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Re: [Phys-l] Symmetries and the cosmological constant puzzle



This has been a topic of interest on other physics list. I post it here for
general interest.



In a message dated 4/12/2007 7:28:56 A.M. Eastern Daylight Time,
RBZannelli@AOL.COM writes:


We outline the evaluation of the cosmological constant in the framework of
the standard field-theoretical treatment of vacuum energy and discuss the
relation between the vacuum energy problem and the gauge-group spontaneous
symmetry breaking. We suggest possible extensions of the 'tHooft-Nobbenhuis
symmetry, in particular, its complexification till duality symmetry and discuss the
compatible implementation on gravity. We propose to use the discrete
time-reflection transform to formulate a framework in which one can eliminate the
huge contributions of vacuum energy into the effective cosmological constant and
suggest that the breaking of time--reflection symmetry could be responsible
for a small observable value of this constant.
_http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.1436v1.pdf_
(http://arxiv.org/PS_cache/arxiv/pdf/0704/0704.1436v1.pdf)







While this paper joins an apparent flood of papers which utilize vacuum
state time symmetry ( negative energy states) to solve the ZPE and CC problem it
should be noted by interested persons that is postulates that the observed
value of dark energy is the result of CP symmetry violation. ( an idea I
proposed a few months ago.) Apparently the idea that a CC can be exist due to
time symmetry violation has also been proposed by M.P. Bronstein in 1933. Of
course there would have no particle physics basis for this proposal at that
time.

This model is based on the tHooft/ Nobbenhuis version which is similar to
the proposal by Linde and Klauber.

The gravitational actions are

S_g(+)= - 1/16*pi*G_n*Integral d^4 [ R(+) - 2*Lamda(+)


S_g( -) =1/16*pi*G_n*Integral d^4 [ R(-) - 2*Lamda(-)

G_n< 0


The basic premise being that


Lamda(+) > Lamda(-)

Lamda_eff = Lambda(+) + Lamda(-)


The following section is worth quoting somewhat extensively. The language is
a little strained , the authors are Russian, Spanish and Italian.

Begin Quote

" The control of vacuum fluctuations is really important. The idea of
the ( almost) complete cancellation of the vacuum fluctuations seems very
attractive because it permits to resolve both the cosmological and field
theoretical problems, connected with its treatment. Our idea is very simple. We are
inspired by two facts.

1) The classical equations of motion are invariant in respect to the time
inversion.


2) Gravity being reparametrisation-invariant theory , does not have a time.
( ref 8) Indeed , at least for the closed cosmological models the
Hamiltonian of the theory is equal to zero and the naive notion of time looses sense.

.......


However, one can invoke a suitable small breaking of the time symmetry.
Indeed , the violation of CP invariance is an experimental fact , and the
conservation of CPT symmetry implies unavoidably the breakdown of time symmetry.

In a way our approach reminds that of the mirror world or mirror
particles see ( ref 15) and references within. The mirror symmetry is as well known
as the symmetry with respect to spatial reflections or P parity symmetry.


The idea of the presence of fields evolving backward in time and
co-existing with "normal" fields evolving forward in time was used in many different
contexts. First of all one could cite the works by Wheeler and Feynman on time
symmetric electrodynamics together with the so called transactional
interpretation of quantum mechanics. We should emphasize once again that there are no
particles moving backward in time in our forward in time world. The only
influence which this time reversed world makes on us is just the presence of
vacuum energy in the right hand side of the Einstein equations. "

End Quote

So we could write the ZPE equation as

< rho>= ( 1+K*delta_cp) [ N_b/4*pi^2* Integral { 0 to k_pl} w*k^2dk -
N_F/4*pi^2* Integral { 0 to k_pl}

w*k^2dk + (1-k*delta_cp) *[ N_F/4*pi^2* Integral { 0 to k_pl} w*k^2dk -
N_b/4*pi^2* Integral { 0 to k_pl}

w*k^2dk

<rho> = 2*k*delta_cp*[ N_b/4*pi^2* Integral { 0 to k_pl} w*k^2dk -
N_F/4*pi^2* Integral { 0 to k_pl} w*k^2dk

Where delta_cp is the CP phase , K is an arbitrary constant, N_b and
N_F are the degrees of freedom of the boson and fermion fields respectively.


Bob Zannelli














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