IRGAC 2006 Barcelona, 15-7-2006. Multigravity and Spacetime Foam. Remo Garattini Università di Bergamo I.N.F.N. - Sezione di Milano. The Cosmological Constant Problem. For a pioneering review on this problem see S. Weinberg, Rev. Mod. Phys. 61 , 1 (1989).
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For a pioneering review on this problem see S. Weinberg, Rev. Mod. Phys. 61, 1 (1989).
For more recent and detailed reviews see V. Sahni and A. Starobinsky, Int. J. Mod. Phys.
D 9, 373 (2000), astro-ph/9904398; N. Straumann, The history of the cosmological
constant problem gr-qc/0208027; T.Padmanabhan, Phys.Rept. 380, 235 (2003),
A factor of 10118
L can be seen as an eigenvalue
Let us consider the 3-dim. metric gij and perturb around a fixed background, (e.g. Schwarzschild)
gij= gSij+ hij
M. Berger and D. Ebin, J. Diff. Geom.3, 379 (1969). J. W. York Jr., J. Math. Phys., 14, 4 (1973); Ann. Inst. Henri Poincaré A 21, 319 (1974).
W.K.B. method and graviton contribution to the cosmological constant
The finite part becomes
L0 must be treated as running
a maximum for
[L. Crane and L. Smolin, Nucl. Phys. B (1986) 714.].
[J.B. Hartle and G.T. Horowitz, Phys. Rev. D 24, (1981) 257.].
Merging of point 1) and 2) with N gravitational fields (instead of scalars and fermions) leads to multigravity
Hope for a better
Pioneering works in 1970s known under the name
f-g theory (bigravity)
[C.J. Isham, A. Salam, and J. Strathdee, Phys Rev. D 3, 867 (1971), A. D. Linde, Phys. Lett. B 200, 272 (1988).]
For each action, introduce the lapse
and shift functions
Choose the gauge
Define the following
Depending on the structure You are looking, You could have a ‘ideal’gas of geometries.
Our specific case: Schwarzschild wormholes
The single eigenvalue
problem turns into
The initial problem
Nw copies of
the same gravity
Take the maximum
Nevertheless, there is no
Proof of this