Cosmological Constant

jmcmurtry

What is the current thinking as to the value of the cosmological constant
given the most recent observations of the universe expansion?

Uncle Al

jmcmurtry wrote:
>
> What is the current thinking as to the value of the cosmological constant
> given the most recent observations of the universe expansion?

AIP Conf. Proc. 586 316 (2001)
2.036x10^(-35)/sec^2
Int. J. Theoret. Phys. 41(1) 131 (2002)
1.934x10^-35/sec^2
http://www.qc.fraunhofer.de/qg/lambda
http://arxiv.org/abs/gr-qc/0609004
Note length not time units for lambda

The Lambda-CDM model includes the cosmological constant measured to be
on the order of 10^(-35)/sec^2, or 10^(-47) GeV^4, or 10^(-29) g/cm^3,
or about 10^(-120) in reduced Planck units, below.

http://en.wikipedia.org/wiki/Lambda-CDM_model
http://super.colorado.edu/~michaele/Lambda/obs.html
bottom, through 1999
Mod. Phys. Lett. A 18(08) 561 (2003)

The conventionally defined cosmological constant "lambda" is
proportional to the vacuum energy density "rho",

(lambda) = [8(pi)G/3c^2](rho)

"rho", less than 10^(-25) kg/m^3, is proportional to the density
parameter "omega,"

(omega) = [8(pi)G/3H^2c^2](rho)

H is the Hubble constant, measured to be 70(+/-)2 km/sec-megaparsec as
of January 2007.

Omega breaks down to contributions from matter (omega)_m and the
vacuum omega)_(lambda).

(omega)_(lambda) - (omega)_m is between -0.1 and +0.8.

If one allows zero point fluctuations of the vacuum, 1/2
photon/allowed EM mode to the Planck energy,

(rho)_vacuum ~ 10^92 erg/cm^3
(omega)_(lambda) ~ 10^120

Even theorists are embarrassed to disappear an omega that big to
exactly obtain the necessary fractional residue.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2

markwh04@yahoo.com

On May 2, 4:32 pm, Uncle Al <Uncle...@hate.spam.net> wrote:
> If one allows zero point fluctuations of the vacuum, 1/2
> photon/allowed EM mode to the Planck energy,
>
> (rho)_vacuum ~ 10^92 erg/cm^3
> (omega)_(lambda) ~ 10^120
>
> Even theorists are embarrassed to disappear an omega that big to
> exactly obtain the necessary fractional residue.

It need not be anything more than a self-constitency principle that
restricts what the actual spectrum of fermions and bosons must be. In
that case, this goes from a liability to a major asset.

Finiteness for a total ZPE can be obtained if
sum_b m_b^n = sum_f m_f^n
over all boson modes (b) and fermion modes (f), for n = 0 , 2, 4;
where m_b or m_f is the mass associated with the respective mode.
Making it small requires further constraining the respective mass
spectra.

If you explain away mass as a dynamic effect of the Higgs, then this
becomes a constraint on the couplings of the fermions and bosons to
the Higgs.

The cosmological constant already arises from non-Abelian Yang-Mills
fields through the contribution
Lambda = 1/4 sum f^{abc} f_{abc}
where the structure constants f_{ab}^c are with indices raised and
lowered by the gauge group metric k_{ab}.

In a U(1) theory, k_{ab} is just (epsilon_0 c), the vacuum
permittivity. If you assume k is constant, then the scale of the
Lambda contribution becomes fixed, and you're in the middle of the
"fine tuning problem".

If, on the other hand, k is variable; then this contribution can vary
and become asymptotically small or zero. The fine-tuning issue is
potentially evaded. Moreover, you also acquire extra contributions to
the Lagrangian involving the gradient of k -- "dark energy" terms.
Since you're lowering 2 indices, and raising only one, Lambda then
scales proportionally with k.

The k metric components are equivalent to the Jordan-Brans-Dicke
scalars; and also to dilatons (the dilaton is equivalent to the
logarithm of the determinant of the k metric). In terms of the Maxwell
U(1) field, k is just the dielectric coefficient of the vacuum; so
that the extra terms are none other than the representation of the
dielectric energy stored in the vacuum(!) I.e., a vindication of
Maxwell's notion of a universal dielectric medium.

Some (or maybe even most) quintessence models use Jordan-Brans-Dicke
scalars (or scalar-tensor-matter) as their basis. If you want to
revert this back to the Kaluza-Klein representation k = g_{55} or k =
(g_{ab};a,b=5,6,...), a confirmation of a link between the
cosmological constant and vacuum energy to the extra terms arising the
gauge group's metric would represent an indirect confirmation of the
geometric interpretation of the gauge fields as extra-dimensional
gravity; and of the general notion of physical extra dimensions.

The effective Lagrangians mentioned above are those which come out of
the total metric
h_{mn} = e^{2U} g_{mn} + k_{ab} A^a_m A^b_n
h_{mb} = k_{ab} A^a_m
h_{an} = k_{ab} A^b_n
h_{ab} = k_{ab}
where different choices of U can be used to define what the effective
"base space" metric is. The choice e^{2U} = k^{-1/2} for a 4-D base
space gives you an Einstein-Hilbert Lagrangian of the form root(|h|)
R_h = root(|g|) R_g + ... Otherwise, you get a power of k out in front
for the leading term (which is sometimes used to model a variable G).

Phillip Helbig---remove CLOTHES to reply

In article <ZsvZh.1996$KP1.1795@trnddc02>, jmcmurtry <nospam@alo.com>
writes:

> What is the current thinking as to the value of the cosmological constant
> given the most recent observations of the universe expansion?

It has the observed value. Prior to having measured a value
observationally, various pundits put forward (conflicting) arguments as
to why it had to have a particular value (such as very near 0).

Or do you mean thinking as to why it has the value it does? It would
have been interesting if someone had predicted the value beforehand, but
no-one did, thus lending credence to the idea that none of the
predictions was really worth considering in the first place. I wouldn't
be surprised if the weak anthropic principle comes out as the best
explanation.

Of course, as Martin Rees has pointed out, the recent obsession with the
values of the cosmological parameters (i.e. not just measuring them, but
deriving them from more fundamental arguments) might go the same way
Kepler's obsession with the planetary orbital radii went, i.e. it turned
out they were just due to chance, anthropic arguments (in the case of
the Earth) and some simple physics (orbital resonances) and don't have
any "deeper" meaning.

markwh04@yahoo.com

On May 4, 4:27 pm, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
remove CLOTHES to reply) wrote:
> might go the same way
> Kepler's obsession with the planetary orbital radii went, i.e. it turned
> out they were just due to chance

The jury's still out on that. Complex dynamics can entail regularities
not easily seen or predicted from the fundamental laws. This is
already observed, for instance, in the patterns seen in Saturn's
rings; the various resonances seen between orbits and/or rotation
periods of the celestial bodies; etc.

It may simply be the case that a (quasi-)stable long-term requires or
exists only as you approach certain configurations, such as that
approximated by Bode's Law.