### Conveners

#### Ghost-Free Models of Modified Gravity: Massive Gravity, Horndeski and DHOST Theories, Other Related Models; Their Properties and Solutions.: Block 1

- Dmitry Galtsov ()
- Mikhail Volkov (University of Tours, France)

#### Ghost-Free Models of Modified Gravity: Massive Gravity, Horndeski and DHOST Theories, Other Related Models; Their Properties and Solutions.: Block 2

- Dmitry Galtsov ()
- Mikhail Volkov (University of Tours, France)

### Description

This section will focus on theoretical aspects of various models of modified gravity which are free from unphysical ghostly degrees of freedom with a negative norm. The well known examples are the theories of ghost-free massive gravity and bigravity, which are free from the Boulware-Deser ghost. Related to them are the Galileon models and, more generally, Horndeski and DHOST theories free from the Ostrogradsky ghost. Other examples are provided by the theory of non-local gravity, etc. All of these theories are interesting from the purely theoretical viewpoint and may provide a description of the Dark Energy and/or Dark Matter. Their various aspects may be discussed, as for example their Hamiltonian formulation and constraints; the causal structure and Cauchy problem; disformal dualities and solutions — cosmologies, black holes, ultracompact objects; observational constraints; quantum aspects; etc.

The last few years have witnessed a great enthusiasm for modified theories of gravity and particularly for scalar-tensor theories. The motivations to modify gravity are to test the limits of general relativity on the one hand and also to propose "answers" to open

questions of cosmology and astrophysics. In this context, many theories have emerged and a very complex landscape of theories...

It was found recently that the anisotropies in the homogeneous Bianchi~I cosmology considered within the context of a specific Horndeski theory are damped near the initial singularity instead of being amplified. In this work we extend the analysis of this phenomenon to cover the whole of the Horndeski family. We find that the phenomenon is absent in the K-essence and/or Kinetic Gravity...

I will discuss the general aspects of the Analytic Infinite Derivative (AID) gravity theories. It will be shown in details why an infinite number of derivatives is required to eradicate ghosts. Explicit ghost-free construction will be presented. Then it will be explained how unitarity is maintained in this non-local setup upon accounting loop corrections. Observational aspects will be briefly touched.

The emergence of $R^2$ (Starobinsky) inflation from the semi-classical modification of gravity due to matter quantum fields clearly points out the importance of fundamental physics and the first principles in the construction of successful cosmological models. Along with the observational success, $R^2$ gravity is also an important step beyond general relativity (GR) towards quantum gravity....

We study exact solutions of infinite derivative gravity within the class of so-called almost universal spacetimes. For such an ansatz, the field equations reduce to a single non-local but linear equation which is exactly solvable with the ghost-free choice $\exp(-\ell^2 \Box)$ of the non-local form factor by eigenfunction expansion or using the heat kernel method. This procedure allows us to...

We study the gravitational field of ultrarelativistic spinning objects (gyratons) in a modified gravity theory with higher derivatives. In particular, we focus on a special class of such theories with an infinite number of derivatives known as “ghost-free gravity” that include a nonlocal form factor such as exp(-\Box\ell^2), where \ell is the scale of nonlocality. First, we obtain solutions of...

We discuss different types of solutions (globally regular, black holes, wormholes and cosmological solutions), in the framework of the new two-parameter Palatini scalar-tensor theory with the derivative coupling of a scalar to the Ricci tensor. The metric version of the theory for generic values of two coupling constants is ghostly, but in Palatini version it is ghost-free. The theory admits...

In this talk we will explicitly show how ghost degrees of freedom arise in a sub-class of metric-affine theories unless projective symmetry is enforced. Then, we will generalise the techniques employed in that particular case to argue why ghosts will arise in generic metric-affine theories of gravity around arbitrary backgrounds. We will also discuss some results on possible ways to avoid them.

We developed a CMB Boltzmann solver to test gravity theories in the framework of the degenerate higher-order scalar-tensor (DHOST) theory. This theoretical framework includes the wide class of dark energy models such as the Horndeski theory and its extensions as certain limits, and the general relativity can be also recovered. In this talk, we show how to formulate the linear perturbations of...

Higgs inflation is known to be a minimal extension of the Standard Model allowing for the description of the early Universe inflation. This model is considered as an effective field theory since it has a relatively low cutoff scale, thus requiring further extensions to be a valid description of the reheating phase. We present a novel unified approach to the problem of unitarization and UV...

We comment on the recently introduced Gauss-Bonnet gravity in four dimensions. We argue that although the naive D->4 limit of the Gauss-Bonnet gravity does not work, a well-defined theory is obtained by generalizing a conformal trick employed by Mann and Ross to obtain a limit of the Einstein gravity in D=2 dimensions. This yields a scalar-tensor theory of the Horndeski type that can also be...

Scalar-tensor theories enjoying a shift symmetry can describe black holes with scalar hair. I will discuss which of these theories can give rise to acceptable black holes with hair, based on three requirements. These are stability under generic perturbations, consistency from the point of view of effective field theory, and the existence of a standard UV completion.

I will argue that in the...

We study asymptotically flat black holes with massive graviton hair within the ghost-free Bigravity theory. There have been contradictory statements in the literature about their existence: such solutions were reported some time ago, but later a different group claimed the Schwarzschild solution to be the only asymptotically flat black hole in the theory. We have analyzed the issue ourselves...