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Energy Conservation and the BIVERSE
There are various cosmological models which attempt to explain the creation
of the Universe(s). Vic Stenger's "A Scenario for a Natural Origin of the
Universe" based on the No Boundary Model published in Philo is a good
example. These models are based on what Cosmologists call "Third Quantization."
In this class of models we can equate the creation of Universes with the
creation of virtual particles in the vacuum of space. We get the following
Particle = Universe
Interaction Vertex= Topology change
Matter field = wave function of the Universe
Free Laplacian = Wheeler De Witt Operator
Vacuum = Void
In these models Universes are created in Pairs for the same reason
particles and virtual black holes are created in pairs, to ensure conservation
principles. This is indicated by the quote below.
In addition, in these models the interaction vertex is replaced by a
topological structure known as an Instanton (two merons). This topological
structure provide a mechanism for CPT reversing across the saddle point, the
origin of these Universes.
However, in this post I will, using a semi Newtonian description,
demonstrate a connection between energy conservation and the BIVERSE model by
"proving" that the creation of a single Universe rather than a BIVERSE violates
energy conservation. This therefore is another argument for the BIVERSE
It is often said that inflation is the ultimate free lunch. This is
because mass energy is created by also creating equal and opposite signed
gravitational energy. In fact it's this negative gravitational energy which causes
the inflating Universe to fall up. This is easy to see. Given the gravity
potential energy equation
We can that in "falling down" which is defined by
takes the system to a lower more stable energy level. However, in the
state of false vacuum with a non zero Vacuum energy density, the more stable
condition is accomplished by the Universe "falling up." We get;
M= rho_vav*V = rho*(4pi*R^3/3)
Assuming rho_vac is constant we get
Given that during inflation
E_m= - E_G
we see that
After inflation is launched.
But this is not the whole story. As related by DR Whittle of the
University of Virginia
"To Actually Start the expansion, we need a minimum of amount of vacuum, a
seed patch, if you like, to get the process off and running. It's actually
not too difficult to see why. Going back to the Sphere, if it expands to
add to this shell (additional energy at launch) the extra gravitational
energy released is G*M_sphere*M_shell/R and this must be greater than
M_shell*c^2 in order to make the extra shell. Notice that the M_shell's cancel , so
for inflation to get going we need G_M_sphere/R >c^2. Basically you need a
big enough sphere to generate enough gravitational energy to create the new
Therefore we can take this at the minimum point and say
Assuming inflation at the GUT scale where
R= 3E-29 M
E_inf= 4E15 Joules ( 44 gms)
Based on this we can see that inflation can't be launched in a proto
Universe with a flat space metric. This connects well with our understanding of
the tunneling process which is proposed to create new Universes. In their
landmark paper "Origin of the Universe as Quantum Tunneling event" David
Atkatz and Heinz Pagels prove that only finite Universes may tunnel into
existence. As we shall this will connect well with Whittle's assertions above.
But first we must look at the energy condition of a Universe (Hubble Volume)
as a function of its overall geometry.
The total energy any comoving observers "sees" is given by
E(R) = E_mass(R) + E_grav(R)
Based on the homogeneous nature of the Universe we can write
E(R)= E_mass(R) - 2*G*E_mass(R)*M(R)/(R*c^2)
M(R) = O*rho_crit*V
Where O is the density parameter and R_H is the Hubble Radius.
E(R)= E_mass(R)- O*E_mass(R)*R^2/R_H^2
E(R)= 1- O*R^2/R_H^2
For the Hubble volume we get
We can see from this only in flat space in the total energy of the Hubble
volume zero. But based on the assertion by Atkatz and Pagels it would take
an infinite energy fluctuation to tunnel into existence a flat Universe.
Now let's go back to Whittle's assertions and see where this takes us. Based
on Whittle we have
We can easily see that this gives us
We know from the Friedmann equations that
O= rhp_vac/rho_crit = 2
E_H= E_mass*(1-O) = E_mass*(1-2) = - E_mass
Therefore in an inflating Universe at the moment of launch
A Universe that is falling up.
However if Universes are created in pairs we also have
E_H= - E_mass*(1_O)= + E_mass
E_Biverse= E_H(+)+ E_H(-)=0
A zero energy creation event. ( Actually the supplemental energy states
are needed to sum energy to zero, the implications of this is still under
consideration. This is made apparent in the Venziano-Gasperini model.)
In addition since
We get the interesting equation
Given inflation at the GUT scale we find that
t(efold)= 1E-37 sec
Which is the correct value predicted by the inflationary models.
While the above is in no way rigorous, it nevertheless seems useful.