A Matter density crude estimates

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Crude estimates from the 1980s suggested that the universe's actual density was likely close to the critical density, as indicated by Liddle (2015) and supported by earlier works, including Weinberg's 1972 analysis. Weinberg noted that if the deceleration parameter was around unity, the universe's density would be approximately double the critical density, implying a need for additional mass beyond visible galaxies. This early recognition hinted at the existence of dark matter, although the full implications of energy density components were not understood at that time. The discussion highlights significant early contributions to cosmology that foreshadowed later findings from CMB measurements. Overall, the need for dark matter was acknowledged decades before modern precision measurements confirmed these theories.
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Resources on crude estimates of matter density before 1990
Liddle (2015, p.67) writes: "From the crude estimates that a typical galaxy weighs about ##10^{11}M\odot## and that galaxies are typically about a megaparsec apart, we know that the Universe cannot be a long way from the critical density."

Was this fact (i.e. that the actual density is likely close to the critical density) known from these crude counting estimates in the 1980s before the CMB precision measurements in the 2000s confirming flat geometry? If yes, does anyone have specific references to papers providing such crude estimates **before 1990**?

Reference: Liddle, A. (2015). An introduction to modern cosmology. John Wiley & Sons.

Thank you!
 
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Floyd_13 said:
Was this fact (i.e. that the actual density is likely close to the critical density) known from these crude counting estimates in the 1980s before the CMB precision measurements in the 2000s confirming flat geometry? If yes, does anyone have specific references to papers providing such crude estimates **before 1990**?
Absolutely! Here's a relevant 1972 quotation from Steven Weinberg, Gravitation and Cosmology, pg. 476:

"...and (15.2.1) gives the ratio of the present density to the critical density (15.2.3) as $$\frac{\rho_{0}}{\rho_{c}}=2q_{0}\tag{15.2.6}$$For ##q_0>\frac{1}{2}## the universe is positively curved, with ##\rho_0>\rho_c## , whereas for ##q_0<\frac{1}{2}## the universe in negatively curved, with ##\rho_0<\rho_c## . If we give credence to the values ##q_{0}\simeq1## and ##H_{0}\simeq75\text{ km/sec/Mpc}## deduced from the red shift versus luminosity relation (see Section 14.6), then we must conclude that the density of the universe is about ##2\rho_c## , or about ##2\times10^{-29}\text{ g/cm}^{3}##."

Weinberg then goes on to say "Unfortunately, this result does not agree with the observed density of galactic mass." and offers on pg. 478 the galactic-density estimate ##\frac{\rho_{G}}{\rho_{c}}=\text{0.028}##. Presciently, he then writes "However, if one tentatively accepts the result that ##q_0## is of order unity, then one is forced to the conclusion that the mass density of about ##2\times10^{-29}\text{ g/cm}^{3}## must be found somewhere outside the normal galaxies. But where?"

So an inkling of the need for dark matter was recognized over 50 years ago!
 
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renormalize said:
So an inkling of the need for dark matter was recognized over 50 years ago!
Well … Zwicky’s paper was published in 1933. Rubin’s in 1970 …

Some 70ish % of the energy density is also not matter at all. This was definitely not known when Weinberg wrote that and changes the entire evolution due to different equation of state.
 
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https://en.wikipedia.org/wiki/Recombination_(cosmology) Was a matter density right after the decoupling low enough to consider the vacuum as the actual vacuum, and not the medium through which the light propagates with the speed lower than ##({\epsilon_0\mu_0})^{-1/2}##? I'm asking this in context of the calculation of the observable universe radius, where the time integral of the inverse of the scale factor is multiplied by the constant speed of light ##c##.
The formal paper is here. The Rutgers University news has published a story about an image being closely examined at their New Brunswick campus. Here is an excerpt: Computer modeling of the gravitational lens by Keeton and Eid showed that the four visible foreground galaxies causing the gravitational bending couldn’t explain the details of the five-image pattern. Only with the addition of a large, invisible mass, in this case, a dark matter halo, could the model match the observations...
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