Paik-1 Standard Model And Relativity Test (SMART) Ho Jung Paik, Lvyuan Chen, M. Vol Moody University of Maryland and Inseob Hahn, Konstantin Penanen, Mark Weilert Jet Propulsion Laboratory July 6-10, 2008, Warrenton, VA

Paik-2 Theoretical Background  Equivalence Principle (EP) is a cornerstone of GR, which led Einstein to the concept of curved spacetime and the tensor theory of gravity.  However, most quantum theories of gravity prefer a scalar-tensor theory and suggest a violation of this principle.  The EP violating force comes from a quantum exchange potential, which can be written as  This leads to an EP-violation amplitude of where  is mass in the atomic mass unit u and is a dimensionless integral.

Paik-3 Scientific Value of EP Tests  In string theory, the (10-D) tensor gravitational field G  has two partners: scalar field  (the dilaton) and antisymmetric tensor field B . They are coupled to the other fields in the theory with gravitational strength, but in ways generally violating the EP.  Many scalar and pseudo-scalar partners of the graviton may survive as massless particles in the four-dimensional low energy world (dilatons, axions, moduli fields, etc.).  The observed accelerating expansion of the universe is consistent with a cosmological constant , which is 120 orders of magnitude smaller than the quantum corrections to the vacuum-energy density.  It is important to test the founding principles of GR, such as the EP, to the highest possible precision because the failure to quantize gravity and the cosmological constant problem may be partly due to incompleteness of GR.

Paik-4 Objectives of SMART  SMART aims to test EP to 10  18 at range  10 4 km (same as STEP) but with a simpler instrument.  SMART tests GR and other theories beyond Einstein, and searches for new interactions and particles beyond Standard Model. Sensitivity of the SMART EP test and the existing limits versus range

Paik-5 Principle and Design  Force experienced by a test mass of finite volume can be expanded as where are the multipole moments of test mass A, and  N and  Y are the Newtonian and Yukawa potential of the source.  The differential acceleration between test masses A and B is: Monopole ( = 0): Vanishes identically Dipole ( = 1): Vanishes by c.m. matching Quadrupole ( = 2): Vanishes by choosing right shapes Octupole ( = 3): Vanishes by reflection symmetry Cylinder inside a cylinder or a sphere inside a sphere

Paik-6 Spherical Outer Test Mass SMART test mass pairs (Example) STEP test mass pair  A spherical shell approximates a point mass more closely.  Smaller moments for  3  Closure conditions satisfied:

Paik-7 Suspension and Alignment Meander-pattern suspension coil for STEP  Suspension and alignment by current along a single tube  Axisalignment  rad  CMRR  10 8 with error compensation  Centering by currents on 4 auxiliary tubes  Drag-free system may not be needed

Paik-8 Accelerometer Orientation Orientations of the EP test masses with respect to the spacecraft spin axis (z) x y z

Paik-9 Sensing Circuit Superconducting sensing circuit for an x-axis differential accelerometer

Paik-10 Error Budget Error budget and control requirement Error Source EP Test (f = Hz) Error (10 –18 m s –2 )Control requirement Metrology 10  m finish Random(12 days) Intrinsic3.2Q D = 10 6 Linear acceleration1.710 –7 m s –2 Hz –1/2 Angular acceleration< –2 rad Hz –1/2 Gravity error< 10.5 nm c.m. match Electric charge< 1 Casimir, patch force< 1 Temperature< 1 5  K Other (30% margin)2.7 Total5.0

Paik-11 SGG Technology SGG for 1-m 1/r 2 law test  Diff linear accelerometer  CMRR  10 7  4  10  13 g Hz  1/2 noise  Best resolution (10  4 ) of 1/r 2 law at 1 m SGG for airborne gravity  Diff angular acc.  CMRR  10 8 SGG for submillimeter 1/r 2 law test  Differential linear accelerometer  Search for extra dimensions to 20  m Superconducting Gravity Gradiometer (SGG)  Wire-based S/C technology

Paik-12 Fabrication of Spherical Shell Figure 10. Fabrication steps of a spherical-shell test mass. (1)Solid sphere is fabricated by grinding; 5 holes are drilled. (2)Sphere is split into 2 halves by wire EDM; mating surfaces are ground flat; 4 holes for dowel pins are drilled. (3)2 solid hemispheres are joined by a bolt & nut, and dowel pins; outer spherical surface is ground to final dimension. (4)Inner spherical surface is machined (or ground); center hole is counterbored from the inside of the shell. (5)Mushroom-shaped plug, made of the same material, is inserted into counterbore and diffusion- bonded to each hemisphere. (6)2 hemispherical shells are joined together during assembly by dowel pins.