%\markright{GGonGround \underline{\textbf{Part B2}}}


\section{GGonGround project proposal: Part B2}
%\label{sec:PartB2}


\section{B2--a1: Curriculum Vitae of corresponding PI Anna M. Nobili}
\label{sec:B2SectionA}

\noindent{\underline {Born in Italy on September 1949}}
\vskip 3truemm


\noindent{\textbf {Positions in Italy and abroad}}

\begin{itemize}

\item{1992-present: associate professor in Astronomy,  University of Pisa, Italy (subjects taught: Elements of celestial mechanics, Physics I, Space Mechanics)}\\[-22pt]

\item{1991-1992: visiting scientist at Obervatoire de  Medoun, Paris, France (on leave from Pisa University)}\\[-22pt]

\item{1988-1989: visiting scientist (``Bepi Colombo'' ESA fellow) at Cornell University, Space Sciences, NY, USA (on leave from Pisa University)}\\[-22pt]

\item{1984-1985: visiting scientist at University of Glasgow, Glasgow, UK (on leave from Pisa University)}\\[-22pt]

\item{1981-1982: visiting scientist at Queen Mary College, London, UK (on leave from Pisa University)}\\[-22pt]

\item{1979-1992: permanent researcher at University of Pisa,  Italy}\\[-22pt]

\item{1976-1979: temporary researcher at University of Pisa,  Italy}\\[-22pt]

\item{1974-1976: temporary researcher at University of Bologna,  Italy}\\[-22pt]

\item{1973-1974: research fellow at SNS (Scuola Normale Superiore) Pisa, Italy}\\[-22pt]

\item{(1973: Laurea degree in Physics {\it summa cum laude})}\\[-22pt]

\item{1968-1970: Physics student at SNS (Scuola Normale Superiore) Pisa, Italy (to my knowledge, I was the second female student in the history of SNS to be admitted for Physics)}

\end{itemize}

\noindent{\bf {Responsibility in national and international research projects}}

\begin{itemize}

\item{2004-present: PI of GGG (GG on Ground) national experiment funded by the  II National Scientific
committee of INFN (Istituto Nazionale di Fisica Nucelare)}\\[-22pt]

\item{2008-2010: PI of GG Phase A2 Study with development of GGG experimental apparatus, funded by ASI (Agenzia Spaziale Italiana) }\\[-22pt]

\item{2007-2010: member of the ASI funded  national project ``Cosmology and fundamental Physics  in space '' as PI of the Fundamental Physics part }\\[-22pt]

\item{2001-2003: PI of the national project on ``The fundamentals of gravity:
measuring the universal constant of gravity G and testing the Equivalence Principle'' selected and  funded by the Italian Ministry of Research as a project of national interest}\\[-22pt]


\item{2001-2002: PI of GG Advanced Phase A funded by ASI to investigate feasibility in sun-synchronous orbit }\\[-22pt]


\item{1998-2002: PI of project  ``PGB-Enabling vibration free activity onboard the International Space Station (ISS)'', funded by ASI and  selection for flight on the  ISS; it was canceled in 2003 as a result of the Columbia shuttle disaster (co-owner of an Italian patent on PGB) }\\[-22pt]

\item{1997-1998: PI of GG Phase A Study funded by ASI after   national competition for a small mission}\\[-22pt]

\item{1996: PI of GG Pre-Phase A Study funded by ASI in preparation for a STEP-GG  competitive review at ESA}\\[-22pt]

\item{1989-1993: member of ESA-NASA science team on STEP (Satellite Test of the Equivalence Principle) mission - also  PI of sub-group an G-measurement with STEP; funded by ESA}\\[-22pt]


\item{1987-1994: PI of European project COGEOS on the  observation of geosynchronous satellites for geodynamics; funded by the European Commission}\\[-22pt]

\item{1986-1988: member of Italian-British project LONGSTOP  on the stability of the outer planets}

\end{itemize}
\vskip 3truemm

\noindent{\bf {Research interests}}
\vskip 3truemm

I have worked in solar system dynamics and was among the first to discover chaos in the solar systems (Nobili \& Burns, Solar system chaos, Science  244, 1425, 1989; Milani \& Nobili, An example of stable chaos in the Solar System, Nature, 357, 569-570, 1992). In space geodesy I have contributed to  understanding the small forces which affect the  motion of laser tracked satellites (I am co-author of a book on ``Non gravitational forces and satellite geodesy'', Adam Hilger Ltd., Bristol and Boston 1987).
%\vskip -1mm

I have always tried to { use} my understanding of the  space environment for a precision experiment in fundamental physics. At first, I tried to measure the fundamental constant of gravity $G$  by {\it manufacturing} a very elegant planet-satellite system inside a spacecraft in geosysnchronous orbit (Nobili et al., ESA Journal 14, 389-408, 1990). The interest for testing the equivalence principle in space was much stronger than that for measuring $G$, and I was offered by ESA the opportunity to work in the joint ESA-NASA science team which was set-up to investigate the Stanford proposed mission  STEP (Satellite Test of the Equivalence Principle) aiming at a breakthrough improvement in testing the equivalence principle (to  $10^{-17}$). In those years I became more and more convinced that a radically new type of sensor  could make the experiment and the mission much simpler -- first of all, by not requiring cryogenics. This is how in the mid 1990s the ``Galileo Galilei (GG)''  project was initiated.

The GG concept was so innovative and unconventional that at first it was not accepted. It involves macroscopic proof  masses in rapid rotation while trying to measure  extremely small forces between them, which at first glance is not a good idea. \href{http://eotvos.dm.unipi.it/eval/esa/index.html}{A high level review panel of ESA  made written statements which turned out to be wrong by many orders of magnitude}. Papers were published to demonstrate the validity of the idea and the feasibility of the space experiment, but at some point I became convinced that it was necessary to provide experimental evidence. GG on Ground (GGG) was initiated. The apparatus has now reached an interesting level of sensitivity, with a significant recent improvement  due to  the contribution of Raffaello Pegna.  More importantly,  we can convincingly argue that it is possible to improve it by serval orders of magnitude, thus making the case for the experiment in space really strong. But {\it ``new blood''} must be injected into the project, because  an advanced low noise laser gauge read out must be implemented. The PI Guido Zavattini, with the collaboration of Mike Shao from JPL, is up to the task. I am fully dedicated to this project and determined to bring the mission in orbit. The dedication of  Guido Zavattini to challenging experiments in fundamental physics is apparent from his CV; if this proposal is approved, this will become his  new challenging experiment.

\vskip 3truemm


\noindent{\bf {Awards}}

\vskip 3truemm

In 2006 I have been awarded  the prize {\it Premio Pisa donna 2006} by the city of Pisa

\vskip 3truemm

\noindent{\bf {Funding}}

\vskip 3truemm

I have devoted considerable efforts to fund my research projects, taking the responsibility to lead the project proposals. I have been funded by the Italian Ministry of Research, by the European Commission, by the Italian Space Agency (ASI) and by INFN (Istituto Nazionale di Fisica Nucleare). Funds provided by ASI in the years 2008-2010 --in addition to INFN funds-- have allowed us to build a new ad hoc vacuum chamber which  accommodates a new weakly suspended GGG apparatus. In the current year GGG is funded by INFN; application for next year is due by the fall when INFN panel (Commissione Nazionale Scientifica II) reviews all projects and decides about next year funding. INFN resources are devoted to the equipment only.

\clearpage

\section{B2--b1: 10-yr track-record of corresponding PI Anna M. Nobili}
\label{sec:B2SectionB}

10 papers published in refereed journals during the last 10 years:

\begin{enumerate}


\item \textbf{R. Pegna, \underline{A.M. Nobili}, M. Shao, S.G. Turyshev, G. Catastini, A. Anselmi, R. Spero, S.
Doravari, G.L. Comandi, A. De Michele}, Abatement of thermal noise due to internal damping
in 2D oscillators with rapidly rotating test masses, \textit{Phys. Rev. Lett.} 107, 200801--5, 2011 \textbf{Citations:~0}\\


\item \textbf{\underline{A.M. Nobili}, G.L. Comandi, S. Doravari, D. Bramanti, R. Kumar, F. Maccarrone, E. Polacco,
S. G. Turyshev, M. Shao, J. Lipa, H. Dittus, C. Laemmerzhal, A. Peters, J. Mueller, C. S.
Unnikrishnan, I. W. Roxburgh, A. Brillet, C. Marchal, J. Luo, J. van der Ha, V. Milyukov, V.
Iafolla, D. Lucchesi, P. Tortora, P. De Bernardis, F. Palmonari, S. Focardi, D. Zanello, S.
Monaco, G. Mengali, L. Anselmo, L. Iorio \& Z. Knezevic}, ``Galileo Galilei'' (GG) a small
satellite to test the equivalence principle of Galileo, Newton and Einstein, \textit{Exp Astron} 23, 689--710, 2009 \textbf{Citations:~7}\\


\item \textbf{\underline{A.M. Nobili}, G.L. Comandi, D. Bramanti, S. Doravari, D. Lucchesi, F. Maccarrone}, Limitations
to testing the equivalence principle with satellite laser ranging, \textit{General Relativity and
Gravitation}, 40, 1533--1544, 2008  \textbf{Citations:~2}\\


\item \textbf{\underline{A.M. Nobili}, G.L. Comandi, S. Doravari, F. Maccarrone, D. Bramanti, E. Polacco},
Experimental validation of a high accuracy test of the Equivalence Principle with small satellite
``Galileo Galilei--GG'', \textit{International Journal of Modern Physics} D, 16, 2259--2270, 2007  \textbf{Citations:~3}\\


\item \textbf{G.L. Comandi, R. Toncelli, M.L. Chiofalo, D. Bramanti and \underline{A.M. Nobili}}, Dynamical Response
of the Galileo Galilei rotor for a Ground test of the Equivalence Principle: theory, simulation
and experiment. Part II: the rejection behavior, \textit{Review of Scientific Instruments}, 77, 034502(1--10), 2006 \textbf{Citations:~0}\\


\item  \textbf{G.L. Comandi, M.L. Chiofalo, R. Toncelli, D. Bramanti, E. Polacco and \underline{A.M. Nobili}},
Dynamical Response of the Galileo Galilei rotor for a Ground test of the Equivalence Principle:
theory, simulation and experiment. Part I: the normal modes, \textit{Review of Scientific Instruments},
77, 034501(1--15), 2006   \textbf{Citations:~0}\\


\item \textbf{G.L. Comandi, \underline{A.M. Nobili}, D. Bramanti, R. Toncelli, E. Polacco, M.L.Chiofalo}, ``Galileo
Galilei on the Ground -- GGG'': experimental results and perspectives, \textit{Physics Letters} A, 318,
213--222, 2003  \textbf{Citations:~1}\\


\item \textbf{\underline{A.M. Nobili}, D. Bramanti, G.L. Comandi, R. Toncelli, E. Polacco, M.L. Chiofalo}, ``Galileo
Galilei -- GG'': design, requirements, error budget and significance of the ground prototype,
\textit{Physics Letters} A, 318, 172--183, 2003   \textbf{Citations:~5}\\



\item \textbf{\underline{A.M. Nobili}, D. Bramanti, G.L. Comandi, R. Toncelli, E. Polacco}, A rotating differential
accelerometer for testing the equivalence principle in space: results from laboratory tests of a
ground prototype, \textit{New Astronomy}, 8, 371--390, 2003   \textbf{Citations:~3}\\


\item \textbf{\underline{A.M. Nobili}, D. Bramanti, G.L. Comandi, R. Toncelli, E. Polacco}, Radiometer effect in the
Microscope space mission, \textit{New Astronomy}, 7, 521--529, 2002 \textbf{Citations:~3} \\
\end{enumerate}



Overall I am co-author of 71 papers published  in refereed journals, 1 book, 36 invited papers/reviews, and 1 Italian patent

In the last 10 years I have given about 20 invited presentations at international conferences and have organized 2 international workshops in Pisa


\clearpage


\section{B2--a2: Curriculum Vitae of  PI Guido Zavattini}
\label{sec:B2SectionA}

Born in Switzerland, April 1963

\bigskip

Present Position:
Associate Professor in Physics

\bigskip


Studies

{}- I graduated in Physics at the University of Pisa on 2 March 1989
with 110/110 votation

{}- PhD program in Physics at the University of Bologna: 3/1990-3/1993

{}- PhD title: \ 23/9/1993

{}- Post-Doc at INFN-Trieste: \ 3/1993-3/1994

\bigskip

FERRARA UNIVERSITY:

29/12/2008 - present: Associate Professor in Physics at the University
of Ferrara

28/2/2008: \ Qualified as Associate Professor in Physics (FIS/07)

15/8/2002 - 15/8/2003: On leave at the University of California at
Davis, Davis, California, USA

1/9/1994 -- 29/12/2008: \ \ University researcher

\bigskip

OTHER PROFESSIONAL POSITIONS

4/2007 - present: Member of the Scientific and Technical Advisory
Committee (STAC) for the VIRGO project

7/98 - 7/2002: Ferrara coordinator for the II National Scientific
committee for INFN

7/2004 - present: Ferrara coordinator for the II National Scientific
committee for INFN

\bigskip

FOREIGN LANGUAGES

English and Italian: \ Mother tongue

French: Excellent


\rule{\textwidth}{0.2mm}

\bigskip

Principle research activities

FUNDAMENTAL PHYSICS

THE PVLAS EXPERIMENT (Trieste 1993 - 1994; Ferrara 1994 - present)

Funding: INFN (Istituto Nazionale di Fisica Nucleare) grant and MIUR
(Ministero dell{\textquoteright}Istruzione, Università e della Ricerca)
grant.

I am the spokesperson and PI for both the INFN and MIUR grants.

The PVLAS experiment, financed by INFN, aims at the first measurement of
the magnetic birefringence of vacuum induced by an intense magnetic
field.

This effect, predicted by QED, is connected to photon-photon scattering
by means of the {\textquotedbl}vacuum polarization{\textquotedbl}

Furthermore the PVLAS experiment will put new laboratory limits on the
mass and coupling constant of hypothetical neutral particles which
couple to two photons. The hypothetical particles could contribute to
dark matter solution.

The experiment is in a phase of being upgraded in sensitivity after a
long period of data taking and analysis.

The best limits on the vacuum magnetic birefringence and consequently on
the low energy photon-photon cross sections have been set by this
experiment. Furthermore the experiment has produced new precise
measurements of the Cotton-Mouton constant for various gases.

\underline{Experience}:

{}- Design, production and optimization of the phase locking system for
a Nd:YAG laser to a very high finesse cavity

{}- Modification of the Pound-Drever-Hall phase locking scheme to a
cavity.

{}- Optimization of a very sensitive ellipsometer based on a Fabry-Perot
cavity.


{}- Design and implementation of an ellipsometer with a 6.4 m long
cavity with finesse F =$ 10^5$ at the National Laboratories of INFN.

{}- Measurement of the intrinsic birefringence of interferential
mirrors.

{}- Sensitivity measurements with the ellipsometer.

{}- Use of superconducting magnet.

{}- Data analysis.

{}- Study of the consequences of the intrinsic birefringence of cavity
mirrors within a sensitive ellipsometer.

\rule{\textwidth}{0.2mm}

GAL Experiment (Pisa 1988-1989, Thesis work)

Experiment on the equivalence between gravitational and inertial mass.

The aim of the experiment was to measure the relative difference in
free-fall gravity for different materials to a level of $\Delta$g/g
{\textless} $10^{-10}$

{}- Development at Pisa of a collimator capable of measuring parallelism
between beams to a level 1e-6 rad.

{}- Development at CERN of an interferometer with parallel, vertical
arms, each 7 m long.

{}- Precesion optics and mechanics.

\rule{\textwidth}{0.2mm}
\bigskip

My experience with Fabry-Perot interferometers and highly sensitive optical systems qualifies me for the development of the differential laser gauge necessary for measuring the relative movement of the two test masses in the proposal. Furthermore Ferrara will have the collaboration of Mike Shao who has already developed and tested a similar laser gauge system with the desired performances.\\



OTHER FIELDS OF INTEREST

MEDICAL PHYSICS (Ferrara, 1994 - present)

PET (Positron emission tomography) and SPECT (Single Photon Emission
Tomography) allow functional imaging of organs
\textit{in-vivo}.

At the Department of Physics of the University of Ferrara collaborators
and I developed an integrated high resolution PET-SPECT small animal
tomograph for small animal imaging. The system is based on YAP:Ce
(Ytirum Aluminum Perovskite doped with Cerium) scintillator matrices
coupled to position sensitive photomultiplier tubes. The capability of
imaging both in PET and SPECT remains unique.

At present the integration of a CT scanner is underway on the same
scanner so as to provide both functional and morphological images
simultaneously. The prototype has already been tested on a benchtop
system with promising results.

We are also in the process of designing a new PET scanner for small
animals based on multilayers of silicon double sided detectors.
Simulations have shown the enormous capabilities of such a scanner both
in spatial resolution as in sensitivity. Such a scanner would be
limited only by the positron range of the radionuclides eliminating all
other sources of error.

\bigskip

Optical fluorescence tomography

At the University of California at Davis, we began a new in-vivo imaging
technique for small animals based on the fluorescent light emitted by
fluorophores which can be bound to biological molecules.

In fact light with wavelength longer than 600 nm is principally diffused
by biological tissues and not absorbed. This technique has the
advantage of using fluorophores which do not decay in time, as do
radionuclides used in PET and SPECT. Processes can therefore be
monitored for longer periods of time.

\clearpage

\section{B2--b2: 10-yr track-record of  PI Guido Zavattini}
\label{sec:B2SectionB}

Reviewed papers:

Co-Author of 82 papers\\


\textbf{1) M. Bregant, G. Cantatore, F. Della Valle, G. Ruoso,
}\underline{\textbf{G. Zavattini}}\textbf{ }Frequency locking to a high-finesse
Fabry-Perot cavity of a frequency doubled Nd:YAG laser used as the
optical phase modulator \ \textit{Review of Scientific Instruments}
\textbf{73} no. 12 (2002) pp. 4142-4144. \textbf{Citations:~4}


\textbf{2) M. Bregant, G. Cantatore, S. Carusotto, R. Cimino, F. Della
Valle, G. Di Domenico, U. Gastaldi, M. Karuza, E. Milotti, E. Polacco,
G. Ruoso, E. Zavattini, }\underline{\textbf{G. Zavattini}} Measurement of the Cotton-Mouton effect in krypton and xenon at 1064 nm with the PVLAS apparatus. \textit{Chemical Physics Letters},
\textbf{392} (2004) pp. 276-280. \textbf{Citations:~12}


\textbf{3) M. Bregant, G. Cantatore, S. Carusotto, R. Cimino, F. Della
Valle, G. Di Domenico, U. Gastaldi, M. Karuza, E. Milotti, E. Polacco,
G. Ruoso, E. Zavattini, }\underline{\textbf{G. Zavattini}} A precise measurement of
the Cotton Mouton effect in Neon. \textit{Chemical Physics Letters},
\textbf{410} (2005) pp. 288-292. \textbf{Citations:~11}


\textbf{4) \underline{G. Zavattini}, G. Ruoso, E. Milotti, M. Karuza, G. Di
Domenico, F. Della Valle, R. Cimino, G. Cantatore, }On Measuring
Birefringences and Dichroisms using Fabry-Perot Cavities.
\textit{Applied Physics B,} \ \textbf{83} (2006) pp. 571-577. \textbf{Citations:~5}


\textbf{5) \underline{G. Zavattini}, M. Bregant, G. Cantatore, S. Carusotto, R. Cimino, F. Della
Valle, G. Di Domenico, U. Gastaldi, M. Karuza, E. Milotti, E. Polacco,
G. Raiteri, G. Ruoso, E. Zavattini, } PVLAS. \textit{In: Venice 2007, Neutrino Telescopes. Venezia, 06/03/2007 - 09/03/2007, Padova: Papergraph, p. 373-395.}


\textbf{6) E. Zavattini, \underline{G. Zavattini}, G. Ruoso, et al., }New PVLAS
results and limits on magnetically induced optical rotation and
ellipticity in vacuum. \textit{Physical Review D, }\textbf{77 }(2008) p
032006. \textbf{Citations:~59}


\textbf{7) M. Bregant, G. Cantatore, S. Carusotto, R. Cimino, F. Della
Valle, G. Di Domenico, U. Gastaldi, M. Karuza, V. Lozza, E. Milotti, E.
Polacco, G. Raiteri, G. Ruoso, E. Zavattini and \underline{G. Zavattini} }Limits on
low energy photon-photon scattering from an experiment on magnetic
vacuum birefringence. \textit{Phys Rev. D, }\textbf{78} (2008) p
032006. \textbf{Citations:~10}

{\selectlanguage{english}
\textbf{8) M. Bregant, G. Cantatore, S. Carusotto, R. Cimino, F. Della
Valle, G. Di Domenico, U. Gastaldi, M. Karuza, V. Lozza, E. Milotti, E.
Polacco, G. Raiteri, G. Ruoso, E. Zavattini and \underline{G. Zavattini}, }New
precise measurement of the Cotton-Mouton effect in helium,
\textit{Chem. Phys. Lett, }\textbf{471} (2009) pp 322-325}. \textbf{Citations:~4}


\textbf{9) \underline{G. Zavattini} and E. Calloni, }Probing for new physics and
detecting non-linear vacuum QED effects using gravitational
interferometer antennas, \textit{Europ. Physic. Journal C} \textbf{62}
(2009) pp 459-466.  \textbf{Citations:~4}


\textbf{10) F. Della Valle, G. Di Domenico, U. Gastaldi, E. Milotti, R.
Pengo, G. Ruoso and \underline{G. Zavattini}, }Towards a direct measurement of
vacuum magnetic birefringence: PVLAS achievements. \textit{Optics
Communications} \textbf{283 }(2010) pp 4194-4198.  \textbf{Citations:~1}


\clearpage

\section{B2--c: Extended Synopsis of GGonGround project proposal }
\label{sec:B2SectionC}


{\bf The science case}. {\it General Relativity} (GR) is the best theory of gravity to-date. It governs physics at   the macroscopic and cosmic scales and has been highly successful. However, all attempts at merging gravity with the other forces of nature have failed and most of the mass of the universe is unexplained.

General Relativity  is based on the hypothesis that the gravitational force is composition independent: in a gravitational field all bodies fall with the same acceleration regardless of their mass and composition. This property is unique to gravity.  It is referred to as the {\it Universality of Free Fall} (UFF) and it is a direct consequence of the {\it Equivalence Principle} (EP). It was first tested experimentally  by Galileo in Pisa. Newton regarded testing it as so important that he reported the results of his own experiments ``{\it very accurately made}''   in the opening paragraph of the  {\it Principia}   to justify the assumption that ``{\it mass}'' and ``{\it weight}'' are equivalent --i.e. the equivalence between inertial and gravitational mass.  Einstein went much further and stated what he later referred to as the ``{\it happiest thought of my life}'':  if all bodies fall equally fast, in a freely falling frame gravity has --locally--  no dynamical effects.  UFF is therefore equivalent  to making the  ``{\it hypothesis of complete physical equivalence}'' between a gravitational field  and an accelerated frame(\cite{Einstein1907}, Ch. V {\it ``Principle of relativity and gravitation''}, Sec. $17$ {\it ``Accelerated reference system and gravitation''}).  Starting from this hypothesis --published in $1907$--  and extending it globally,  nine years later Einstein formulated the  {\it General Theory of Relativity},  which  is therefore founded on the UFF.    Any violation of UFF (hence of EP)  would violate General Relativity as well as all metric theories of gravity.

UFF experiments are unique tests of General Relativity in that --unlike all others-- they address the assumed composition independence of gravity which sets it aside from all other forces of nature; this fact  makes them the most deeply probing tests in the search for new physics beyond General Relativity and the current {\it impasse}.

It is widely recognized that experimental evidence of a violation of the UFF (hence of EP) would make for a scientific revolution, opening a totally new era in physics as it rarely happens. Even a null result (no violation) --if proven to very high precision-- would constrain physical theories for decades to come. Either way, improving UFF tests by several orders of magnitude would be ground-breaking.


{\bf State of the art.} Stringent limits to the validity of UFF have been set by small size experiments in which the test masses are mechanically coupled by means of a very sensitive torsion balance that is  slowly rotating. In terms of differential acceleration from the Earth
 they have measured $\Delta a_{\oplus}\simeq1.69\cdot10^{-15}\,\rm ms^{-2}$, finding no violation  to   $\eta=10^{-13}$\,\cite{Adel2008}, ($\eta\equiv\Delta a_{\oplus}/a_{\oplus}$,   $a_{\oplus}\simeq1.69\cdot10^{-2}\,\rm ms^{-2}$ at their latitude). Despite the much larger free fall acceleration,  Galileo-like mass dropping tests have been by far less sensitive than torsion balances. The reasons are twofold:  thw time of fall of just a few seconds and  release errors the test masses.
Careful physical modeling and analysis of laser ranging data to the corner cube reflectors left on the surface of the Moon by the Apollo missions  have set a limit similar to that of torsion balances  for the Moon and Earth falling in the gravitational field of the Sun~\cite{LLR2004}. However, although a violation is expected at some point, no firm prediction exists as to the precise level at which it should occur.

Slowly rotating torsion balances have hit the level of thermal noise~(\cite{adelreview2009}, Fig. 20);  lunar laser ranging tests are close to their limit~\cite{EPwithlaserranging}.  Even one order of magnitude improvement may be difficult with these techniques. Tests based on dropping  cold atoms have achieved $\eta=10^{-7}$\,\cite{coldatoms2004} ($6$ orders of magnitude worse than torsion balances) and have yet to match the best result $\Delta g/g\simeq3\cdot10^{-9}$ obtained in measuring the local gravitational acceleration by dropping a single species of atoms~\cite{peters1999}.

A  radically new type of experiment is necessary to improve the current experimental limit in UFF and EP tests by several orders of magnitude thus deeply probing this physical domain so far unexplored.



{\bf The case for a test of UFF and EP in low Earth orbit}. Back in the 1970s it was realized that a torsion balance kind of experiment  in which two weakly coupled test masses orbit the Earth inside a low altitude spacecraft would be equivalent to dropping them from an ``infinitely'' tall tower,  yielding both a stronger signal from Earth (by about $3$ orders of magnitude) and a time of fall around it as long as the mission duration (and no mass release problems). A violation signal (pointing to the center of the Earth) would appear at the (low) orbital frequency of the satellite --of a few $10^{-4}\,\rm Hz$-- to  be upconverted to higher frequency by rotation of the spacecraft in order to reduce noise~(\cite{ChapmanHanson},~\cite{WordenThesis},~\cite{WordenAA1987}).    Absence of weight and isolation of the laboratory (the spacecraft) are additional great advantages. Overall, in low Earth orbit an improvement by  $4$  orders of magnitude, down to $\eta=10^{-17}$, is within reach and the idea  has attracted the interest of NASA and later on of other space  agencies.

At  $h\simeq600\, \rm km$ altitude where the attraction from the Earth is $g(h)\simeq8\,\rm ms^{-2}$, the goal $\eta=10^{-17}$ sets the differential acceleration between the proof masses which must be measured: $a=\eta\,g(h)\simeq8\cdot10^{-17}\, \rm ms^{-2}$. This shows that a sensor in space only a factor  $20$ better than torsion balances would make a $10^4$ times better test.  If the masses are coupled with a natural period of differential oscillation  $T_d$, the relative displacement to be measured  is $r=a\,(T_d^2/4\pi^2)$: the weaker the coupling, the longer the differential period, the more sensitive the instrument.

{\bf The case for \href{http://eotvos.dm.unipi.it/}{``Galileo Galilei'' (GG)} to test UFF and EP to $10^{-17}$}.  All investigators agree that in orbit the proof masses should be ``concentric''  cylinders --with the centers of mass as close as possible to each other to reduce classical differential effects due to  non uniformity of the gravitational field--  and should rotate, so as to upconvert the signal to higher frequency (the higher the better). The question is:  should the concentric test cylinders be sensitive (i.e. weakly coupled) along the symmetry axis ($1$D accelerometer) and rotate around an axis perpendicular to it, or else should they rotate around the symmetry axis and  be sensitive  in the plane perpendicular to it ($2$D accelerometer)?

Although spinning around an axis which is not the symmetry axis is unnatural, the choice of coupling the test cylinders in $1$D prevailed, despite the fact that it essentially rules out fast rotation because it is well known that forcing an oscillator above its natural frequency causes the forcing signal to be attenuated. This choice made it necessary to solve the main critical issues of a high sensitive space experiment by brute force, most notably by requiring that the experiment be carried out in cryogenic conditions, close to absolute zero temperature~\cite{radiometerPRD}.

The signal to be measured asks for both weak coupling and fast spin, a situation which is known in {\it Rotordynamics}  as {\it rotation in supercritical regime}: it makes fast rotation possible through autocentering, but it is an established fact that it cannot work in $1$D --it works only if coupling occurs in $2$D  (\cite{DenHartog},~\cite{Crandall1970}). The ``Galileo Galilei'' (GG) space experiment was proposed in the mid $1990$s by A. M. Nobili and colleagues  who realized that this choice makes most of the critical issues disappear by design: fast rotation does not attenuate the target low frequency signal; the centers of mass of the test cylinders center on each other by physics laws; many dangerous effects are DC; cryogenics is not required; fast rotation and cylindrical symmetry allow passive $1$-axis stabilization of the spacecraft and significantly reduce its size and complexity; etc... (\cite{JAS1995},~\cite{NA_GG_1998}). Papers have been published showing the advantages of the novel idea  of a differential accelerometer  with the proof masses weakly coupled in $2$D  and rotating faster than their natural oscillation frequency (\cite{CQG1999},~\cite{radiometerPRD},~\cite{radiometerMicroscope}). The GG  space mission has been investigated with funding from  ASI (Agenzia Spaziale Italiana) (\cite{GGStudyReports}). More importantly, the new sensor design has allowed  a full-size  $1$-g version of it --with the same number of degrees of freedom and the same dynamical features-- to be built and tested on ground. GG on Ground  (GGG) has been set up with funding from ASI and INFN  (\cite{NA_GGG_2003}~$\div$~\cite{IJMPD}); the latest experimental results  (Fig.\ref{fig:GGGPictureandLSD}) demonstrate that weak coupling  of large proof masses and sensitivity to small forces are compatible with rapid rotation; in fact, it is rapid rotation that makes sensitivity to small forces possible.

%
\begin{figure}[t]
\begin{center}
\includegraphics[height=6cm]{Fig4.jpg}
%\hspace{1mm}
\includegraphics[height=6cm]{XnrXsdWd-a.jpg}
\caption{{\it Left:} the GGG  apparatus (at INFN lab in San Piero-Pisa, built with ASI and INFN funding). The proof masses are concentric cylinders ($10\,\rm kg$ each) with the symmetry axis in the vertical direction, weakly coupled in the horizontal plane by  high quality $CuBe$ joints in $2$D. Together they form   a very peculiar beam balance in which the beam is vertical --hence the balance  is sensitive to differential forces in the horizonal plane-- and the masses are concentric. The relative displacements of the cylinders in the horizontal plane are  read by $2$ orthogonal capacitance bridges whose plates are located halfway in between them. The balance rotates around the vertical axis  upconverting low frequency signals to the spin frequency. The rotating shaft is held by ceramic ball bearings. An additional $2$D weak joint is located just below the bearings in order to reduce low frequency tilts and horizontal accelerations from terrain microseismic noise and  bearings noise on the shaft. Note that both terrain and bearings noise are absent in space  because the spacecraft is isolated  (no terrain) and  after initial spin up  by the launcher no  motor or bearings are needed (angular momentum conservation).  {\it Right:} Spectral density of the relative displacements and the relative accelerations of the test cylinders in the horizontal plane in a $28\, \rm d$ ongoing run  after demodulation from the rotating frame ($\nu_{spin}=0.19\,\rm Hz$). The frequency of interest is the orbital frequency $\nu_{GG}=1.7\cdot10^{-4}\, \rm Hz$ of the GG satellite  at which a violation signal is expected in space. At  $\nu_{GG}$ the measured displacement noise is $2\cdot10^{-7}\, \rm m/\sqrt{\rm Hz}$ and the measured acceleration noise is $7.9\cdot10^{-8}\,\rm m/\sqrt{Hz}$ (the measured natural period is $10$~s). In  $30\,\rm d$ the differential acceleration noise  is $\simeq8\cdot10^{-11}\,\rm ms^{-2}$, limited mainly by ball bearings noise.}
\label{fig:GGGPictureandLSD}
\end{center}
\end{figure}
%

%\vskip -2truemm

The most relevant physical property of the GG/GGG novel sensor has been demonstrated very recently~\cite{PRLthermalnoise}: thermal noise due to internal damping which competes with the low frequency signal of interest is reduced as  $1/\sqrt{\nu_{spin}}$ (with no signal attenuation) making rapid rotation more effective than cryogenics in reducing thermal noise. Taking into account also residual gas damping and eddy currents it turns out that GG can perform a full test to $10^{-17}$  in just $1$~d~\cite{IntegrationTime}; in a  $9$-month mission all necessary checks against systematics can be performed so that the question as to whether the result is new physics or else it is due to a tiny known disturbance --hence it is a null result-- can be established beyond doubt~\cite{nullchecks}.

Recent collaboration with JPL (Jet Propulsion Laboratory, CalTech-NASA) has shown that an optical read-out based on the very low noise laser interferometry gauge developed and demonstrated at JPL will allow  GG  to fully exploit its very short integration time. The collaboration has led to an agreement between JPL and ASI  to submit GG to the EXPLORER program as a NASA led mission and the partnership of ASI, with M. Shao (JPL) as PI and A. M. Nobili as Co-PI. EXPLORER  is a long time program of  NASA dedicated to  flying small size missions every few years  years; the Nobel prize winner COBE was one of them. The $2010$ Decadal Astronomy has ranked the EXPLORER program as its second highest priority and has advised NASA to further strengthen it. EXPLORER is the right framework for a small mission like GG --which is well below the size of ESA missions-- and given that ASI cannot afford a full mission but is willing contribute to a NASA led mission with a significant Italian r\^{o}le.



{\bf The case for GGonGround}. GG is a high precision physics experiment which can reach its goal  only in orbit, but that is just the final run of an experiment whose performance can and must be tested and demonstrated in the lab.
The EXPLORER program is the only possible route to space for GG, but for GG to enter in the EXPLORER competition and eventually be selected for flight the GGG lab experiment must prove --by sufficiently isolating the sensor from ground noise sources and with an adequate read out--  that the sensor in space can meet its target.

Synergy between the Corresponding PI Nobili, who has led GG and GGG so far, and the PI  Zavattini, who will lead the efforts for implementing a low noise laser gauge  can considerably  improve GGG to meet the goal set in Table~\ref{tab:GGGErrorBudget1}.
 Fig.~\ref{fig:GGGPictureandLSD}  shows that GGG  has reached a sensitivity of $\simeq8\cdot10^{-11}\, \rm ms^{-2}$ in $30$~d,  while GG must reach   $a_{GG}=8\cdot10^{-17}\, \rm ms^{-2}$ to meet its goal. We state with confidence that GGG  can improve by $5$ orders of magnitude its current performance to reach $a_{GGG}=10a_{GG}\simeq8\cdot10^{-16}\,\rm ms^{-2}$

\clearpage


\begin{table}[t]\footnotesize
\begin{center}
\begin{tabular}{|l|p{3.9cm}|p{4cm}|p{2.85cm}|p{1.5cm}|}
\hline
\hline
\hline
\multicolumn{5}{|c|}{\textbf{GGonGround goal vs GG goal in space}} \\
\hline
\hline
\hline
  &Differential acceleration between test masses       &$a \, [\rm{ms^{-2}}]$                         &$r=a\frac{T_d^2}{4\pi^2}\, [{\rm m}]$&Integration time $T_{int}$\,[$\rm d$]\\
  &$a$~@~$1.7\cdot10^{-4}\, \rm Hz$                     &                                                    &                &      \\
\hline
\hline
{\bf GG goal in space}      &$a_{GG}=\eta g(h)$                                   &$8\cdot10^{-17}$                                     &$6\cdot10^{-13}$&$1$      \\
                    &(upconverted to $1\,\rm Hz$)                         &($\eta=10^{-17}\, ,\, h\simeq600\, \rm km$)            &($T_d\simeq540\,\rm s$)    &       \\
\hline
\hline
{\bf GGonGround}   &$a_{GGG}=10 a_{GG}$                                &$8\cdot10^{-16}$                                    &$3.2\cdot10^{-14}$  &$30$    \\
{\bf goal}          &(upconverted to $0.2\div 3\,\rm Hz$)                 &                                                    &($T_d\simeq40\,\rm s$)    &       \\
\hline
\hline
\hline
\end{tabular}
\begin{tabular}{|l|l|p{2.3cm}|p{2cm}|p{2.1cm}|p{4.6cm}|}
\hline
\multicolumn{6}{|l|}{\textbf{GGonGround noise budget @~$1.7\cdot10^{-4}\, \rm Hz$}} \\
\hline
Noise Source &$\Delta a$                                   &Integrated $\Delta a$   &$\Delta r$                             & Integrated $\Delta r$ & Conditions and physical data\\
             &                                              &($T_{int}=30$~d)      &($T_{d}\simeq40$~s)                     &($T_{int}=30$~d)     &           \\
             &$[10^{-13}\frac{\rm{ms}^{-2}}{\sqrt{\rm{Hz}}}]$ &$[10^{-16}\rm{ms}^{-2}]$ &$[10^{-11}\frac{\rm{m}}{\sqrt{\rm{Hz}}}]$ & $[10^{-14}\rm{m}]$     &           \\
\hline
\multicolumn{6}{|l|}{\it {Tilt noise sources:} $a_{tilt}=\frac{k_c}{mgL}\frac{k_{shaft}}{M_{tot}gL_{shaft}}g\theta_{tilt}\ , \ \theta_{tilt}=\theta_{terrain}+\theta_{airbearing}$}\\
\hline
terrain          & 8.2&5.1 &3.3 &2.1 & $\theta_{terrain}\simeq8\cdot10^{-6}\, \frac{\rm{rad}}{\sqrt{\rm{Hz}}}$\\
\cline{1-5}
air bearing      &4.1 &2.5 &1.7 &1.0 & $\theta_{airbearing}\simeq4\cdot10^{-6}\, \frac{\rm{rad}}{\sqrt{\rm{Hz}}}$\\
                 &    &    &    &    & $k_c\simeq k_{shaft}\simeq0.04\, \rm Nm/rad$ \\
                 &    &    &    &    & $m=10\,\rm kg$  $L=0.5\,\rm m$ \\
                 &    &    &    &    & $M_{tot}\simeq80\,\rm kg$ $L_{shaft}\simeq4\,\rm m$\\
\hline
\multicolumn{6}{|l|}{\it Thermal noise sources\cite{PRLthermalnoise},\cite{IntegrationTime}} \\
\hline
suspensions      &1.3 &0.8 &0.5 &0.3 & Q=20000, $\nu_{spin}=0.2$~Hz\\
\hline
eddy currents    &1.3 &0.8 &0.5 &0.3 & no $\mu$metal magnetic shield\\
\hline
residual gas     &0.5 &0.3 &0.2 &0.1 & 2 cm gap, $\rm{P}=10^{-4}$~Pa\\
\hline
\multicolumn{6}{|l|}{{\it ReadOut noise:} $a_{ROnoise}=(4\pi^2/T_{d}^2)r_{ROnoise}$} \\
\hline
laser gauge      &7.4 &4.6 &3.0 &1.8 & $T_{d}\simeq40$~s\\
\hline
\bf{Total noise}       &12 &7.4 &4.8  &3.0 & \\
\hline
\end{tabular}
\label{tab:GGGErrorBudget1}
\caption{GGonGround goal and noise budget  }
\end{center}
\end{table}



\begin{table}[h!]\footnotesize
\begin{center}
\begin{tabular}{p{0.5cm} p{1.6cm} p{13.5cm} }
\hline
\multicolumn{3}{|c|}{\textbf{GGonGround} Roadmap} \\
\hline
\multicolumn{3}{l}{Time (Months)} \\
\hline
\multicolumn{3}{c}{Performance achieved} \\
&$t_0$ & $a_0=8\cdot10^{-11}\,\rm{ms^{-2}}$ (INFN lab San Piero, Pisa; ASI and INFN funding; Fig.\,\ref{fig:GGGPictureandLSD})\\
\hline
\multicolumn{3}{c}{First 18--month period targets} \\
6&$t_0+6$ & $a_1=2.8\cdot10^{-12}\,\rm{ms^{-2}}$ ($T_d=14.8\,\rm{s} \ \ r_{capRO}=1.45\cdot 10^{-8}\,\rm{m/\sqrt{Hz}}$; can be done with capacitance read out and ball bearings,
requires weaker joints by a factor 4)\\
12&$t_0+12$ & $a_2=7.7\cdot10^{-14}\ ms^{-2}$ ($T_d=40\,\rm{s} \ \ r_{capRO}=3\cdot 10^{-9}\,\rm{m/\sqrt{Hz}}$; can be done with capacitance readout and ball bearings,
requires 10 times longer suspension shaft)\\
18&$t_0+18=t_1$ & $a_3=5.6\cdot10^{-15}\,\rm{ms^{-2}}$ ($T_d=40\,\rm{s} \ \ r_{laserRO}=2.2\cdot10^{-10}\, \rm{m/\sqrt{Hz}}$; requires preliminary version of air bearings and
 laser metrology)\\
\hline
\multicolumn{3}{c}{Second 18--month period targets} \\
24&$t_1+6$ & reduce air bearings and rotation noise \\
30&$t_1+12$ & reduce laser gauge read out noise\\
36&$t_1+18=t_2$ &  $a_4=7.7\cdot10^{-16}\,\rm{ms^{-2}}$ ($T_d=40\,\rm{s} \ \ r_{laserRO}=3.0\cdot10^{-11}\,\rm{m/\sqrt{Hz}}$; requires air bearings to full performance and
improved laser metrology)\\
\hline
\multicolumn{3}{c}{Third 18--month period targets} \\
42&$t_2+6$ & Install rotating whirl control (as required in GG)\\
48&$t_2+12$  &  Measure patch effects and demonstrate that they are not relevant; improve sensitivity to effect from Sun @ $24\,\rm h$ by Phase Sensitive Detection in preparation for analysis of space data   \\
54&$t_2+18=t_3$ & Optimize test masses different composition, manufacture test masses, measure their quadrupole moments and confirm
requirements \\
\hline
\multicolumn{3}{c}{Fourth 18--month period targets} \\
60&$t_3+6$ & Manufacture suspensions required for GG in space, measure their elastic constants and quality factors and confirm fulfilment  GG requirements\\
66&$t_3+12$ & Demonstrate on bench laser gauge read out noise to $r_{laserRO}\simeq10^{-12}\,\rm{m/\sqrt{Hz}}\ @ \ 1\div2\,\rm{Hz}$ \\
72&$t_3+18=t_4$ & Test PZTs and inchworms to demonstrate feasibility of balancing in space\\
\hline
\hline
\end{tabular}
\label{tab:GGGRoadmap}
\caption{GGonGround Roadmap}
\end{center}
\end{table}

\clearpage

{\noindent}(slightly better than torsion balances)  because --as the noise budget in the same table shows-- there are no fundamental limitations. The  main limitations are terrain  and bearings low frequency tilt noise. Terrain tilt input noise at $\nu_{GG}$ has been  measured~(\cite{ComandiThesis},\,\cite{IafollaTilts}), its effect on the test cylinders is understood (it is  expressed by a simple analytical formula with few parameters) and there is no doubt that the current suspensions can be improved (only a factor 4 is needed) and the apparatus properly modified  to meet the goal.
Air bearing is known to be several orders of magnitude less noisy than ball bearing (the vacuum chamber enclosing the torsion balance rotates on air bearing) and a solution is under study for  GGG in which only the experiment rotates, not the chamber.  This is feasible and can be realized  by A. M. Nobili with the collaboration of Dr. R. Pegna who has significantly contributed to the current GGG performance and can effectively co-lead this activity.  At full performance the capacitance bridges are no longer adequate and must be replaced by the laser gauge; this effort can be successfully led by the PI G. Zavattini based on his experience in  Fabry-Perot interferometry, with collaboration and advise from Dr. M. Shao (JPL, CA, USA) who has already developed, built and demonstrated a very low noise laser gauge.


 The roadmap Table~\ref{tab:GGGRoadmap} shows that this remarkable progress can be done in steps within the first $3$ years of the project, to secure the success of GG  through the various stages of the EXPLORER selection process (release of next Call is expected at the end of 2013). The remaining $3$ years will be devoted --as outlined in Table 3-- to bridge the remaining gap with  laser gauge noise required in space and to manufacture and test  the most crucial components of the space sensor. The final goal is to ensure the success of the experiment in space and to strengthen its European contribution.

Required funding (9592600~{\EURtm} total for $6$~yr) and PIs time on the the project are given in the Budget Tables.  Both PIs are strongly dedicated to this project, for their time is limited only by teaching duties (AMN will leave teaching the second year).  Funding is dominated  by personnel cost due to the lack of funds in Italy  to employ researchers and the very limited number of permanent ones; and  also to the wide variety of disciplines relevant to this project and need to be mastered.


 EGO  is the best Institution to host a  European project in experimental gravitation. GGonGround needs a specific but limited laboratory space (roughly $50\,\rm m^2$ with about $6\,\, m$ high roof) where the current apparatus and equipment (acquired with ASI and INFN funds)  will be moved. All activity will be carried out by the two PIs and their collaborators.

 %\vskip 40truemm



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%\clearpage

