52 research outputs found
Vector instabilities and self-acceleration in the decoupling limit of massive gravity
We investigate vector contributions to the Lagrangian of massive
gravity in the decoupling limit, the less explored sector of this theory. The
main purpose is to understand the stability of maximally symmetric
%self-accelerating vacuum solutions. Around self-accelerating configurations,
vector degrees of freedom become strongly coupled since their kinetic terms
vanish, so their dynamics is controlled by higher order interactions. Even in
the decoupling limit, the vector Lagrangian contains an infinite number of
terms. We develop a systematic method to covariantly determine 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 -form Galileons arise, avoiding the emergence of a sixth BD
ghost mode. However, a careful analysis shows that there are directions along
which the Hamiltonian is unbounded from below. This instability can be
interpreted as one of the available fifth physical modes behaving as a ghost.
Therefore, we conclude that self-accelerating configurations, in the decoupling
limit of -massive gravity, are generically unstable.Comment: 16 pages, 2 figure
Analytic solutions in non-linear massive gravity
We study spherically symmetric solutions in a covariant massive gravity
model, which is a candidate for a ghost-free non-linear 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
, where is the graviton mass and is the
Schwarzschild radius of a matter source. Another branch of exact solutions
exists, corresponding to Schwarzschild-de Sitter spacetimes where the curvature
scale of de Sitter space is proportional to the mass squared of the graviton.Comment: 5 pages, 1 figure, version accepted by PR
Strong interactions and exact solutions in non-linear 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.Comment: 20 pages, no figures. Version accepted by PR
Effective theory for the Vainshtein mechanism from the Horndeski action
Starting 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.Comment: 6 pages, matches version published by PRD, references adde
On the galaxy 3-point correlation function in Modified Gravity
The next generation of galaxy surveys will provide highly accurate
measurements of the large-scale structure of the Universe, allowing for more
stringent tests of gravity on cosmological scales. Higher order statistics are
a valuable tool to study the non-Gaussianities in the matter field and to break
degeneracies between modified gravity and other physical or nuisance
parameters. However, understanding from first principles the behaviour of these
correlations is essential to characterise deviations from General Relativity
(GR), and the purpose of this work. This work uses contemporary ideas of
Standard Perturbation Theory on biased tracers to characterize the three point
correlation function (3PCF) at tree level for Modified Gravity models with a
scale-dependent gravitational strength, and applies the theory to two specific
models ( and DGP) that are representative for Chameleon and Vainshtein
screening mechanisms. Additionally, we use a multipole decomposition, which
apart from speeding up the algorithm to extract the signal from data, also
helps to visualize and characterize GR deviations.Comment: 25 pages, 5 figure
Classical Propagation of Strings across a Big Crunch/Big Bang Singularity
One of the simplest time-dependent solutions of M theory consists of
nine-dimensional Euclidean space times 1+1-dimensional compactified Milne
space-time. With a further modding out by Z_2, the space-time represents two
orbifold planes which collide and re-emerge, a process proposed as an
explanation of the hot big bang. When the two planes are near, the light states
of the theory consist of winding M2-branes, describing fundamental strings in a
particular ten-dimensional background. They suffer no blue-shift as the M
theory dimension collapses, and their equations of motion are regular across
the transition from big crunch to big bang. In this paper, we study the
classical evolution of fundamental strings across the singularity in some
detail. We also develop a simple semi-classical approximation to the quantum
evolution which allows one to compute the quantum production of excitations on
the string and implement it in a simplified example.Comment: 38 pages, 19 figure
The string wave function across a Kasner singularity
A collision of orbifold planes in eleven dimensions has been proposed as an
explanation of the hot big bang. When the two planes are close to each other,
the winding membranes become the lightest modes of the theory, and can be
effectively described in terms of fundamental strings in a ten dimensional
background. Near the brane collision, the eleven-dimensional metric is an
Euclidean space times a 1+1-dimensional Milne universe. However, one may expect
small perturbations to lead into a more general Kasner background. In this
paper we extend the previous classical analysis of winding membranes to Kasner
backgrounds, and using the Hamiltonian equations, solve for the wave function
of loops with circular symmetry. The evolution across the singularity is
regular, and explained in terms of the excitement of higher oscillation modes.
We also show there is finite particle production and unitarity is preserved.Comment: 28 pages, 10 figure
Characterising Vainshtein Solutions in Massive Gravity
We study static, spherically symmetric solutions in a recently proposed
ghost-free model of non-linear 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 non-linearities
of the helicity-0 mode. We determine analytically the number and properties of
local solutions which exist asymptotically on large scales, and of local
(inner) solutions which 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 behaviour of the
gravitational field. We analyse 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 non
asymptotically 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 characterise precisely in which regions of
the phase space the Vainshtein mechanism takes place.Comment: 21 pages, 7 figures, published versio
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