Alex Kehagias

The Black hole and FRW geometries of non-relativistic gravity

Abstract We consider the recently proposed non-relativistic Hořava–Lifshitz four-dimensional theory of gravity. We study a particular limit of the theory which admits flat Minkowski vacuum and we discuss thoroughly the quadratic fluctuations around it. We find that there are two propagating polarizations of the metric. We then explicitly construct a spherically symmetric, asymptotically flat, black hole solution that represents the analog of the Schwarzschild solution of GR. We show that this theory has the same Newtonian and post-Newtonian limits as GR and thus, it passes the classical tests. We also consider homogeneous and isotropic cosmological solutions and we show that although the equations are identical with GR cosmology, the couplings are constrained by the observed primordial abundance of 4 He.

New model of inflation with nonminimal derivative coupling of standard model Higgs boson to gravity.

In this Letter we show that there is a unique nonminimal derivative coupling of the standard model Higgs boson to gravity such that it propagates no more degrees of freedom than general relativity sourced by a scalar field, reproduces a successful inflating background within the standard model Higgs parameters, and finally does not suffer from dangerous quantum corrections.

NEW TYPE IIB VACUA AND THEIR F{THEORY INTERPRETATION ?

Abstract We discuss a D3-D7 system in type IIB string theory. The near-horizon geometry is described by AdS5×X5 where X5 is a U(1) bundle over a Kahler-Einstein complex surface S with positive first Chern class c1>0. The surface S can either be P 1 × P 1 , P 2 or P n 1 ,…,n k , a blow up of P 2 at k points with 3≤k≤8. The P 2 corresponds to the maximally supersymmetric AdS5×S5 vacuum while the other cases lead to vacua with less supersymmetries. In the F-theory context they can be viewed as compactifications on elliptically fibered almost Fano 3-folds.

On the Starobinsky Model of Inflation from Supergravity

We discuss how the higher-derivative Starobinsky model of inflation originates from N=1N=1 supergravity. It is known that, in the old-minimal supergravity description written by employing a chiral compensator in the superconformal framework, the Starobinsky model is equivalent to a no-scale model with F-term potential. We show that the Starobinsky model can also be originated within the so-called new-minimal supergravity, where a linear compensator superfield is employed. In this formulation, the Starobinsky model is equivalent to standard supergravity coupled to a massive vector multiplet whose lowest scalar component plays the role of the inflaton and the vacuum energy is provided by a D-term potential. We also point out that higher-order corrections to the supergravity Lagrangian represent a threat to the Starobinsky model as they can destroy the flatness of the inflaton potential in its scalar field equivalent description.

UV-Completion by Classicalization

We suggest a novel approach to UV-completion of a class of non-renormalizable theories, according to which the high-energy scattering amplitudes get unitarized by production of extended classical objects (classicalons), playing a role analogous to black holes, in the case of non-gravitational theories. The key property of classicalization is the existence of a classicalizer field that couples to energy-momentum sources. Such localized sources are excited in high-energy scattering processes and lead to the formation of classicalons. Two kinds of natural classicalizers are Nambu-Gold stone bosons (or, equivalently, longitudinal polarizations of massive gauge fields) and scalars coupled to energy-momentum type sources. Classicalization has interesting phenomenological applications for the UVcompletion of the Standard Model both with or without the Higgs. In the Higgless Standard Model the high-energy scattering amplitudes of longitudinal W -bosons self-unitarize via classicalization, without the help of any new weakly-coupled physics. Alternatively, in the presence of a Higgs boson, classicalization could explain the stabilization of the hierarchy. In both scenarios the high-energy scatterings are dominated by the formation of classicalons, which subsequently decay into many particle states. The experimental signatures at the LHC are quite distinctive, with sharp differences in the two cases.

Relativistic quantum gravity at a Lifshitz point

We show that the Hořava theory for the completion of General Relativity at UV scales can be interpreted as a gauge fixed Tensor-Vector theory, and it can be extended to an invariant theory under the full group of four-dimensional diffeomorphisms. In this respect, although being fully relativistic, it results to be locally anisotropic in the time-like and space-like directions defined by a family of irrotational observers. We show that this theory propagates generically three degrees of freedom: two of them are related to the four-dimensional diffeomorphism invariant graviton (the metric) and one is related to a propagating scalar mode of the vector. Finally, we note that in the present formulation, matter can be consistently coupled to gravity.

Symmetries and Consistency Relations in the Large Scale Structure of the Universe

Abstract We study the symmetries enjoyed by the Newtonian equations of motion of the non-relativistic dark matter fluid coupled to gravity which give rise to the phenomenon of gravitational instability. We also discuss some consistency relations involving the soft limit of the ( n + 1 ) -correlator functions of matter and galaxy overdensities.

Operator product expansion of inflationary correlators and conformal symmetry of de Sitter

We study the multifield inflationary models where the cosmological perturbation is sourced by light scalar fields other than the inflaton. The corresponding perturbations are both scale invariant and special conformally invariant. We exploit the operator product expansion technique of conformal field theories to study the inflationary correlators enjoying the symmetries present during the de Sitter epoch. The operator product expansion is particularly powerful in characterizing inflationary correlation functions in two observationally interesting limits, the squeezed limit of the three-point correlator and the collapsed limit of the four-point correlator. Despite the fact that the shape of the four-point correlators is not fixed by the symmetries of de Sitter, its exact shape can be found in the collapsed limit making use of the operator product expansion. By employing the fact that conformal invariance imposes the two-point cross-correlations of the light fields to vanish unless the fields have the same conformal weights, we are able to show that the Suyama–Yamaguchi inequality relating the coefficients fNLfNL of the bispectrum in the squeezed limit and τNLτNL of the trispectrum in the collapsed limit also holds when the light fields are intrinsically non-Gaussian. In fact, we show that the inequality is valid irrespectively of the conformal symmetry, being just a consequence of fundamental physical principles, such as the short-distance expansion of operator products. The observation of a strong violation of the inequality will then have profound implications for inflationary models as it will imply either that multifield inflation cannot be responsible for generating the observed fluctuations independently of the details of the model or that some new non-trivial degrees of freedom play a role during inflation.

On running couplings in gauge theories from type-IIB supergravity

Abstract We construct an explicit solution of type-IIB supergravity describing the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling with an ultraviolet stable fixed point corresponding to the N =4 SU(N) super-Yang–Mills theory at large N. The running coupling has a power law behaviour, argued to be universal, that is consistent with holography. Around the critical point, our solution defines an asymptotic expansion for the gauge coupling beta-function. We also calculate the first correction to the Coulombic quark–antiquark potential.

A conical tear drop as a vacuum-energy drain for the solution of the cosmological constant problem

We propose a partial solution to the cosmological constant problem by using the simple observation that a three-brane in a six-dimensional bulk is flat. A model is presented in which Standard Model vacuum energy is always absorbed by the transverse space. The latter is a tear-drop like space with a conical singularity, which preserves bulk supersymmetry and gives rise to conventional macroscopic 4D gravity with no cosmological constant. Its cone acts like a drain depleting vacuum energy from the three-brane to the tear drop increasing its volume. We stress that although gravity is treated classically, Standard Model is handled quantum-field theoretically and the model is robust against Standard Model corrections and particular details. The price paid is the presence of boundaries which are nevertheless physically harmless by appropriate boundary conditions.