Experimental Gravitation
Fulvio Ricci
Dipartimento di Fisica
Università di Roma La Sapienza
&
INFN Sezione di Roma
Napoli 2 Aprile 2014
Theoretical motivations
supporting the new deal of
experiments in Gravitation
Gravitation and the other fundamental
interactions
Fundamental
Interaction
Crucial years
Fundamental
constant
Normalized Intensity
Gravity
1687
Gmp2/hc
5.1x10-39
Weak
nuclear force
1934
GFermi (mpc2)2
1.03x10-5
Electromagn
etism
1864
e2/(4 p eohc)
7.3x10-3 ~ 1/137
as
0.119
Strong
1935/1947
nuclear force
The open question
• Why the weak force is 1032 times stronger than gravity?
– This is the hierarchy problem.
• Many theoretical physicists have devoted significant fractions of
their careers to trying to solve this problem:
– new particles and new forces are needed (supersymmetry,
technicolor , little Higgs, etc.) ?
– gravity is mistaken? Do they exist new unknown dimensions (“extra
dimensions”), where the gravity strength leak off?
• If extra dimensions exist, they could be as big as a millimeter and no
experiment would have detected them!
In any case Gravity itself would be only way to solve the mistery
"seeing" for example these extra dimensions.
The Dirac large number hypothesis
Electric /Gravity force ratio between an electron and a proton
N1 = e2 /(4 p eo G me mp) ~ 2x1039
(Universe horizon ) / (Classical electron radius) ratio
N2 = (c Ho-1)/[e2 (4 p eo mec2) -1] ~ 5x1040
(Ho-1  is the Hubble time 68 km/s/Mpc ~ 1.4 x 1010 years)
The two numbers are nearly coincident, N1≈ N2 and, since the Universe is expanding,
if this numerical coincidence is ALWAYS verified
G=G(t)
or
a= a(t)
the coupling constants are not…….. any more constant
Do they change with energy converging
to a common value ?
Standard Model
Super-simmetric Model
Source: David Kaplan
>1O16 GeV  not far to the Planck scale
where the Gravity is crucial
Cosmology
The Big Bang associated to the
inflationary scenario, a rapide
expansion between 10-33 and 10-35 s,
at present is the dominant theory of
the creation of the universe:
Baryongenesis happened in an
epoch before inflation, when CP
violation mechanism prefer matter
to antimatter
Quarks and anti-quarks combined at
10-5 s.
Nucleosynthesis started at about 3
min.
380,000 years neutral atoms started
to form and matter and radiation
were separated ( decoupling)
Cosmology and Great Unification Theory
In principio
erat verbum
The
Gravity
Planck
decoupled
Era
scale
W.&
EM.
un. tested Strong force
@LEP&LHC decoupled
Weak
interaction
decoupled
Present
universe
Forces unified
Time
Length
[m]
Temperature
[GeV]
1 GeV  1.2
1013 K
Gravity,
Strong, Weak
and E. M.
forces
0
0
∞
Nuclear, Weak
and E.M
forces
10-43 [s]
10-35
1019
Weak and
Electromagnet
ic forces
10-35 [s]
10-27
1014
All interaction
splitted in
Nature
10-11 [s]
10-3
102
“” “” “”
10 10 [y] - 3
10 17 [s]
1026
10-12
Does Cosmology challenge GR?
•
Experiments in laboratories have confirmed that on Earth GR is valid to
extremely high precision. Moreover, peculiarities about the orbits of Mercury
(perihelia shift) or pulsars are very well explained with GR.
•
On the other hands Cosmic Microwave Background (CMB) in 1965 confirmed a
key prediction of the Big Bang Cosmology. Then, the observation of CMB
anisotropies supported the inflationary scenario, i.e. that quantum
fluctuations in the microscopic inflationary region, magnified to cosmic size,
become the seeds for the growth of structure in the universe
•
However, GR alone fails in describing structures as cluster of Galaxies and
Galaxies: we need an extra mass, the gravitating dark matter, to stabilize the
observed structures.
CMB measurements show that just the 4.5 % of the universe content is
ordinary matter while we need the 28% of gravitating matter to fit data (dark
matter particles interact only through gravity and possibly the weak force).
•
Moreover, the expansion rate of the universe measured by observing the
distant galaxies and supernovae push toward the hypothesis of the existence
of a negative pressure (dark energy), related to the vacuum energy: it should
contribute to the GR stress-energy tensor causing the accelerating expansion.
The cosmological standard model
• A pure GR approach, as presented and accepted by A. Einstein, is
not sufficient to explain the modern cosmological observations
• A standard cosmological model has to include dark matter and an
expanding universe: the present standard model is LCDM.
• The model assumes a scale invariance in the spectrum of primordial
perturbations and describes a universe without spatial curvature.
•
L is the cosmological constant ( firstly introduced by Einstein and
then rejected by himself). It represents the vacuum energy, which
would explain the accelerated expansion of the universe and
constitute 70% of the energy density contained in it.
ΛCDM success and….weakness
• ΛCDM describe successfully the large scale structure of the Universe and it
predicts the existence of the baryon acoustic oscillation feature, the CMB
polarization and the statistics of the weak gravitational lensing
• The model is based on six parameters, which are estimated by matching
the model with the cosmological observations.
However, LCDM does not explain the nature of the dark matter and the dark energy field;
it is in contrast with other experimental evidences as for example
- the central density profile of galaxies,
- the luminosity of dwarf galaxies: in hydro-dynamical simulations it is almost two orders
of magnitude higher than expected for haloes of this mass,
- etc., etc,…………………….
• L is an energy density in an expanding Universe. As consequence the
energy is not conserved in this model, and we are pushed to postulate
that the Universe may not be an isolated system, i.e. it should exist a
“Dark Side” of the Universe.
(The cosmologist J. A. Peackock is used to say:
<<Vacuum should act as a reservoir of unlimited
energy, which can supply as much as is required
to inflate a given region to any required size at
constant energy density.>>)
Alternative approaches
MoND ( and Mond+):
F= m m(a/ao) a
(ao~10-10 m/s2 and m(a/ao)  1 for a/ao ∞)
f(R) gravity: family of generalized GR theories, each one with a different assumption on the
structure of the Ricci scalar
Tensor-Vector Theories (TeVeS): equivalent to MoND in the non-relativistic limit
String cosmology: orginated by G. Veneziano, open the door even to a pre-big bang scenario
Beyond General Relativity: how to get
experimental evidence?
• GR experimental proofs are all related to the case of very weak limit
In the near future the strong regime will be explored by detecting
Gravitational Waves.
Gravitational waves may contain direct signatures of the universe’s
inflationary period ( see BICEP2!) or of the electroweak phase transition or
ultimately may present direct traces of quantum gravity.
• A complementary approach, emerged as one of the most rapidly growing
subfields of modern physics, is to carry on precision laboratory tests of
gravity.
Laboratory and space-based experiments are designed to test the foundations
of General Relativity and to probe theories that predict deviations from
General Relativity.
The starting point: GR is a complete gauge theory based on
the assumption of Einstein Equivalence Principle (EEP)
New physics can be hidden beyond the violation of this assumption
The Einstein Equivalence Principle
(EEP)
• Local Lorentz Invariance (LLI):
The result of any non-gravitational experiment is independent of the speed of
the apparatus (in free fall)
• Local Position Invariance (LPI):
The result of any non-gravitational experiment is independent of where and
when it is brought to completion in the Universe.
• Universality of Free Falling (UFF or WEP):
If an uncharged test body is placed at an initial event in space-time and given
an initial velocity there, then its subsequent trajectory will be independent of
its internal structure and composition
Each experiment, devoted to falsify one of these assumptions,
is classified as an effort to search for new physics
The way to classify and compare
experimental results
• The experiments challenging the EEP are compared using two
different approaches:
– Standard Model Extension (SME). This is an approach aimed by the
particle physicists. It is the generalization of the usual Standard Model
and General Relativity allowing for violations of Lorentz and CPT
symmetry. The violation is controlled by a set of coefficients whose
values can be determined or constrained by experiment. (Colladay, D., and V. A.
Kostelecky ́, 1997, Phys. Rev. D 55, 6760. Colladay, D., and V. A. Kostelecky ́, 1998, Phys. Rev. D 58, 116002.)
– The Parameterized Post Newtonian (PPN) formalism is an approach
aimed by the gravitational physicists. The PN expresses Einstein’s
equation of Gravity in terms of the lowest-order deviation from the
Newton’s law. In the PPN formalism a set of parameters are defined,
in which a general theory of gravity can differ from GR gravity. This
theoretical frameworks held in the case of weak field limit (see Will, C. M.
Theory and Experiment in Gravitational Physics, University Press, Cambridge, 1993)
The two approaches don’t communicate so well each other !!!
Verifying LLI
• The results of various experiments can be interpreted as a local
verification the laws of Special Relativity (SR), for example when we
check
– the role played by the Lorentz group in relativistic kinematics (the fourmomentum conservation).
– the decay times of elementary particles
Consequence of the SR violation
- In vacuum the light does not travel at a constant speed c in all frames of
reference,
Regardless of the motion of the source and the observer
- The laws of physics have not the same form in all inertial reference systems
Verifying LLI
A violation of Lorentz invariance can be described by adding to the "dynamic
invariant" additional vector or tensor fields ("background” fields), constant or
slowly time-varying, which are coupled directly with the matter
• c is not any more constant
c’ = c + k v
Measuring the arrival time of pulses
from the binary X ray sources
k< 2 10-9
• the space-time is not any more isotropic
Current experiments
•
•
•
•
Limits set from astronomical observations
– Measurements on light from GRB show that the speed of light does not
vary with energy.
Clock-Comparison Experiments
– Study of the energy level of nucleons to find anisotropies in their
frequencies
QED tests in Penning Traps
– (g-2) measurement in Electron-Positron and Proton-Antiproton
(examined g= ws/wc ~ 2 , i.e. the anomaly wa =|ws- wc| measured directly,
2.4 x 10-21 me , or for sidereal orientation under consideration of Earth's
orientation, 1.6 x10-21 me)
Muonium spectroscopy
– search for deviations in the anomaly frequency of m – anti-m, direct and
for sidereal variations
•
Spin-polarized torsion pendulum
- search for anisotropies with respect
to electron spins
(The octagonal pattern of magnets has an overall spin
polarization in the octagon’s plane, defining preferred
direction in the space. The whole apparatus is
mounted on a turntable and when we turn the LI viol.
determine a torque on the balance)
University of
Washington
Verifying LPI
• An historical test of GR: the Pound and Rebka
experiment
 
Consequence of LPI violation is that
Z
rec
 rec
em
U
 (1  a ) 2
c
Gravitational Red-Shift Experiments
Glen Rebka at the lower end
of the Jefferson Towers,
Harvard University
Recent LPI limits
(A. Bauch and S. Weyers: PHYSICAL REVIEW D, 65, 081101-R)
(David Norris – Phys G -Spring 2007)
• Four NIST H masers ( / =2x10-16 1/day compared to Cs
clock standards from NIST, Germany, France, and Italy over a
period from 1999 to 2006.
– The variation of frequency correlated with changes in the
gravitational potential due to the earth’s orbit was extracted:
|a|< 1.4 x 10-6
• LPI violation implies the change of fundamental physical
constants such as for example the fine structure constant.
– Measurement of concentration ratio of Sm149 / Sm147 in the Oklo
mine (a natural nuclear reactor in Gabon) compared to the
expectation on the base of the assumption of the variation of the
fission cross-section
da e
a e  5 /1015 years
dt
Experimental CPT tests  LI tests
Requires antihydrogen at
mK temperature (laser cooling)
Results achieved on Hydrogen
1S-2S v=2 466 061 413 187 103 (46) Hz
Natural width: 1.3 Hz
/= 1.5 10-14 Cold beam
PRL84 5496 (2000) M. Niering et al
/= 10-12 Trapped H
E  100 mK
E  100mK
PRL 77 255 (1996) C. Cesar et al
GS-HFS measured to 1 mHz:
/= 10-13
Credit M. Giammarchi –INFN Milano
Verifying UFF
The violation of UFF can be associated to the any kind of energy content of the sample
mP  mI   A E A / c 2
E
A
A
Internal energy of the sample associate to the interaction A
 A UFF violation factor associate to the interaction A
To evaluate the experimental results we introduce the EÖTVÖS ratio
  def
| a1  a2 |
2 | a1  a2 |

| a1  a2 | / 2 | a1  a2 |

mP 2
 A E2A 
g
a2 
g  1  
2 
mI 2
A mI 2 c 


mP1
 A E1A 
g
a1 
g  1  
2 
mI 1
A mI 1c 

For a weak violation
 E1A
E2A 

   

2
2 
mI 2 c 
A
 mI 1c
A
UFF and the nature of the mass
In the case of laboratory experiments the typical main energetic
contribution is due to the strong nuclear interaction
ES
2
 2 1/ 3
2
2
2


1
.
7

10

1
.
9

10
A

2
.
5

10
(
1

2
Z
/
A
)

1
.
41
A

2
mc
Z Atomic Number, A Mass Number
=1 ==>> A even, Z odd
 =0 ==>> A odd
 = -1 ==>> A even, Z even
A
E2A 
E1S
E2S
A  E1
S
 |  | 
   


 10 12
2
2 
2
2
mI 2 c 
mI 1c
mI 2 c
A
 mI 1c
|S | < 5 10-10
For example in the case Al - Pl
(ES / mc2)Pl - (ES / mc2)Al 2 x 10-3
The basic instrument of Experimental
Gravitation
• The torsion Balance
200 years of
evolution:
•G measurement
•UFF test
•Search of LI
violation
Composition dependent experiments;
a couple of original examples
Fg1
The torsional
pendulum of
Loránd von
Eötvös
8-Body Torsion
Pendulum used
in the Eöt-Wash
III Instrument
g sun
1
Fin1
Fg2
DICKE:
torsional
pendulum
2
Fin2
8-Body Torsion Pendulum used in
the Eöt-Wash III Instrument
Composition Dependent - II
Free-Fall experiment
Composition dependent test –III
Gravity and anti-matter
•No direct measurements
on gravity effects on
antimatter
10-18
WEP tests on matter system
10-16
10-14
•“Low” precision
measurement (1%) will be
the first one
10-12
10-10
10-8
10-6
10-4
10-2
1700
1800
1900
Can be done with a beam of Antiatoms flying to a detector!
L
H
g
Credit M. Giammarchi – INFN Milano
2000
AEGIS
first
phase
AEGIS strategy
Moire’ deflectometer and detector
1) Produce ultracold antiprotons (100 mK)
Cold antiprotons
2) Accumulate e+
3) Form Positronium (Ps) by e+ interaction with porous
target
4) Laser excite Ps to get Rydberg Ps
5) Form Rydberg cold (100 mK) antihydrogen by
*
p  ( Ps)  H  e
*
Porous target
e+

6) Form a beam using an inhomogeneous electric field to
accelerate the Rydberg antihydrogen
7) The beam flies toward the deflectometer which
introduces a spatial modulation in the distribution of the
Hbar arriving on the detector
8) Extract g from this modulated distribution
Credit M. Giammarchi – INFN Milano
Composition independent tests:
studying Gravity vs. distance
General relativity (GR) predicts deviations from Newtonian gravity at the several-meter level
in the lunar orbit. So millimeter-level measurement precision puts GR to a hard test and
those can be obtained by the Lunar Laser Ranging (LLR). Limits on PPN b 5103
Apollo 11 mirror
Apollo 15
retroreflector
consisting of
300 cornercube 3.8 cm
set in
hexagonal
array.
• Ex. : (mem)Brane theory
predicts Moon anomalous
LLR @McDonald
precession of ~ 1 mm/orbit, in
Observatory
addition to GR geodetic
precession
• Now LLR accuracy few mm
(thanks to APOLLO station). In
the future by MoonLIGHT 
100 μm
Wenzel LLR station (Germany)
Gravity
at planetary distances
m
Orbit equation in central field a u()
F  F (r )rφ
S
(u  1 / r )
2
2
d u
m

u


F (1 / u )
2
2 2
d
Lu
( L | r  mv | mr 2 )
By Iincluding a the perturbation effect due to a Yukawa potential
to the 1/r2 law , we get a perielium precession
2
 aP   aP / 
 e
 
  ( n 1   n )  2p  pa 
Limit on lunar orbit precession
a< 3 10-11 for  ~ 108 m
Gravity at interplanetary distances -
Gravity at interplanetary distances - II
The Pioneer anomaly has been registered on two deep space probes with the best navigation
accuracy: Pioneer 10 and 11.
The effect is the observed deviation from
predicted acceleration after they passe
about 3 1012 m ( 20 A.U.) on their
trajectories
- The two probes are identical.
-The two trajectories are similar .
- No trajectory correction via thrusters
- The spacecrafts are spin stabilized
Launched in 1972 and 1973, the first hint
of the effect is dated 1980 and the last
contact in 2003
Newer spacecraft have used spin stabilization for some or all of their mission, including both
Galileo and Ulysse. These spacecraft indicate a similar effect, but too faint to be conclusif.
T
Gravity at interplanetary distances - III
Anderson et al Phys Rev. D 65 (2002) 082004
Doppler observable f/fo = 1 – 2vP/c
vp – v model = - ap(t- tin)
ap=(8.73 + 1.33) 10-10 m/s2
Gravity at interplanetary distances - IV
S.G. Turyshev et al.
PRL 108, 241101 (2012)
The 2012 Explanation:
thermal recoil force
The spacecraft is powered
by a radioisotope generator
(RTG), which can emit heat
in a preferred direction
determining the opposite
movement of the
spacecraft.
However, all thermal
models predict a decrease
in the effect with time,
which did not appear in the
initial analysis.
ANDERSON et al. PHYS. REV. D 65 082004 (2002)
A long effort was needed
to recover old thermal data
for showing the effective
decrease with time
Gravity at short distance
• For solving the hierarchy problem, i.e. the enormity of the
difference between the electroweak scale mEW∼103 GeV and the
Planck scale MPl=GN−1/2∼1018 GeV, it has been pointed out that one
way is to probe the gravity law at distance well below 10 mm.
• While electroweak interactions have been probed at distances
approaching ∼mEW−1, gravitational forces have not remotely been
probed at distances ∼MPl−1.
• Our interpretation of MPl as a fundamental energy scale (where
gravitational interactions become strong) is based on the
assumption that gravity is unmodified over the 32 orders of
magnitude between where it is measured at ∼ 10-3 mm down to
the Planck length ∼10−35 m
• Moreover, small value of the cosmological constant L could be
stabilized by particles of wavelength ~ 0.1 mm (R. Sundrum, J. High Energy Phys,
9907, 001(1999))
Testing gravity by means of
gravimeters
Use of gravimeters to measure the
modulation of the gravity due to the
change of the water level in artificial
lakes
g(0)
MM
g(z)
M
a< 10-3 for  ~ 10 m
Gravimeters on a
television tower
a< 104 for  ~1 km
Gravimeters
in a mine
M
Few classical tests
•
R.Spero et al., Phys.Rev.Lett. 44, 1645-1648 (1980)
   measured   theoretical  (0.02  0.14) 1013 N  m
a< 10-4 for  from 2 to 5 cm
w
CC
uu
a
FF
ee
Astone P. et al,
Eur. Phys. Jour. C
5, 651-664, (1998)
Beyond GR ?
Gravity below 1 cm
Gold Test Mass
Fiber for interferometer
f0
Cantilever
Cover wafer
25 µm
Au/Si Drive Mass
Shield wafer
(not shown in
zoomed image)
Credit to
S.
J. Smullin, Stanford
University
Piezo Actuator
(+/- 120 µm at f0/3)
Metallization
Drive mass
Figure Not to Scale
Andrew A. Geraci, Sylvia J. Smullin, David M. Weld, John Chiaverini, and Aharon Kapitulnik, Phys. Rev. D 78, 022002 (2008)
Gravity at short distance – II :
the fiber interferometer
Fiber Coupler
Laser
Diode
Feed-through
Cryostat
Signal
Reference
PD
PD
Cantilever
Specifications
•  = 1310 nm
• Cantilever end of fiber cleaved
• Power striking cantilever ~10 mW
• Above 1kHz, noise floor ~0.01 Å/√Hz
• May subtract/divide Reference
Credit to S. J. Smullin, Stanford University
Fiber
Fabry-Perot
Cavity
Cantilever
Gravity at short distance III
The Stanford limits set
measuring forces in the
10-18 N (atto) range.
A long list of limiting noise
-Thermal noise of the cantilever
-Interferometer Noise
-Electrostatic patches
-Magnetic background
Then , they have to correct for a bias effect: the Casimir force
The Casimir effect: the vacuum energy in
z
an
e.m.
cavity
1
U  w
L
The CASIMIR effect
2
z
a
y
x
x
hcL
U
2
d k
 np 
2
k 


2

 a 
n   ( 2p )
2 n 
2
U
p 2 L2 hc
FC  

a
240a 4
In a total reflecting. cavity
the permitted e.m. modes
are the
y kz = np/a
for any value of kx e ky
2
U reg  
p 2 L2 hc
720a 3
FC
0.013
2

dyne
/cm
L2
a4
Bressi,
G. Carugno,
R. Onofrio,
G. Ruoso: Casimir
Phys Rev
Lettbetween
88, Au and Si of,
In the•G.
case
of Stanford
they computed
the differential
force
41804
primo
sistema
con2 piatti
allowing
to(2002):
set a limit
at a force
value
x10-20 metallici
N, for a =1 and = 20 mm.
Weighing the vacuum: the
gravitational mass of the e.m. vacuum
Towards measuring the Archimedes force of vacuum
E.Calloni, M.De Laurentis, R. De Rosa, F. Garufi, L. Rosa, L, Di
Fiore,G. Esposito, C.Rovelli, P. Ruggi, F. Tafuri
arXiv:1401.6940
Vacuum energy
?
Gravitational Mass
Space-time curvature
Measuring the Archimede force of the Vacuum
The idea is to create a lack of vacuum energy in a volume :
- if
- the vacuum energy gravitates
-then
-this volume floats in the sea of virtual photons around us
Measuring the Archimedes force of vacuum
The floating force per unit surface is extremely tiny,
FArch
1 p h g
15
16


10

10
Pa
2
3
L
720 c a
so that we need to modulate the vacuum energy contained in the cavity

Cavity plates transparent  the weight of virtual photons is higher
Cavity plates reflective  virtual photons will be expelled and the weight
decreases.
The proposed technique;
- take advantage of the high Tc superconducting transition of special
mirrors ( from semi- to super- conductors)
Measuring weak forces
Measuring the effect by modulating
at low frequency and exciting
the a torsion pendulum at the
resonance
Measuring the effect by using
Advanced VIRGO with Tobs= 6 month
Summary of the limits at short
distances
Summary of the limits up to 1014 m
Conclusion
Measurement of fine effects in experimental physics,
especially in gravitational experiments, needs high
technology and nontrivial methods.
New experiments, which are now in progress thanks
to the technological development in the various
world gravitational centers, will be a successive stage
in the knowledge of the nature of the gravitational
interaction.
Our wish is that the new gravitational laboratory at
the department of Physics of the FEDERICO II
university can give crucial contributions to unification
scenario of all the fundamental interactions
Extra slides
The hierarchy problem
• A hierarchy problem occurs when the fundamental parameters, such as
coupling constants or masses are vastly different than the parameters
measured by experiment.
• This can happen because measured parameters are related to the
fundamental parameters by a prescription known as renormalization.
• Hierarchy problems are related to fine-tuning problems. In some cases, it
appears that there has been a delicate cancellation between the
fundamental quantity and the quantum corrections.
• Studying the renormalization in hierarchy problems is difficult, because
such quantum corrections are usually power-law divergent, which means
that the shortest-distance physics are most important.
• Researchers postulate new physical phenomena that resolve hierarchy
problems without fine tuning.