# Cosmological Constant

by jmcmurtry
Tags: constant, cosmological
 P: n/a What is the current thinking as to the value of the cosmological constant given the most recent observations of the universe expansion?
 P: n/a 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
 P: n/a On May 2, 4:32 pm, Uncle Al 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).
P: n/a

## Cosmological Constant

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.

 P: n/a 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.

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