40 research outputs found
The Force of Gravity from a Lagrangian containing Inverse Powers of the Ricci Scalar
We determine the gravitational response to a diffuse source, in a locally de
Sitter background, of a class of theories which modify the Einstein-Hilbert
action by adding a term proportional to an inverse power of the Ricci scalar.
We find a linearly growing force which is not phenomenologically acceptable.Comment: 10 pages, LaTeX 2 epsilon, no figures. Minor conceptual change
The Axial Anomaly in D=3+1 Light-Cone QED
We consider -dimensional, Dirac electrons of arbitrary mass,
propagating in the presence of electric and magnetic fields which are both
parallel to the axis. The magnetic field is constant in space and time
whereas the electric field depends arbitrarily upon the light-cone time
parameter . We present an explicit solution to the
Heisenberg equations for the electron field operator in this background. The
electric field results in the creation of electron-positron pairs. We compute
the expectation values of the vector and axial vector currents in the presence
of a state which is free vacuum at . Both current conservation and the
standard result for the axial vector anomaly are verified for the first time
ever in -dimensional light-cone QED. An interesting feature of our
operator solution is the fact that it depends in an essential way upon
operators from the characteristic at , in addition to the usual
dependence upon operators at . This dependence survives even in the
limit of infinite . Ignoring the operators leads to a progressive loss
of unitarity, to the violation of current conservation, to the loss of
renormalizability, and to an incorrect result for the axial vector anomaly.Comment: 31 pages, LaTeX 2 epsilon, no figures, some typoes corrected for
publicatio
Possible Enhancement of High Frequency Gravitational Waves
We study the tensor perturbations in a class of non-local, purely
gravitational models which naturally end inflation in a distinctive phase of
oscillations with slight and short violations of the weak energy condition. We
find the usual generic form for the tensor power spectrum. The presence of the
oscillatory phase leads to an enhancement of gravitational waves with
frequencies somewhat less than 10^{10} Hz.Comment: 27 pages, 11 figures, LaTeX.2
A Nonlocal Metric Formulation of MOND
We study a class of nonlocal, but causal, covariant and conserved field
equations for the metric. Although nonlocal, these equations do not seem to
possess extra graviton solutions in weak field perturbation theory. Indeed, the
equations reduce to those of general relativity when the Ricci scalar vanishes
throughout spacetime. When a static matter source is present we show how these
equations can be adjusted to reproduce Milgrom's Modified Newtonian Dynamics in
the weak field regime, while reducing to general relativity for strong fields.
We compute the angular deflection of light in the weak field regime and
demonstrate that it is the same as for general relativity, resulting in far too
little lensing if no dark matter is present. We also study the field equations
for a general Robertson-Walker geometry. An interesting feature of our
equations is that they become conformally invariant in the MOND limit.Comment: 22 pages, LaTeX 2 epsilon, no figure
Matter loops corrected modified gravity in Palatini formulation
Recently, corrections to the standard Einstein-Hilbert action are proposed to
explain the current cosmic acceleration in stead of introducing dark energy. In
the Palatini formulation of those modified gravity models, there is an
important observation due to Arkani-Hamed: matter loops will give rise to a
correction to the modified gravity action proportional to the Ricci scalar of
the metric. In the presence of such term, we show that the current forms of
modified gravity models in Palatini formulation, specifically, the 1/R gravity
and gravity, will have phantoms. Then we study the possible
instabilities due to the presence of phantom fields. We show that the strong
instability in the metric formulation of 1/R gravity indicated by Dolgov and
Kawasaki will not appear and the decay timescales for the phantom fields may be
long enough for the theories to make sense as effective field theory . On the
other hand, if we change the sign of the modification terms to eliminate the
phantoms, some other inconsistencies will arise for the various versions of the
modified gravity models. Finally, we comment on the universal property of the
Palatini formulation of the matter loops corrected modified gravity models and
its implications.Comment: 11 pages, 1 figures, References adde
Palatini formulation of the modified gravity with an additionally squared scalar curvature term
In this paper by deriving the Modified Friedmann equation in the Palatini
formulation of gravity, first we discuss the problem of whether in
Palatini formulation an additional term in Einstein's General Relativity
action can drive an inflation. We show that the Palatini formulation of
gravity cannot lead to the gravity-driven inflation as in the metric formalism.
If considering no zero radiation and matter energy densities, we obtain that
only under rather restrictive assumption about the radiation and matter energy
densities there will be a mild power-law inflation , which is
obviously different from the original vacuum energy-like driven inflation. Then
we demonstrate that in the Palatini formulation of a more generally modified
gravity, i.e., the model that intends to explain both the current
cosmic acceleration and early time inflation, accelerating cosmic expansion
achieved at late Universe evolution times under the model parameters satisfying
.Comment: 14 pages, accepted for publication by CQ
corrections to the cosmological dynamics of inflation in the Palatini formulation
We investigate the corrections to the inflationary cosmological dynamics due
to a term in the Palatini formulation which may arise as quantum
corrections to the effective Lagrangian in early universe. We found that the
standard Friedmann equation will not be changed when the scalar field is in the
potential energy dominated era. However, in the kinetic energy dominated era,
the standard Friedmann equation will be modified and in the case of closed and
flat universe, the Modified Friedmann equation will automatically require that
the initial kinetic energy density of the scalar field must be in sub-Planckian
scale.Comment: 11 pages, no figures. Accepted by Class.Quant.Grav.v2:References
adde
Consistent modified gravity: dark energy, acceleration and the absence of cosmic doomsday
We discuss the modified gravity which includes negative and positive powers
of the curvature and which provides the gravitational dark energy. It is shown
that in GR plus the term containing negative power of the curvature the cosmic
speed-up may be achieved, while the effective phantom phase (with less than
-1) follows when such term contains the fractional positive power of the
curvature. The minimal coupling with matter makes the situation more
interesting: even 1/R theory coupled with the usual ideal fliud may describe
the (effective phantom) dark energy. The account of term (consistent
modified gravity) may help to escape of cosmic doomsday.Comment: LaTeX file, 9 pages, based on the talk given by S.D. Odintsov (Int.
Conference Mathematical Methods in Physics, Rio de Janeiro, Augest, 2004), to
appear in CQG, Letter
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