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john hunter
31-August-2006, 10:17 AM
According to WMAP data the value of omega(matter) is approx 0.3 (http://map.gsfc.nasa.gov/m_mm.html)

Here is a suggestion that the value is 1/3

According to the rescaling principle, energy should be conserved if the universe rescales, (all length dimensions changing, and all physical constants with a length dimension changing in proportion) - www.gravity.uk.com/cosmological_model.html

In this theory gravity is caused by a rescaling, and the value of G (attractive gravitational mass of each mass m) is determined by the rescaling constant H, and the density of surrounding matter. The total energy due to each mass in the universe is conserved (remains at zero) as the universe rescales.

so (simplistically) for a mass m
mc^2 - GmM/R = 0 and as the speed of light and G rescale, the value remains at zero. Giving G=Rc^2/M
M is the mass of the universe , R is the radius of the universe = c/H,
H is half of the Hubble constant - www.gravity.uk.com/redshift_of_light.html


more detail: mc^2 = integral 0 to R of [Gm(4pi*r^2*rho)/r] dr, this is a sum of the potential energy of shells of thickness dr
This gives G= c^2/(2pi*R^2*rho), and using R=c/H .....G=H^2/(2pi*rho)........rho=H^2/2pi*G (here H is the rescaling constant)

so omega = rho/rho(critical) = rho/[3H^2/8*pi*G] can be calculated to be 4/3, the H in denominator being the Hubble constant, this introduces a factor 1/4 and gives omega = 1/3

John Hunter.

P.S the volume of a hypershere is 2pi^2*r^3, (the proper volume), a similar integral to above with surface area as the derivitive of this formula (6pi^2*r^2), gives a value for omega of 8/(9pi), which is also approx 0.3.

Thanatos
31-August-2006, 10:48 AM
It appears you are mixing surface area calculations with volume in this model. Do not be terribly discouraged. Plotting vector in 4D space is difficult.

john hunter
31-August-2006, 10:55 AM
Dear Thanatos,

Thankyou for your wise comments.

John Hunter.

john hunter
31-August-2006, 05:42 PM
Dear Thanatos,

Do you have any relevant comments about the value of omega from the rescaling universe proposal, being close to the WMAP value?

From your last post, it sounds as though you are very knowledgable about this kind of thing, so further specific advice on this matter would be appreciated.

John Hunter.

Thanatos
02-September-2006, 08:33 AM
I started by plotting the relationship between surface area and volume in a simple spherical model - euclidian space. In deformed space [like GR] the plots are not so clear. So, I'm not disagreeing with you, just saying any model must be able to reproduce observations. So how do you derive a value for the comological constant from this mess? Uncertain. I think it could be a form of surface tension.