Exact Solutions and Scalar Fields in Gravity - Instituto Avanzado de ...

198 EXACT SOLUTIONS AND SCALAR FIELDS IN GRAVITY
This solution is a quantum wormhole, satisfying the Hawking–Page
regularity boundary conditions, i.e., the wavefunction is exponentially
damped for large spatial geometry, and is regular when the spatial geometry
degenerates [5].
Case Now, we take this
case is equivalent to a cosmological term linear in the scalar field
solution to WDW equation is,
The
where is a modified Bessel function and
For and a quantum wormhole solution is
2.2. GAUGE N=1/X
With and the new variables,
the action becomes
where we have chosen the cosmological term as
with constants. The corresponding WDW equation is
The universe wavefunction for this model is
where is the separation constant.