Download Can Gravity Explain the Pioneer 10-11 Anomaly

Modified Gravity and its
Consequences for the Solar
System, Astrophysics and
Cosmology
J. W. Moffat
Perimeter Institute For Theoretical Physics
Waterloo, Ontario, Canada
Talk given at Workshop: From Quantum
to Cosmos: Fundamental Physics
Research in Space, Airlie Conference
Center, Virginia, USA, May 21-24, 2006
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Contents
1. Introduction
2. Modified Gravity (MOG)
3. Fitting galaxy rotation curves and galaxy clusters
4. Explaining the Pioneer 10/11 anomalous acceleration
5. Time Delay Predictions in MOG
6. Cosmology
7. Conclusions
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1. Introduction
• A fully relativistic modified gravity (MOG) called Scalar-TensorVector-Gravity (STVG) leads to a self-consistent, stable gravity
theory that can describe solar system, astrophysical and
cosmological data. The theory has an extra degree of freedom, a
vector field called a “phion” field whose curl is a skew field that
couples to matter (“fifth force”). The gravitational field is
described by a symmetric Einstein metric tensor.
• The effective classical theory allows the gravitational coupling
“constant” G to vary as a scalar field with space and time. The
effective mass of the skew symmetric field and the coupling of
the field to matter also vary as scalar fields with space and time.
• The variation of the constants can be explained in a quantum
gravity renormalization group (RG) flow scenario in which gravity
is an asymptotically-free theory (Reuter and Weyer, JWM, 2005).
The constants run with momentum k as in QCD, and a cutoff
procedure leads to space and time varying constants. The STVG
theory is an effective classical description of the RG flow
scenario. The quantum gravity theory is constructed to be nonperturbatively renormalizable.
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• The modified Newtonian acceleration law for weak fields can
fit a large amount of galaxy rotation curve data without nonbaryonic dark matter (Brownstein and JWM, 2006). It also
can fit data for X-ray galaxy clusters without dark matter. The
modified acceleration law is consistent with the solar system
data and can possibly explain the Pioneer 10/11 anomalous
acceleration (Brownstein & Moffat, 2006).
A MOG should explain the following:
• The CMB data including the power spectrum data;
• The formation of proto-galaxies in the early universe and
the growth of galaxies;
• Gravitational lensing data for galaxies and clusters of
galaxies;
• N-body simulations of galaxy surveys;
• The accelerating expansion of the universe.
We seek a unified description of solar system, astrophysical
and large-scale cosmological data.
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2. Modified Gravity (MOG)
Our action takes the form
where
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Here,
denotes the covariant derivative with respect to
g. Moreover, V denotes a potential for the fields and
The total energy-momentum tensor is
The field equations are
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The modified weak field acceleration law can be written
The pioneer anomalous acceleration directed towards the center
of the Sun is obtained from (Anderson, Turyshev, Nieto..):
We assume the following parametric forms for the
“running” of the constants
and
:
where
and b are constants.
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4. Fitting Galaxy Rotation Curves
• A fitting routine has been applied to fit a large number of galaxy
rotation curves (101 galaxies), using photometric data (58
galaxies) and a core model (43 galaxies) (Brownstein and JWM,
2005). The fits to the data are remarkably good and for the
photometric data only one parameter, the mass-to-light ratio M/L, is
used for the fitting once two parameters alpha and lambda are
universally fixed for galaxies and dwarf galaxies. The fits are close
to those obtained from Milgrom’s MOND acceleration law (Milgrom
1983) in all cases considered. A large sample of X-ray mass profile
cluster data (106 clusters) has also been well fitted (Brownstein
and JWM, 2006). The fitting of the radial dependence of the
dynamical cluster mass is effectively a zero-parameter fit, for the
two parameters alpha and lambda are fitted to the determined bulk
mass.
• The rotational velocity curves become at large distances from the
galaxies (satellites) the Kepler-Newtonian curves.
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5. Fitting the Pioneer Anomalous
Acceleration
The pioneer anomaly directed towards the center of the Sun
is given by (Anderson, Turyshev, Nieto…):
We use the following parametric representations of the “running”
of alpha (r) and lambda (r):
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A consequence of a variation of G and GM_sun for the solar
system is a modification of Kepler’s third law
For given values of a_pl and T_pl we can determine
G(r)M_sun. We define the standard semi-major axis value
at 1 AU:
For a distance varying G(r)M_sun we derive (Talmadge et al.
1988):
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5) Time Delay Predictions in MOG
The STVG correction to the GR time delay is
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6. MOG Cosmology
• An important extra-degree of freedom in MOG is the light,
electrically uncharged vector particle called a phion. In the
early universe at a temperature T < T_c, where T_c is a
critical temperature, the phions become a Bose-Einstein
condensate (BEC) fluid. The phion condensates couple
weakly with gravitational strength to ordinary baryonic
matter. This cold fluid has zero classical pressure and zero
shear viscosity and dominates the density of matter at
cosmological scales and, because of its clumping due to
gravitational collapse, allows the formation of structure and
galaxies at sub-horizon scales well before recombination.
• We do not postulate the existence of cold dark matter in
the form of heavy, new stable particles such as
supersymmetric WIMPS. The phions undergo a 2nd-order
phase transition through a spontaneous symmetry breaking
for T < T_c. The non-zero vacuum expectation value
<phi>_0 can weakly break Lorentz invariance.
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• The correlation function for the temperature differences
across the sky for a given angle theta takes the form:
• I use a modified form of the analytic calculation of C_l
given by Mukhanov (2006) to obtain a fit to the acoustical
peaks in the CMB for l > 100 < 1200. The adopted density
parameters are
• Without the dominant BEC phion-matter, the Silk and finite
thickness scales l_s and l_f erase any peaks above the second
peak (baryon drag). The speed of sound c_s^2 ~ 14
Omega_{b,0} depends on the baryon density today.
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• For local late-time bound systems such as galaxies and
clusters of galaxies the symmetry breaking is relaxed and
the phion Bose-Einstein condensates become ultra-light and
relativistic. For galaxies and clusters of galaxies ordinary
baryonic matter and neutral hydrogen and helium gases
now constitute the dominant form of matter.
• The phion field and the spatial variation of G modify for
late-time galaxies Newton’s acceleration law. The rotational
velocity curves are flattened, because of the altered
dynamics of the gravitational field at the outer regions of
spiral galaxies and not because of the presence of a
dominant dark matter halo.
• The dual role played by the phion field in describing
galaxies and the large-scale structure of the universe is a
generic feature of our MOG theory.
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7. Conclusions
• A stable and self-consistent modified gravity (MOG) theory is
constructed from a pseudo-Riemannian geometry and a
massive skew field obtained from the curl of a massive vector
field (phion field). The static spherically symmetric solution of
the field equations yields a modified Newtonian acceleration
law with a scale dependence. The gravitational “constant” G,
the effective mass and the coupling strength of the skew field
run with distance scale r according to an infra-red RG flow
scenario based on an “asymptotically” free quantum gravity.
This can be described by an effective classical STVG action.
• A fit to 101 galaxy rotations curves is obtained and mass
profiles of x-ray galaxy clusters are also successfully fitted for
those clusters that are isothermal.
• A possible explanation of the Pioneer 10-11 anomalous
acceleration is obtained from the MOG with predictions for the
onset of the anomalous acceleration at Saturn’s orbit and for
the periods of the outer planets.
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• The phion boson field forms Bose-Einstein condensates
through a spontaneous symmetry breaking at large cosmological
scales, which can explain the formation of proto-galaxies and at
late times the structure of galaxies and clusters.
• A fit to the CMB acoustical power spectrum data can be
achieved with a 2-component BEC and baryon-photon fluid for
which the BEC density Omega_\phi > Omega_b.
• For late-time local virialized clusters of galaxies and galaxies,
the BEC symmetry breaking is relaxed and the baryons and
neutral gases dominate, Omega_b > Omega_phi, and the MOG
acceleration law explains galaxy rotation curves and mass
profiles of clusters.
• Heavy WIMP dark matter particles will not be observed in
laboratory experiments.
• The MOG theory gives a unified description of solar system,
astrophysical and cosmological data.
END
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Bibliography
1) J. W. Moffat, Gravitational Theory, Galaxy Rotation
Curves and Cosmology without Dark Matter, JCAP 0505
(2005) 003, astro-ph/0412195
2) J. W. Moffat, Scalar-Tensor-Vector Gravity Theory,
JCAP 0603 (2006) 004, gr-qc/0506021
3) J. R. Brownstein and J. W Moffat, Galaxy Rotation
Curves without Non-Baryonic Dark Matter, Astrophys. J.
636 (2006) 721, astro-ph/0506370
4) J. R. Brownstein and J. W Moffat, Galaxy Cluster
Masses Without Non-Baryonic Dark Matter, Mon. Not.
Roy. Astron. Soc. 367 (2006) 527, astro-ph/0507222
5) J. R. Brownstein and J. W Moffat, Gravitational
Solution to the Pioneer 10/11 Anomaly, Class. Quant.
Grav. 23, 3427 (2006), gr-qc/0511026
6) J. W. Moffat, Spectrum of Cosmic Microwave
Fluctuations and the Formation of Galaxies in a Modified
Gravity Theory, astro-ph/0602607
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