ϕ %
ffiffiffiffiffiffiffiffi ffi
γ
4πG
r
Á ln
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
8πGV 0
γ Á 3γ À 1
ð
Þ
r
Á t
&
'
ð3:3Þ
Here a min is a minimum value of the scale factor (Beckwith 2018; Camara et al.
2004) which may have an electromagnetic contribution as given in Camara
et al. (2004).
3.2 Next from Klauder Details Which Are Used to Give
More Q.M. Structure
Note (Beckwith 2018) we are using a restricted quantum action principle (Klauder
2015) S 2 , Eq. (3.4), when we assume for simplicity that Λ is a constant.
S 2 ¼
Z T
0
dt Á p t
ð Þ_ q t
ð Þ À H N p t
ð Þ, q t
ð Þ
ð
Þ
½
Š
% S 1 ¼
1
2κ
Z ffiffiffiffiffiffi ffi
Àg
p Á d
4 x Á ℜ À 2Λ
ð
Þ
ð3:4Þ
Hence
Λ %
À p ~ t
ð Þ_ q ~ t
ð Þ À H N p ~ t
ð Þ, q ~ t
ð Þ
ð
Þ
½
Š
1
κ
R ffiffiffiffiffiffi ffi
Àg
p Á d
3 x
þ
1
2κ
R ffiffiffiffiffiffi ffi
Àg
p Á d
3 x Á ℜ ¼ 6 Á
€ a
a þ
_
a
a
À Á 2 þ
ℵ
a 2
t¼~ t
1
2κ
R ffiffiffiffiffiffi ffi
Àg
p Á d
3 x
ð3:5Þ
3.3 Filling in the Details of the Above Using Details from
Klauder (2015) with Explanations
First
(a) That S 2 % S 1 from pre-Planckian to Planckian space-time when we avoid the
cosmic singularity (Beckwith 2018). We ask that our model be consistent with
the cosmology associated with a cosmic bounce, instead of a traditional singularity (Beckwith 2017)
3 Using “Enhanced Quantization” to Bound the Cosmological Constant, (for a. . .
23