Gustavo Niz

Strong interactions and exact solutions in nonlinear massive gravity

We investigate strong coupling effects in a covariant massive gravity model, which is a candidate for a ghost-free non-linear completion of Fierz-Pauli. We analyse the conditions to recover general relativity via Vainshtein mechanism in the weak field limit, and find three main cases depending on the choice of parameters. In the first case, the potential is such that all non-linearities disappear and the vDVZ discontinuity cannot be avoided. In the second case, the Vainshtein mechanism allows to recover general relativity within a macroscopic radius from a source. In the last case, the strong coupling of the scalar graviton completely shields the massless graviton, and weakens gravity when approaching the source. In the second part of the paper, we explore new exact vacuum solutions, that asymptote de Sitter or anti de Sitter space depending on the parameter choice. The curvature of the space is proportional to the mass of the graviton, thus providing a cosmological background which may explain the present day acceleration in terms of the graviton mass. Moreover, by expressing the potential for non-linear massive gravity in a convenient form, we also suggest possible connections with a higher dimensional framework.

Analytic Solutions in Nonlinear Massive Gravity

We study spherically symmetric solutions in a covariant massive gravity model, which is a candidate for a ghost-free nonlinear completion of the Fierz-Pauli theory. There is a branch of solutions that exhibits the Vainshtein mechanism, recovering general relativity below a Vainshtein radius given by (r(g)m(2))(1/3), where m is the graviton mass and r(g) is the Schwarzschild radius of a matter source. Another branch of exact solutions exists, corresponding to de Sitter-Schwarzschild spacetimes where the curvature scale of de Sitter space is proportional to the mass squared of the graviton.

The Self-Accelerating Universe with Vectors in Massive Gravity

A bstractWe explore the possibility of realising self-accelerated expansion of the Universe taking into account the vector components of a massive graviton. The effective action in the decoupling limit contains an infinite number of terms, once the vector degrees of freedom are included. These can be re-summed in physically interesting situations, which result in non-polynomial couplings between the scalar and vector modes. We show there are self-accelerating background solutions for this effective action, with the possibility of having a non-trivial profile for the vector fields. We then study fluctuations around these solutions and show that there is always a ghost, if a background vector field is present. When the background vector field is switched off, the ghost can be avoided, at the price of entering into a strong coupling regime, in which the vector fluctuations have vanishing kinetic terms. Finally we show that the inclusion of a bare cosmological constant does not change the previous conclusions and it does not lead to a ghost mode in the absence of a background vector field.

Effective theory for the Vainshtein mechanism from the Horndeski action

tarting from the general Horndeski action, we derive the most general effective theory for scalar perturbations around flat space that allows us to screen fifth forces via the Vainshtein mechanism. The effective theory is described by a generalization of the Galileon Lagrangian, which we use to study the stability of spherically symmetric configurations exhibiting the Vainshtein effect. In particular, we discuss the phenomenological consequences of a scalar-tensor coupling that is absent in the standard Galileon Lagrangian. This coupling controls the superluminality and stability of fluctuations inside the Vainshtein radius in a way that depends on the density profile of a matter source. Particularly, we find that the vacuum solution is unstable due to this coupling.

Vector instabilities and self-acceleration in the decoupling limit of massive gravity

We investigate in detail the vector contributions to the Lagrangian of Λ 3 massive gravity in the decoupling limit, the less explored sector of this theory, with the main aim to study the stability of maximally symmetric self-accelerating solutions. Around self-accelerating configurations, vector degrees of freedom become strongly coupled since their kinetic terms vanish; their dynamics is controlled by contributions to the Lagrangian that arise at higher orders in perturbations. Even in the decoupling limit, the vector Lagrangian contains an infinite number of terms. We develop a systematic method to determine in a covariant way the vector Lagrangian at each order in perturbations, fully manifesting the symmetries of the system. We show that, around self-accelerating solutions, the structure of higher order p -form Galileons arise, avoiding the emergence of a sixth ghost Boulware-Deser mode. However, a careful analysis of the corresponding Hamiltonian shows that there are directions along which the Hamiltonian is unbounded from below, signaling an instability that can be interpreted as one of the available fifth modes behaving as a ghost. Hence, we conclude that self-accelerating configurations in the decoupling limit of Λ 3 massive gravity are generically unstable.

Characterizing Vainshtein solutions in massive gravity

We study static, spherically symmetric solutions in a recently proposed ghost-free model of nonlinear massive gravity. We focus on a branch of solutions where the helicity-0 mode can be strongly coupled within certain radial regions, giving rise to the Vainshtein effect. We truncate the analysis to scales below the gravitational Compton wavelength, and consider the weak field limit for the gravitational potentials, while keeping all nonlinearities of the helicity-0 mode. We determine analytically the number and properties of local solutions that exist asymptotically on large scales, and of local (inner) solutions that exist on small scales. We find two kinds of asymptotic solutions, one of which is asymptotically flat, while the other one is not, and also two types of inner solutions, one of which displays the Vainshtein mechanism, while the other exhibits a self-shielding behavior of the gravitational field. We analyze in detail in which cases the solutions match in an intermediate region. The asymptotically flat solutions connect only to inner configurations displaying the Vainshtein mechanism, while the nonasymptotically flat solutions can connect with both kinds of inner solutions. We show furthermore that there are some regions in the parameter space where global solutions do not exist, and characterize precisely in which regions of the phase space the Vainshtein mechanism takes place.

Exact solutions in massive gravity

Massive gravity is a good theoretical framework to study the modifications of General Relativity. The theory offers a concrete set-up to study models of dark energy, since it admits cosmological self-accelerating solutions in the vacuum, in which the size of the acceleration depends on the graviton mass. Moreover, nonlinear gravitational self-interactions, in the proximity of a matter source, manage to mimic the predictions of linearized General Relativity; hence, agreeing with solar-system precision measurements. In this paper, we review our work in the subject, classifying, on one hand, static solutions, and on the other hand, self-accelerating backgrounds. For the static solutions, we exhibit black hole configurations, together with other solutions that recover General Relativity near a source via the Vainshtein mechanism. For the self-accelerating solutions, we describe a wide class of cosmological backgrounds, including an analysis of their stability.

Stability of the self-accelerating universe in massive gravity

We study linear perturbations around time dependent spherically symmetric solutions in the Lambda_3 massive gravity theory, which self-accelerate in the vacuum. We find that the dynamics of the scalar perturbations depend on the coordinate choice for the background solutions. For particular choices of coordinates there is a symmetry enhancement, leaving no propagating scalar degrees of freedom at linear order in perturbations. In contrast, any other coordinate choice propagates a single scalar mode. We find that the Hamiltonian of this scalar mode is unbounded from below for all self-accelerating solutions, signalling an instability.

Black Holes and Abelian Symmetry Breaking

Black hole configurations offer insights on the non-linear aspects of gravitational theories, and can suggest testable predictions for modifications of General Relativity. In this work, we examine exact black hole configurations in vector-tensor theories, originally proposed to explain dark energy by breaking the Abelian symmetry with a non-minimal coupling of the vector to gravity. We are able to evade the no-go theorems by Bekenstein on the existence of regular black holes in vector-tensor theories with Proca mass terms, and exhibit regular black hole solutions with a profile for the longitudinal vector polarization, characterised by an additional charge. We analytically find the most general static, spherically symmetric black hole solutions with and without a cosmological constant, and study in some detail their features, such as how the geometry depends on the vector charges. We also include angular momentum, and find solutions describing slowly-rotating black holes. Finally, we extend some of these solutions to higher dimensions.

Evolution and stability of cosmic string loops with Y-junctions

Neil Bevis, ∗ Edmund J. Copeland, † Pierre-Yves Martin, 4, ‡ Gustavo Niz, § Alkistis Pourtsidou, ¶ Paul M. Saffin, ∗∗ and D. A. Steer †† Theoretical Physics, Blackett Laboratory, Imperial College, Prince Consort Road, London, SW7 2BZ, United Kingdom School of Physics & Astronomy, University of Nottingham, University Park, Nottingham, NG7 2RD, United Kingdom APC, University Paris 7, 10, Rue Alice Domon et Léonie Duquet, 75205 Paris Cedex 13, France Glaizer Group, 32 rue Guy Moquet, 92240 Malakoff, France (Dated: October 9, 2018)