Modified Gravity vs. the Dark Sector:
Was Einstein Right?
DARK SECTOR
MODIFIED GRAVITY
SEPTEMBER 26. 2010
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Galactic Rotation Curves
Kepler: v=[GM/R]1/2
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Consider the United States in 1790
•Over-densities of order 50
•Concentrated in East
•Vast Voids with low density
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Consider the United States Today
 Over-densities of
order 10,000
 Concentration in
coasts
 Traces of primordial
density (BostonWashington; East >
West)
 Vast Voids
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The story of this evolution is the story of
the United States
When we understand the evolution
from one map to another, we can
understand
 the sociological, economic, and
political forces acting on the US
 the people, or the constituents, of
the US
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The Universe Would Be Too Smooth
Without Dark Matter
At t=400,000 years, the universe
was smooth to one part in
10,000.
WMAP
General Relativity predicts that
perturbations have grown since
then by a factor of 1000
Sloan Digital Sky Survey
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Dark Matter Solves Cosmic Structure
Problem
Dark matter was
much clumpier
than baryons were
at the time of the
picture of cosmic
microwave
background (CMB).
Enough time for
structure to grow!
Clumpiness
Large Scales
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Dark Energy
Distant supernovae
allow us to probe the
expansion history of
the universe
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The Universe is Accelerating
Accelerating
Brighter
Decelerating
Astier et al. 2007
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Gravity typically produces deceleration
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This intuition carries over into Einstein’s
theory … with a twist
ACCELERATION = - [CONSTANT] X
[ENERGY DENSITY + 3 X PRESSURE]
a
4G  


 2  3P 
a
3 c

As long as the energy density and the pressure are
positive, the Universe should be decelerating.
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Strange substance (Dark Energy)
required to produce acceleration
Dark Energy has negative pressure
 Total energy within a given region increases as the
region expands
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Dark Sector has been invoked previously
in astronomy
Formed a design in the beginning of this week, of
investigating, as soon as possible after taking my
degree, the irregularities of the motion of
Uranus, which are yet unaccounted for; in order
to find out whether they may be attributed to
the action of an undiscovered planet beyond it;
and if possible thence to determine the elements
of its orbit, etc.. approximately, which would
probably lead to its discovery.
John Adams
Undergraduate Notebook, July 1841
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Not everyone believed a new planet was
responsible
Adams informed Airy of his plans, but Airy
did not grant observing time.
Astronomer Royal,
George Airy,
believed deviation
from 1/r2 force
responsible for
irregularities
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In June 1845, the French also began the
relevant calculations
Urbain Le Verrier
Contemporary: “I do not know whether M. Le Verrier is actually the most detestable
man in France, but I am quite certain that he is the most detested.”
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By June 1846, both Adams and LeVerrier had
calculated positions
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This first search (by Challis) was unsuccessful
Both Adams and LeVerrier refined their predictions…
In September 1846, Dawes’ friend William Lassell, an
amateur astronomer and a brewer by trade, had just
completed building a large telescope that would be able
to record the disk of the planet. He wrote to Lassell giving
him Adams’ predicted position. However Lassell had
sprained his ankle and was confined to bed. He read the
letter which he gave to his maid who then promptly lost it.
His ankle was sufficiently recovered on the next night and
he looked in vain for the letter with the predicted
position.
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LeVerrier wrote to German astronomer Galle
on September 18, 1846
Galle discovered it in 30 minutes on September 23.
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Anomalous precession of Mercury’s
perihelion went the other way
LeVerrier assumed it was due to a small planet near
the Sun and searched (in vain) for such a planet
(Vulcan).
We now know that this anomaly
is due to a whole new theory of
gravity.
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We have a similar dilemma today
DARK SECTOR
MODIFIED GRAVITY
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Assumptions
For dark matter, we assumed Kepler’s Law, which follows
from Newtonian Gravity
For dark energy, we assumed General Relativity
WEAK GRAVITY
SEPTEMBER 26. 2010
STRONG GRAVITY
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Newton’s insight: same force
governs motion on earth and
in the Heavens
Newtonian Gravity
WEAK GRAVITY
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STRONG GRAVITY
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Then Einstein realized Newtonian
Gravity was valid only for weak fields
Newtonian Gravity
WEAK GRAVITY
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STRONG GRAVITY
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General Relativity was assumed to be
the true theory, reducing to Newtonian
Gravity in the weak field limit
General Relativity
Newtonian Gravity
WEAK GRAVITY
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STRONG GRAVITY
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Maybe both need to be replaced in the
very weak limit
General Relativity
Newtonian
Gravity
WEAK GRAVITY
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STRONG GRAVITY
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Doing away with Dark Matter
In 1983, Mordecai Milgrom proposed
Modified Newtonian Dynamics
(MOND). In very weak fields (edges of
galaxies) the force from gravity changes
from (1/r2) to (1/r).
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Fit Rotation Curves
•Fit Rotation Curves of many
galaxies w/ only one free
parameter.
•Compare to fitting CDM:
http://burro.astr.cwru.edu/Jav
aLab/RotcurveWeb/main.html
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McGaugh 27
Also makes predictions for galaxy
properties
Luminosity
Sanders & Veheijen 1998
L~v4
Velocity
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On cosmology, MOND is silent
WMAP
Sloan Digital Sky Survey
Not a comprehensive theory of gravity so cannot be applied to an
almost homogeneous universe. We don’t even know if the
underlying theory – which reduces to MOND in some limit – is
consistent with an expanding universe.
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Bekenstein’s Theory
Questions a basic assumption of
General Relativity: the metric which
determines geometry is the same one
which dictates how particles move
TeVeS (Tensor Vector Scalar) reduces to MOND on
Galactic scales. Enables us to do cosmology
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Many groups have now applied TeVeS to
cosmology
•The picture of a smooth,
expanding universe is almost
identical to that obtained with
General Relativity.
•Key Question: How do
inhomogeneities grow? Is there
enough time for structure to grow
even without dark matter?
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WMAP
Sloan Digital Sky Survey
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Inhomogeneities in TeVeS grow faster
than in GR
Standard Growth
TeVeS
Dodelson & Liguori
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Cosmic structure explained
without dark matter
Dec 18, 2006
An alternative to Einstein's
theory of general relativity
called "TeVeS" could describe
the formation of cosmic
structure without requiring the
existence of dark matter, say
physicists in the US (Phys. Rev.
Lett. 97 2006).
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Still need to worry about the Shape of
the power spectrum
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Workshop June, 2010
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PROGRAM
Monday 28/06
10h00-10h05: Welcome (H. Wozniak)
10h05-10h30: Outlook of the meeting (B.
Famaey)
10h30-11h30: Modified Newtonian Dynamics for
practicioners (M. Milgrom)
11h30-12h30: Dark energy and modified gravity
(P. Brax)
14h30-15h30: Empirical tests of MOND in
galaxies (S. McGaugh)
15h30-16h00: Bulge-dominated galaxies, a
challenge for MOND? (F. Fraternali)
16h30-17h00: THINGS about MOND (G. Gentile)
Tuesday 29/06
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09h00-09h30: What are the best constraints on
theories from galaxy dynamics (F. Combes)
09h30-10h00: Dynamical friction, galaxy
merging, and radial-orbit instability in MOND (C.
Nipoti)
10h00-10h30: Testing gravity with galaxy
mergers and polar rings (O. Tiret)
10h30-10h45: MOND in the Milky Way (O.
Bienaymé)
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Sample Slide
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Sample Slide
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Thursday: Final Day
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09h00-09h30: Structure formation in the presence of dark interactions (M. Baldi)
09h30-10h00: A dark fluid to explain MOND, dark matter, and dark energy? (H.S. Zhao)
10h00-10h30: N-body simulations for coupled scalar field theories (B. Li)
11h00-12h00: Modified gravity as an alternative to dark energy (L. Amendola)
12h00-12h30: The dilaton and modified gravity (C. Van de Bruck)
12h30-13h00: Asymptotically safe gravity from a bimetric perspective (F. Saueressig)
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13h00-14h00: LUNCH
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14h00-14h30: Cosmography and clusters of galaxies from f(R)-gravity (S. Capozziello)
14h30-15h00: Testing f(R) theories with elliptical galaxies (N. Napolitano)
15h00-15h30: MOND and dark matter in ellipticals (T. Richtler)
15h30-16h00: Dark matter and MOND in NGC 1399 (Y. Schuberth)
16h30-16h50: The MOND fundamental Plane (V. Cardone)
16h50-17h10: Interloper removal in dwarf spheroidals (A.-L. Serra)
17h10-17h30: Dark matter and MOND in ulra-compact dwarf galaxies (J. Dabringhausen)
17h30-18h00: The disk of satellites and other small-scalle issues (P. Kroupa)
18h00-18h30: Meeting Summary and final discussion (led by S. McGaugh & S. Dodelson)
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Bright Side: Improved Jewish-Muslim
Relations
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Why/how do 2 sets of (rational) people
disagree so strongly?
MG proponents argue against DM/DE because they say it
assumes substances that do not necessarily exist
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Why/how do 2 sets of (rational) people
disagree so strongly?
Well yes, but … supersymmetry was introduced for other
reasons
MG also represents a change to the action, the quantity that
encapsulates all laws of nature
And that change is ugly!
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Why/how do 2 sets of (rational) people
disagree so strongly?
Small scale or large scale starting point?
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What about the other component of
the dark sector?
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Need to modify gravity in a different
way
Modify the Einstein-Hilbert Action
1
4
S
d
x  g R  f ( R )

16G
The acceleration equation
generalizes to:
Get acceleration if these
terms are positive even if
pressure is positive

a
4G
f fR 
2
   3P    f R H   

a
3
6 2

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How will we determine who’s right?
Accelerators
LHC
Indirect Detection
Fermi
Direct Detection
Coupp
WIMP’s can be probed in 3 ways … and will be over the coming decade
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How will we determine who’s right?
MG vs. DE is harder: measure growth of structure
GALAXY CLUSTERS
GRAVITATIONAL LENSING
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We are pondering/probing the modern
incarnation of one of the most profound
questions in science
DARK SECTOR
MODIFIED GRAVITY
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