The Physics Factbook
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Tipler, Paul A. College Physics. New York: Worth, 1987: 877.  "The critical density of matter in the universe that separates the two possibilities can be calculated from Einstein's theory. It is now approximately 10^{30} grams per cubic centimetre. Small though this value maybe, it separates two entirely different futures for the universe"  10^{30} g/cm^{3} 
Guth, Alan H. The Inflationary Universe. New York: Addison Wesley, 1997: 22.  "The value of the critical mass density is believed to lie between 4.5 × 10^{30} and 1.8 × 10^{29} grams per cubic centimeter, depending on the value for the expansion rate (i.e. the Hubble constant) that one uses in the calculation. By standards of our everyday experience, this density is astonishingly low. The critical density corresponds to somewhere between 2 and 8 hydrogen atom per cubic yard, a density that is more than ten million times lower than that of the best vacuum that can be achieved in an earthbound laboratory!"  4.5–18 × 10^{30} g/cm^{3} 
Davidson, Keay & Smoot, George. Wrinkles in Time. New York: Avon, 1993: 158163.  "The critical density is calculated to be about five millionths of a trillionth of a trillionth (5 x 10^{30}) of a gram of matter per cubic centimeter of space, or equivalent to about one hydrogen atom in every cubic meter  a few in a typical room"  5 × 10^{30} g/cm^{3} 
Silk, Joseph. Big Bang. New York: Freeman, 1977: 299.  "d_{critical} = 3H^{2}/8πG = 5 × 10^{30} gram cm^{3}"  5 × 10^{30} g/cm^{3} 
What is the density of the Universe and the Size of the Universe? Question Number: 52. ScienceNet Questions and Answers.  "What is the density of the Universe and the size of the Universe? Density = 2.11 × 10^{29} kg/m^{3} Radius = 3 × 10^{26} meters" 
0.0211 × 10^{30} g/cm^{3} 
How old is the universe? What is its future? Much of the work in physics and astrophysics today focuses on these two fundamental questions. However, to answer them, it is necessary to know the density of the universe, also known as "omega" (Ω). The density of the universe means the amount of matter there is per unit volume, averaged for the entire universe. One way to find the average density would be to add up all the matter in the universe and then divide by the number of cubic meters in the universe. However, this process is difficult to accomplish.
Another way to try to find the density would be to study the way the universe is working. Such as, how fast its expanding, whether the expansion is speeding up or slowing down, what forces are involved, and how the contents of the universe have evolved over time. Although this sounds complicated, theorists have formulated an equation for omega. This equation is …
Ω = 2q_{0} = (2/3Λ)(c^{2}/H^{2})
where …
Ω = density
q_{0} = Deceleration Parameter
Λ = Cosmological Constant
c = speed of light
H = Hubble Constant
Although we know the formula for omega, we are unable to determine the density of the universe. Solving the equation for omega requires knowing four numbers, three of which are currently not known with certainty. The only number that is known is the velocity of light. No one yet knows the value for the deceleration parameter or the cosmological constant and there are still disagreements over the Hubble constant. The deceleration parameter measures the rate at which the expansion is slowing down due to the gravitational attraction among all the clusters of galaxies. The Hubble constant denotes the rate at which the universe is expanding.
The density of the universe affects the future of the universe. If omega turns out to be more than one (meaning that there is more than one hydrogen atom per cubic meter) the universe will eventually stop expanding and contract forming a "closed"universe; that is, a universe with finite volume and mass. If omega is less than one (meaning that there is less than one hydrogen atom per cubic meter) the universe will expand forever and will eventually thin out forming an "open"universe. According to Einstein's theory, an "open" universe has a infinite volume and an infinite number of hydrogen atoms. However, if omega equals one, the universe is at the "critical density."The critical density is found to be
3H^{2}/8πG = 5 × 10^{30} grams cm^{3} (3 hydrogen atoms per cubic meter)
where G is the universal gravitational constant. When the universe is at the critical density, it means that the universe will expand at precisely the right rate to avoid recollapse thus forming a "flat universe."Since the exact density of the universe is not known yet, different sources gave different results. An approximate density of the universe would be about equal to the critical density 5 × 10^{30} g/cm^{3}.
Christina Cheng  2000
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