

1:30 p.m. Free Time

Contributed Talks: Contributed Talks (Session 4)

36 Bouncing cosmology; a solution to the singularity problem and more.

Finding a complete explanation for cosmological evolution in its very early stages (about 13 billion years ago) can significantly advance our understanding of physics. Over the past few decades, several models have been proposed, with the majority falling into a category called inflationary universes, where the universe experiences rapid exponential expansion. Despite numerous achievements of inflationary models in explaining the origin of the universe, it has been shown that inflationary models generically suffer from being geodesically past incomplete, which is a representation of singularity. Motivated by addressing the singularity problem, we review a recent model of the early universe, called Cuscuton bounce. This model utilizes a theory of modified gravity by the same name, i.e., Cuscuton, which was originally proposed as a dark-energy candidate, to produce a bouncing cosmology. It has been shown that within the Cuscuton model, we can have a regular bounce without violation of the null energy condition in the matter sector, which is a common problem in most bouncing-cosmology models. In addition, the perturbations do not show any instabilities, and with the help of a spectator field, can generate a scale-invariant scalar power spectrum. We will then set out to investigate if this model has a strong coupling problem or any distinguishing and detectable signatures for non-Gaussianities. We expand the action to the third order and obtain all the interaction terms that can generate non-Gaussianities or potentially lead to a strong coupling problem (breakdown of the perturbation theory). While we do not expect the breakdown of the theory, any distinct and detectable sign of non-Gaussianities would provide an exciting opportunity to test the model with upcoming cosmological observations over the next decade.

Speaker: Mr Amirhossein Dehghanizadeh (The University of Waterloo)

37 Gauss-Bonnet Gravity in 4D and the connection to Horndeski's Theory

In this talk I will review the topic of 4D Einstein-Gauss-Bonnet gravity, which has been the subject of considerable interest over the past years. I will discuss the mathematical complexities involved in implementing this idea, and review recent attempts at constructing well-defined, self-consistent theories that enact it, and their relation to Horndeski gravity. I then move on to consider the interesting phenomenology that results from these theories.

Speaker: Dr Pedro Fernandes (Southern Denmark University)

38 How to study modified gravity as a particle theory and not collapse in the process

The ability to represent perturbative expansions of interacting quantum field theories in terms of simple diagrammatic rules has revolutionized calculations in particle physics. However, in the case of extended theories of gravity, deriving this set of rules requires linearization of gravity perturbation of the scalar fields and multiple field redefinitions making this process very time-consuming and model dependent. In this talk, I will motivate and present FeynMG, a Mathematica extension of FeynRules that automatizes this calculation allowing for the application of quantum field theory techniques to scalar-tensor theories.

Speaker: Dr Sergio Sevillano (Durham University)

39 Scattering amplitudes in high-energy limit of projectable Horava gravity

We study the high-energy limit of projectable Ho\v rava gravity using on-shell graviton scattering amplitudes. We compute the tree-level amplitudes using symbolic computer algebra and analyze their properties in the case of collisions with zero total momentum. The amplitudes grow with collision energy in the way consistent with tree-level unitarity. We discuss their angular dependence and derive the expression for the differential cross section that happens to depend only on the essential combinations of the couplings. One of our key results is that the amplitudes for arbitrary kinematics are finite when the coupling λ in the kinetic Lagrangian is taken to infinity -- the value corresponding to candidate asymptotically free ultraviolet fixed points of the theory. We formulate a modified action which reproduces the same amplitudes and is directly applicable at λ=∞, thereby establishing that the limit λ→∞ of projectable Ho\v rava gravity is regular. As an auxiliary result, we derive the generalized Ward identities for the amplitudes in non-relativistic gauge theories.

Speaker: Jury Radkovski (Perimeter Institute, McMaster University)

40 Theoretical status of Horava gravity

I’ll review the models of quantum gravity postulating invariance with respect to anisotropic (Lifshitz) scaling in the deep ultraviolet domain. At low energies they reduce to scalar-tensor gravity, with a timelike gradient of the scalar field breaking local Lorentz invariance. The models come in two versions differing by the dynamics in the scalar sector. The first, projectable, model has been shown to be perturbatively renormalizable and the full renormalization group (RG) flow of its marginal operators has been computed. The flow possesses a number of asymptotically free fixed points with one of them being connected by RG trajectories to the region of the parameter space where the kinetic term of the theory acquires the general relativistic form. The gravitational coupling exhibits non-monotonic behavior along the flow, vanishing both in the ultraviolet and the infrared. I’ll mention the challenges facing the model in the infrared domain. The second, non-projectable, model is known to reproduce the phenomenology of general relativity in a certain region of parameters. Full proof of its renormalizability is still missing due to its complicated structure. I’ll review recent progress towards constructing such proof.

Speaker: Sergey Sibiryakov (McMaster U. & Perimeter Inst.)

3:30 p.m. Break

41 Town Hall - Fundamental aspects of Modified gravity

Lead: Jerome Quintin

Speakers: Adam Solomon, Andrew Tolley, Astrid Eichhorn, Sergey Sibiryakov

Friday, July 19

42 Simulating a Quantised Black Hole

Speaker: Ruth Gregory (King's College London)

43 Probing quantum gravity at all scales

Speaker: Astrid Eichhorn

10:30 a.m. Break

44 Production of Solar Scalars

I will first introduce screened modified gravity theories and then discuss the chameleon mechanism. Light scalars can be produced from the sun and detected on earth. I will discuss the production of chameleons, including novel production channels, and discuss potential detection in helioscopes.

Speaker: Anne-Christine Davis (University of Cambridge)

45 Effective cuscuton theory

Cuscuton field theory is an extension of general relativity that does not introduce additional propagating degrees of freedom, or violate relativistic causality. We construct a general geometric description of the cuscuton field theory by introducing curvature corrections to both the volume (potential) and the surface (kinetic) terms in the original cuscuton action. Our assumptions involve a stack of spacelike branes, separated by 4-dimensional bulks. We conjecture that the cuscuton, initially a discrete field, becomes continuous in the limit, there are many such transitions. From this we derive an effective action for the cuscuton theory and show that at the quadratic level our theory propagates only the two tensorial degrees of freedom.

Speaker: Maria Mylova (Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU))

46 Closing Remarks

12:30 p.m. // Free time

12:45 p.m. Lunch