Fulvio RicciDipartimento di Fisica

Università di Roma La Sapienza&

INFN Sezione di Roma

Napoli 2 Aprile 2014

Experimental Gravitation

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

Electromagnetism 1864 e2/(4 p eohc) 7.3x10-3 ~ 1/137

Strong nuclear force 1935/1947 as 0.119

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 hypothesisElectric /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 coupling constants are not…….. any more constant

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)

Do they change with energy converging to a common value ?

Standard ModelSuper-simmetric ModelStrong

Weak

E. M.

Strong

WeakE. M.

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

Forces unified Time Length[m]

Temperature [GeV]

1 GeV 1.2 1013 K

In principio erat verbum

Gravity, Strong, Weak

and E. M. forces

0 0 ∞

Gravity decoupled

Nuclear, Weak and E.M forces

10-43 [s] 10-35 1019

Strong force decoupled

Weak and Electromagnet

ic forces10-35 [s] 10-27 1014

Weak interaction decoupled

All interaction splitted in

Nature10-11 [s] 10-3 102

Present universe “” “” “” 10 10 [y] - 3

10 17 [s] 1026 10-12

The Planck

ErascaleW.& EM.

un. tested @LEP&LHC

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,…………………….

Alternative approaches

• 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.>>)

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 limitIn 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 four-

momentum conservation).– the decay times of elementary particles

- 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

Consequence of the SR violation

Extremely well verified in a context of Particle Physics Experiments

Verifying LLI

• c is not any more constantc’ = c + k v

• the space-time is not any more isotropic

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

k< 2 10-9

Measuring the arrival time of pulses from the binary X ray sources

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

University of Washington

• 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)

Verifying LPI• An historical test of GR: the Pound and Rebka

experiment

Glen Rebka at the lower end of the Jefferson Towers, Harvard University

Consequence of LPI violation is that 2)1(

c

UZ

rec

emrec Δ+=

−= α

ννν

Gravitational Red-Shift Experiments

Recent LPI limits(A. Bauch and S. Weyers: PHYSICAL REVIEW D, 65, 081101-R)

(David Norris – Phys G -Spring 2007)

• Four NIST H masers ( / Dn n =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

€

dα e

dtα e < 5 /10

15 years

Credit M. Giammarchi –INFN Milano

mKE 100

KE 100

1S-2S v=2 466 061 413 187 103 (46) HzNatural width: 1.3 Hz

Results achieved on Hydrogen

D / n n = 1.5 10-14 Cold beam PRL84 5496 (2000) M. Niering et al Dn/ n = 10-12 Trapped H PRL 77 255 (1996) C. Cesar et al

Requires antihydrogen at

mK temperature (laser cooling)

Experimental CPT tests LI tests

Dn/ n = 10-13 GS-HFS measured to 1 mHz:

Verifying UFFThe violation of UFF can be associated to the any kind of energy content of the sample

∑+=A

AAIP cEmm 2/η

€

E AInternal energy of the sample associate to the interaction A

Aη UFF violation factor associate to the interaction A

||

||2

2/||

||

21

21

21

21

aa

aa

aa

aadef +

−=

+−

=η

gcm

Eg

m

ma

A I

AA

I

P⎟⎟⎠

⎞⎜⎜⎝

⎛+== ∑ 2

1

1

1

11 1

η gcm

Eg

m

ma

A I

AA

I

P⎟⎟⎠

⎞⎜⎜⎝

⎛+== ∑ 2

2

2

2

22 1

η

To evaluate the experimental results we introduce the EÖTVÖS ratio

⎟⎟⎠

⎞⎜⎜⎝

⎛−≈∑ 2

2

22

1

1

cm

E

cm

E

I

A

I

A

A

AηηFor a weak violation

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

δ2223/1222

41.1)/21(105.2109.1107.1 −−−−− +−⋅+⋅+⋅−= AAZAmc

E S

Z Atomic Number, A Mass Numberd=1 ==>> A even, Z odd = -1 ==>> A even, Z even =0 ==>> A odd

122

2

22

1

12

2

22

1

1 10|| −<−⋅⇒⎟⎟⎠

⎞⎜⎜⎝

⎛−≈∑ cm

Ecm

Ecm

Ecm

E

I

S

I

SS

I

A

I

A

A

A ηηηFor example in the case Al - Pl

(ES / mc2)Pl - (ES / mc2)Al » 2 x 10-3

|hS | < 5 10-10

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

1Fg1 Fin1

Fg2 Fin22g sun

DICKE: torsional pendulum

8-Body Torsion Pendulum used in the Eöt-Wash III Instrument 8-Body Torsion Pendulum used in

the Eöt-Wash III Instrument

The torsional pendulum of Loránd von Eötvös

Composition Dependent - II

Free-Fall experiment

Credit M. Giammarchi – INFN Milano

10-18

10-16

WEP tests on matter system

10-14

10-12

10-10

10-4

10-6

10-8

10-2

1700 19001800 2000

•No direct measurements on gravity effects on antimatter

•“Low” precision measurement (1%) will be the first one

Can be done with a beam of Antiatoms flying to a detector! AEGIS first phaseg

HL

Composition dependent test –IIIGravity and anti-matter

1) Produce ultracold antiprotons (100 mK)

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

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

Cold antiprotons

e+

Porous target

Moire’ deflectometer and detector

eHPsp**)(

AEGIS strategy

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 < 5 10b -3

Apollo 15 retroreflector consisting of 300 corner-cube 3.8 cm set in hexagonal array.

Apollo 11 mirror

Wenzel LLR station (Germany)

LLR @McDonald Observatory

• Ex. : (mem)Brane theory predicts Moon anomalous precession of ~ 1 mm/orbit, in addition to GR geodetic precession• Now LLR accuracy few mm (thanks to APOLLO station). In the future by MoonLIGHT 100 μm

S

)/1(22

2

2

2

uFuL

mu

d

ud−=+

θ

rrFF ˆ)(=r )/1( ru =

Orbit equation in central field a u(q)

)||( 2θ&rmrvmrL =×=

By Iincluding a the perturbation effect due to a Yukawa potential to the 1/r2 law , we get a perielium precession

m

λ

λπαπθθδφ /

2

1 2)( PaPnn e

a −+ ⎟

⎠

⎞⎜⎝

⎛+≈−−=

Limit on lunar orbit precessiona< 3 10-11 for l ~ 108 m

Gravity at planetary distances

Gravity at interplanetary distances - I

Gravity at interplanetary distances - IIThe 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

ap=(8.73 + 1.33) 10-10 m/s2

Anderson et al Phys Rev. D 65 (2002) 082004

Doppler observable f/fo = 1 – 2vP/c

vp – v model = - ap(t- tin)

Gravity at interplanetary distances - IV

ANDERSON et al. PHYS. REV. D 65 082004 (2002)

The 2012 Explanation: thermal recoil forceThe 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.

A long effort was needed to recover old thermal data for showing the effective decrease with time

S.G. Turyshev et al. PRL 108, 241101 (2012)

Gravity at short distance• For solving the hierarchy problem, i.e. the enormity of the difference

between the electroweak scale mEW 10∼ 3 GeV and the Planck scale MPl=GN−1/2 10∼ 18 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 m∼ EW

−1, gravitational forces have not remotely been probed at distances M∼ Pl

−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 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

a < 10-3 for l ~ 10 m DM

g(0)

g(z)M - DM

DM

Gravimeters in a mine

Gravimeters on a television tower

a < 10-4 for l ~1 km

Few classical tests• R.Spero et al., Phys.Rev.Lett. 44, 1645-1648 (1980)

€

Δτ =τmeasured − τ theoretical = (+0.02 ± 0.14) ×10−13N ⋅m

a< 10-4 for l from 2 to 5 cm

Fe

Cu

Fe

Cu

Astone P. et al, Eur. Phys. Jour. C5, 651-664, (1998)

Beyond GR ?

Credit to S. J.

Smullin, Stanford University

25 µm

Gravity below 1 cmGold Test Mass

Au/Si Drive Mass

Piezo Actuator(+/- 120 µm at f0/3)

Fiber for interferometer

Cover waferCantilever

Shield wafer(not shown in zoomed image) Drive mass

Metallization

Figure Not to Scale

f0

Andrew A. Geraci, Sylvia J. Smullin, David M. Weld, John Chiaverini, and Aharon Kapitulnik, Phys. Rev. D 78, 022002 (2008)

Credit to S. J. Smullin, Stanford University

Gravity at short distance – II :the fiber interferometer

LaserDiode

PD PD

Signal Reference

Fiber Coupler

Cryostat

Feed-through

Cantilever

Specifications• = 1310 nm• Cantilever end of fiber cleaved• Power striking cantilever ~10 W• Above 1kHz, noise floor ~0.01 Å/√Hz• May subtract/divide Reference

Fiber

Cantilever

Fabry-Perot Cavity

Gravity at short distance IIIThe 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 an e.m. cavity

22

2

22

)2(2⎟⎠

⎞⎜⎝

⎛+= ∑∫∞=

−∞= an

kkdhcL

Un

n

ππ

x

y

z

a

Lωh∑= 2

1U

The CASIMIR effectIn a total reflecting. cavity the permitted e.m. modes are the kz = np/a for any value of kx e ky

3

22

720a

hcLU reg

π−=

•G. Bressi, G. Carugno, R. Onofrio, G. Ruoso: Phys Rev Lett 88, 41804 (2002): primo sistema con piatti metallici

z

yx

In the case of Stanford they computed the differential Casimir force between Au and Si of, allowing to set a limit at a force value 2 x10-20 N, for a =1 and l= 20 mm.

€

FC

L2≈0.013

a4dyne /cm2

4

22

240a

hcL

a

UFC

π−=

∂∂

−=

Weighing the vacuum: the gravitational mass of the e.m. vacuum

Towards measuring the Archimedes force of vacuumE.Calloni, M.De Laurentis, R. De Rosa, F. Garufi, L. Rosa, L, Di Fiore,G. Esposito, C.Rovelli, P. Ruggi, F. TafuriarXiv:1401.6940

Vacuum energy Gravitational Mass

Space-time curvature?

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 Archimede force of the Vacuum

Measuring the Archimedes force of vacuum

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)

The floating force per unit surface is extremely tiny,

so that we need to modulate the vacuum energy contained in the cavity

€

FArch

L2≈1

720

π h

c

g

a3⇒ 10−16 − 10−15 Pa

Measuring weak forcesMeasuring 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

ConclusionMeasurement 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.