Conference

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.

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.

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.

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.

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.

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.

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.