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**Session 13 - Large Scale Structure & Cosmology.**

*Display session, Monday, January 13*

*Metropolitan Ballroom, *

## [13.09] Quantum Uncertainty and Constraints on Dark Matter

*G. W. Collins II (CWRU)*
Since Robert Dicke pointed out the approximate equality bewteen the gravitational binding and
expansion energies at the current era implied a remarkably fine tuned balance for the young universe,
an exact balance between the two has risen to the status of dogma. The traditional form of the arguement
(known as the Flatness Problem) is usually characterized by the current ratio (omega) between the
matter density and that required to asymptotically stop the expansion of the universe. The current
observed constraint that 10 > omega > 0.1 suggests that at the Planck time the agreement with unity must
have been about 1 part in 10**59. This has been taken to mean that the close agreement with unity is in
reality perfect in which case it is still perfect. However, this also implies that any tiny departure of
omega from unity as an initial condition will lead to significant departures in the present era. Since
an initial condition can only be applied at the beginning of an event, we consider the quantum
uncertainty in omega at the Planck time and find it to be of the order of the Planck mass divided by the
mass of the universe used to determine omega. This implied an uncertainty in the initial value of omega of
about 1 part in 10**59. However, this tiny uncertainty will be amplified by fifty nine powers of ten due
to the expansion of the universe. This suggests we should find a current uncertainty in omega of about
its own value. Thus, demanding greatest perfection in the initial conditions governing the dynamical expansion
of the universe taht is allowed by the quantum nature of the universe leads to a value of omega that is
in full agreement with observation.

**Program
listing for Monday**