18 research outputs found
A generic problem with purely metric formulations of MOND
We give a simple argument to show that no purely metric-based, relativistic
formulation of Milgrom's Modified Newtonian Dynamics (MOND) whose energy
functional is stable (in the sense of being quadratic in perturbations) can be
consistent with the observed amount of gravitational lensing from galaxies. An
important part of the argument is the fact that reproducing the MOND force law
requires any completely stable, metric-based theory of gravity to become
conformally invariant in the weak field limit. We discuss the prospects for a
formulation with a very weak instability.Comment: 4 pages, revtex4, no figure
A Note on Energy-Momentum Conservation in Palatini Formulation of L(R) Gravity
By establishing that Palatini formulation of gravity is equivalent to
Brans-Dicke theory, we show that energy-momentum tensor is
covariantly conserved in this type of modified gravity theory.Comment: 7 page
Nonperturbative late time asymptotics for heat kernel in gravity theory
Recently proposed nonlocal and nonperturbative late time behavior of the heat
kernel is generalized to curved spacetimes. Heat kernel trace asymptotics is
dominated by two terms one of which represents a trivial covariantization of
the flat-space result and another one is given by the Gibbons-Hawking integral
over asymptotically-flat infinity. Nonlocal terms of the effective action
generated by this asymptotics might underly long- distance modifications of the
Einstein theory motivated by the cosmological constant problem. New mechanisms
of the cosmological constant induced by infrared effects of matter and graviton
loops are briefly discussed.Comment: 22 pages, LaTeX, final version, to be published in Phys. Rev.
Ghost Condensation and a Consistent Infrared Modification of Gravity
We propose a theoretically consistent modification of gravity in the
infrared, which is compatible with all current experimental observations. This
is an analog of Higgs mechanism in general relativity, and can be thought of as
arising from ghost condensation--a background where a scalar field \phi has a
constant velocity, = M^2. The ghost condensate is a new kind of
fluid that can fill the universe, which has the same equation of state, \rho =
-p, as a cosmological constant, and can hence drive de Sitter expansion of the
universe. However, unlike a cosmological constant, it is a physical fluid with
a physical scalar excitation, which can be described by a systematic effective
field theory at low energies. The excitation has an unusual low-energy
dispersion relation \omega^2 \sim k^4 / M^2. If coupled to matter directly, it
gives rise to small Lorentz-violating effects and a new long-range 1/r^2 spin
dependent force. In the ghost condensate, the energy that gravitates is not the
same as the particle physics energy, leading to the possibility of both sources
that can gravitate and antigravitate. The Newtonian potential is modified with
an oscillatory behavior starting at the distance scale M_{Pl}/M^2 and the time
scale M_{Pl}^2/M^3. This theory opens up a number of new avenues for attacking
cosmological problems, including inflation, dark matter and dark energy.Comment: 42 pages, LaTeX 2
The Volume of the Past Light-Cone and the Paneitz Operator
We study a conjecture involving the invariant volume of the past light-cone
from an arbitrary observation point back to a fixed initial value surface. The
conjecture is that a 4th order differential operator which occurs in the theory
of conformal anomalies gives when acted upon the invariant volume of the
past light-cone. We show that an extended version of the conjecture is valid
for an arbitrary homogeneous and isotropic geometry. First order perturbation
theory about flat spacetime reveals a violation of the conjecture which,
however, vanishes for any vacuum solution of the Einstein equation. These
results may be significant for constructing quantum gravitational observables,
for quantifying the back-reaction on spacetime expansion and for alternate
gravity models which feature a timelike vector field.Comment: 22 pages, no figures, 5 tables. Version 2 substantially extended to
cover nonzero spatial curvature, and with simplified derivation
Modified gravity without dark matter
On an empirical level, the most successful alternative to dark matter in
bound gravitational systems is the modified Newtonian dynamics, or MOND,
proposed by Milgrom. Here I discuss the attempts to formulate MOND as a
modification of General Relativity. I begin with a summary of the
phenomenological successes of MOND and then discuss the various covariant
theories that have been proposed as a basis for the idea. I show why these
proposals have led inevitably to a multi-field theory. I describe in some
detail TeVeS, the tensor-vector-scalar theory proposed by Bekenstein, and
discuss its successes and shortcomings. This lecture is primarily pedagogical
and directed to those with some, but not a deep, background in General
RelativityComment: 28 pages, 10 figures, lecture given at Third Aegean Summer School,
The Invisible Universe: Dark Matter and Dark Energy, minor errors corrected,
references update
Dynamics with Infinitely Many Derivatives: The Initial Value Problem
Differential equations of infinite order are an increasingly important class
of equations in theoretical physics. Such equations are ubiquitous in string
field theory and have recently attracted considerable interest also from
cosmologists. Though these equations have been studied in the classical
mathematical literature, it appears that the physics community is largely
unaware of the relevant formalism. Of particular importance is the fate of the
initial value problem. Under what circumstances do infinite order differential
equations possess a well-defined initial value problem and how many initial
data are required? In this paper we study the initial value problem for
infinite order differential equations in the mathematical framework of the
formal operator calculus, with analytic initial data. This formalism allows us
to handle simultaneously a wide array of different nonlocal equations within a
single framework and also admits a transparent physical interpretation. We show
that differential equations of infinite order do not generically admit
infinitely many initial data. Rather, each pole of the propagator contributes
two initial data to the final solution. Though it is possible to find
differential equations of infinite order which admit well-defined initial value
problem with only two initial data, neither the dynamical equations of p-adic
string theory nor string field theory seem to belong to this class. However,
both theories can be rendered ghost-free by suitable definition of the action
of the formal pseudo-differential operator. This prescription restricts the
theory to frequencies within some contour in the complex plane and hence may be
thought of as a sort of ultra-violet cut-off.Comment: 40 pages, no figures. Added comments concerning fractional operators
and the implications of restricting the contour of integration. Typos
correcte
On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation
An almost brief, though lengthy, review introduction about the long history
of higher order gravities and their applications, as employed in the
literature, is provided. We review the analogous procedure between higher order
gravities and GR, as described in our previous works, in order to highlight its
important achievements. Amongst which are presentation of an easy
classification of higher order Lagrangians and its employment as a
\emph{criteria} in order to distinguish correct metric theories of gravity. For
example, it does not permit the inclusion of only one of the second order
Lagrangians in \emph{isolation}. But, it does allow the inclusion of the
cosmological term. We also discuss on the compatibility of our procedure and
the Mach idea. We derive a dimensional dependent version of Duff's trace
anomaly relation, which in \emph{four}-dimension is the same as the usual Duff
relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any}
dimension. The square of the Weyl tensor identically satisfies it independent
of dimension, however, this Lagrangian satisfies the previous relation only in
three and four dimensions.Comment: 30 pages, added reference
Non linear equation of state and effective phantom divide in brane models
Here, DGP model of brane-gravity is analyzed and compared with the standard
general relativity and Randall-Sundrum cases using non-linear equation of
state. Phantom fluid is known to violate the weak energy condition. In this
paper, it is found that this characteristic of phantom energy is affected
drastically by the negative brane-tension of the RS-II model. It is
found that in DGP model strong energy condition(SEC) is always violated and the
universe accelerates only where as in RS-II model even SEC is not violated for
and the universe decelerates
Gravitational Coupling and Dynamical Reduction of The Cosmological Constant
We introduce a dynamical model to reduce a large cosmological constant to a
sufficiently small value. The basic ingredient in this model is a distinction
which has been made between the two unit systems used in cosmology and particle
physics. We have used a conformal invariant gravitational model to define a
particular conformal frame in terms of large scale properties of the universe.
It is then argued that the contributions of mass scales in particle physics to
the vacuum energy density should be considered in a different conformal frame.
In this manner, a decaying mechanism is presented in which the conformal factor
appears as a dynamical field and plays a key role to relax a large effective
cosmological constant. Moreover, we argue that this model also provides a
possible explanation for the coincidence problem.Comment: To appear in GR