40 research outputs found
On causality and superluminal behavior in classical field theories. Applications to k-essence theories and MOND-like theories of gravity
Field theories whose full action is Lorentz invariant (or diffeomorphism
invariant) can exhibit superluminal behaviors through the breaking of local
Lorentz invariance. Quantum induced superluminal velocities are well-known
examples of this effect. The issue of the causal behavior of such propagations
is somewhat controversial in the literature and we intend to clarify it. We
provide a careful analysis of the meaning of causality in classical
relativistic field theories, and we stress the role played by the Cauchy
problem and the notions of chronology and time arrow. We show that superluminal
behavior threaten causality only if a prior chronology on spacetime is chosen.
In the case where superluminal propagations occur, however, there is at least
two non conformally related metrics on spacetime and thus two available notions
of chronology. These two chronologies are on equal footing and it would thus be
misleading to choose \textit{ab initio} one of them to define causality.
Rather, we provide a formulation of causality in which no prior chronology is
assumed. We argue this is the only way to deal with the issue of causality in
the case where some degrees of freedom propagate faster than others. We
actually show that superluminal propagations do not threaten causality. As an
illustration of these conceptual issues, we consider two field theories, namely
k-essences scalar fields and bimetric theories of gravity, and we derive the
conditions imposed by causality. We discuss various applications such as the
dark energy problem, MOND-like theories of gravity and varying speed of light
theories.Comment: 15 pages, 2 figures; minor changes, references added, submitted to
Phys.Rev.
Field-theoretical formulations of MOND-like gravity
Modified Newtonian dynamics (MOND) is a possible way to explain the flat
galaxy rotation curves without invoking the existence of dark matter. It is
however quite difficult to predict such a phenomenology in a consistent field
theory, free of instabilities and admitting a well-posed Cauchy problem. We
examine critically various proposals of the literature, and underline their
successes and failures both from the experimental and the field-theoretical
viewpoints. We exhibit new difficulties in both cases, and point out the hidden
fine tuning of some models. On the other hand, we show that several published
no-go theorems are based on hypotheses which may be unnecessary, so that the
space of possible models is a priori larger. We examine a new route to
reproduce the MOND physics, in which the field equations are particularly
simple outside matter. However, the analysis of the field equations within
matter (a crucial point which is often forgotten in the literature) exhibits a
deadly problem, namely that they do not remain always hyperbolic. Incidentally,
we prove that the same theoretical framework provides a stable and well-posed
model able to reproduce the Pioneer anomaly without spoiling any of the
precision tests of general relativity. Our conclusion is that all MOND-like
models proposed in the literature, including the new ones examined in this
paper, present serious difficulties: Not only they are unnaturally fine tuned,
but they also fail to reproduce some experimental facts or are unstable or
inconsistent as field theories. However, some frameworks, notably the
tensor-vector-scalar (TeVeS) one of Bekenstein and Sanders, seem more promising
than others, and our discussion underlines in which directions one should try
to improve them.Comment: 66 pages, 6 figures, RevTeX4 format, version reflecting the changes
in the published pape
Non-standard baryon-dark matter interactions
After summarizing the respective merits of the Cold Dark Matter (CDM) and
Modified Newtonian Dynamics (MOND) paradigms in various stellar systems, we
investigate the possibility that a non-standard interaction between baryonic
and dark matter could reproduce the successes of CDM at extragalactic scales
while making baryonic matter effectively obey the MOND field equation in spiral
galaxies.Comment: 10 pages, to appear in World Scientific, proceedings of DARK 200
Escaping from MOND
We present a new test of modified Newtonian dynamics (MOND) on galactic
scales, based on the escape speed in the solar neighbourhood. This test is
independent from other empirical successes of MOND at reproducing the
phenomenology of galactic rotation curves. The galactic escape speed in MOND is
entirely determined by the baryonic content of the Galaxy and the external
field in which it is embedded. We estimate that the external field in which the
Milky Way must be embedded to produce the observed local escape speed of 550
km/s is of the order of a_0/100, where a_0 is the dividing acceleration scale
below which gravity is boosted in MOND. This is compatible with the external
gravitational field actually acting on the Milky Way.Comment: 4 pages, 1 figure; accepted for publication in MNRA
Dynamics of a lattice Universe
We find a solution to Einstein field equations for a regular toroidal lattice
of size L with equal masses M at the centre of each cell; this solution is
exact at order M/L. Such a solution is convenient to study the dynamics of an
assembly of galaxy-like objects. We find that the solution is expanding (or
contracting) in exactly the same way as the solution of a
Friedman-Lema\^itre-Robertson-Walker Universe with dust having the same average
density as our model. This points towards the absence of backreaction in a
Universe filled with an infinite number of objects, and this validates the
fluid approximation, as far as dynamics is concerned, and at the level of
approximation considered in this work.Comment: 14 pages. No figure. Accepted version for Classical and Quantum
Gravit
Reconciling MOND and dark matter?
Observations of galaxies suggest a one-to-one analytic relation between the
inferred gravity of dark matter at any radius and the enclosed baryonic mass, a
relation summarized by Milgrom's law of modified Newtonian dynamics (MOND).
However, present-day covariant versions of MOND usually require some additional
fields contributing to the geometry, as well as an additional hot dark matter
component to explain cluster dynamics and cosmology. Here, we envisage a
slightly more mundane explanation, suggesting that dark matter does exist but
is the source of MOND-like phenomenology in galaxies. We assume a canonical
action for dark matter, but also add an interaction term between baryonic
matter, gravity, and dark matter, such that standard matter effectively obeys
the MOND field equation in galaxies. We show that even the simplest realization
of the framework leads to a model which reproduces some phenomenological
predictions of cold dark matter (CDM) and MOND at those scales where these are
most successful. We also devise a more general form of the interaction term,
introducing the medium density as a new order parameter. This allows for new
physical effects which should be amenable to observational tests in the near
future. Hence, this very general framework, which can be furthermore related to
a generalized scalar-tensor theory, opens the way to a possible unification of
the successes of CDM and MOND at different scales.Comment: 9 page
Insight into the baryon-gravity relation in galaxies
Observations of spiral galaxies strongly support a one-to-one analytical
relation between the inferred gravity of dark matter at any radius and the
enclosed baryonic mass. It is baffling that baryons manage to settle the dark
matter gravitational potential in such a precise way, leaving no "messy"
fingerprints of the merging events and "gastrophysical" feedbacks expected in
the history of a galaxy in a concordance Universe. This correlation of gravity
with baryonic mass can be interpreted from several non-standard angles,
especially as a modification of gravity called TeVeS, in which no galactic dark
matter is needed. In this theory, the baryon-gravity relation is captured by
the dieletric-like function mu of Modified Newtonian Dynamics (MOND),
controlling the transition from 1/r^2 attraction in the strong gravity regime
to 1/r attraction in the weak regime. Here, we study this mu-function in
detail. We investigate the observational constraints upon it from fitting
galaxy rotation curves, unveiling the degeneracy between the stellar
mass-to-light ratio and the mu-function as well as the importance of the
sharpness of transition from the strong to weak gravity regimes. We also
numerically address the effects of non-spherical baryon geometry in the
framework of non-linear TeVeS, and exhaustively examine how the mu-function
connects with the free function of that theory. In that regard, we exhibit the
subtle effects and wide implications of renormalizing the gravitational
constant. We finally present a discontinuity-free transition between
quasi-static galaxies and the evolving Universe for the free function of TeVeS,
inevitably leading to a return to 1/r^2 attraction at very low accelerations in
isolated galaxies.Comment: 15 pages, 5 figures; improved clarity; accepted for publication in
Phys. Rev.