1. Accelerating universe and the Conformal transformation in the scalar-tensor theory of gravity KMI mini workshop 20 Mar 12 Yasunori Fujii Y.F. & K. Maeda, The scalar-tensor theory of gravitation, Cambridge U Press, 03. Y.F. PLB671(09)207, Y.F. & K. Homma, PTP126(12)531 Y.F. PRD26(82)2580. Y.F. PTP118(07)983. K.Maeda & Y.F. PRD79(09)084026, Waseda University

2. Ｄｉｒａｃ １９３７ Ｊｏｒｄａｎ １９５５ Ｓｃａｌａｒ - ｔ ｅｎｓｏｒ ｔｈｅｏｒｙ Nonminimal coupling term EH term Conformal transformation Special choice J frame E frame G varies or const depending on the choice of frame. -- no invariance required

3. Spatially flat RW metric Brans-Dicke model 1961 Weak Equivalence Principle preserved Time-independent mass, … No WEP violation, the only agent for time-dependence matter through diagonalized noghost even for J frame mass decoupled from

4. Ｓｐａｔｉａｌｌｙ ｆｌａｔ ＲＷ ｓｐａｔｉａ ｌｌｙ ｕｎｉｆｏｒｍ scalar field Ｊ ｆｒａｍｅ Ｒａｄｉａｔｉｏｎ - ｄｏｍｉ ｎａｔ ed ＢＤ ｍｏｄｅｌ Non-observational frame Asymptotic, attractor solution without smooth limit Big cancellation naturally No exponential growth (Dolgov 、１９８ ２ )

5. E frame Radiation-dominated BD model Expanding! Ｏｂｓｅｒｖａｔｉｏｎ ａｌ frame? Most important observational discovery Scenario of a decaying cosmological constant a la Dirac Dark energy Small simply because we are old, no fine-tuning

6. isaster in Dust-dominated Free massive spinor in BD model in terms of tetrads No way of detecting any change of the unit itself Unit is constant in the given conformal frame Own-Unit-Insensitivity-Principle Particle mass provides with microscopic time(length) unit, relative to which expansion of intergalactic distance is measured Two-prong disaster in Dust-dominated expansion is constant according to BD

7. E frame Dust-dominated BD model should be 2/3 BD model to be blamed in Against OUIP ! Unacceptable Intergalactic separation increases at the same rate as the length unit, the inverse of mass. This also implies that the universe looks unchanging if measured relatively to microscopic unit K.Maeda & Y.F. PRD79(09)084026

8. E frame Dust-dom Scale-invariant model Yukawa int, with dimensionless coupling const Decoupled from matter in E frame No more RHSs WEP violation left unobserved through matter fields inheriting BD model by almost equally simple model. Normal expansion Global scale invariance in J frame OUIP Global scale invariance in J frame

9. Spontaneously broken scale invariance Massless NG boson --- dilaton Supporting original theory Broken further by quantum effects due to relativistic quantum field theory Divergences regulated by continuous dimension as WEP violation Non-gravitational interaction Quantum anomaly Scale invariance then broken

10. Pseudo NG boson, likely acquiring a nonzero small mass Non-Newtonian gravity (5th force) perhaps barely below observational upper bounds An experimental search is underway for photon- photon scattering mediated by exchanging sigma, exploiting strong laser beams Past efforts hampered by many uncertainties by appealing to huge objects to overcome weak strength Y.F. & K. Homma, PTP126(12)531

11. J frame has its own raison d’etre as a theoretical frame, or string frame M.Green et al, Superstring theory, Cambridge U Press (87), Eq(3.4.58) Both frames play integral roles, but BD model required replaced by scale-invariant model allowing WEP violation. Searching for the scalar field with this feature （ also as dark energy ） expected.