KMI mini workshop 20 Mar 12
Accelerating universe and the
Conformal transformation in the
scalar-tensor theory of gravity
Yasunori Fujii
Waseda University
Y.F. & K. Maeda, The scalar-tensor theory of gravitation, Cambridge U Press, 03.
Y.F. PRD26(82)2580. Y.F. PTP118(07)983. K.Maeda & Y.F. PRD79(09)084026,
Y.F. PLB671(09)207, Y.F. & K. Homma, PTP126(12)531
Ｄｉｒａｃ １９３７
Ｊｏｒｄａｎ １９５５ Ｓｃａｌａｒ-ｔｅｎｓｏｒ ｔｈｅｏｒｙ
Nonminimal coupling term
J frame
EH term
Conformal transformation
-- no invariance required
Special choice
E frame
G varies or const depending on the choice of frame.
Spatially flat RW metric
Brans-Dicke model
1961
Weak Equivalence Principle preserved
Time-independent mass, …
through
diagonalized
noghost
No WEP violation
even for
matter
J frame mass decoupled from
, the only agent for time-dependence
Ｓｐａｔｉａｌｌｙ ｆｌａｔ ＲＷ
ｓｐａｔｉａｌｌｙ ｕｎｉｆｏｒｍ scalar field
Ｊ ｆｒａｍｅ Ｒａｄｉａｔｉｏｎ-ｄｏｍｉｎａｔed ＢＤ ｍｏｄｅｌ
Non-observational frame
Asymptotic, attractor
solution without smooth
limit
Big cancellation naturally
No exponential growth (Dolgov、１９８２)
E frame Radiation-dominated BD model
Dark energy
Expanding! Ｏｂｓｅｒｖａｔｉｏｎａｌ frame?
Scenario of a decaying cosmological
constant a la Dirac
Most important observational discovery
Small simply because we are old, no fine-tuning
Two-prong disaster in Dust-dominated expansion
Particle mass provides with microscopic time(length) unit,
relative to which expansion of intergalactic distance is
measured
No way of detecting any change of the unit itself
Own-Unit-Insensitivity-Principle
Unit is constant in the given conformal frame
Free massive spinor in BD model in terms of tetrads
is constant according to BD
E frame Dust-dominated BD model
in
should be 2/3 K.Maeda & Y.F. PRD79(09)084026
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
BD model to be blamed
E frame Dust-dom Scale-invariant model
Yukawa int, with dimensionless coupling const
Global scale invariance in J frame
Decoupled from matter in E frame
OUIP
No more RHSs
Normal expansion
WEP violation left unobserved through matter fields
inheriting BD model by almost equally simple model.
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
Scale invariance then broken
as
Quantum anomaly
Non-gravitational interaction
WEP violation
Pseudo NG boson, likely acquiring a nonzero small
mass
Non-Newtonian gravity (5th force) perhaps barely
below observational upper bounds
Past efforts hampered by many uncertainties by
appealing to huge objects to overcome weak strength
An experimental search is underway for photonphoton scattering mediated by exchanging sigma,
exploiting strong laser beams
Y.F. & K. Homma, PTP126(12)531
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.