Cosmology in .NET Print ANSI/AIM Code 128 in .NET Cosmology

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24. Cosmology use .net vs 2010 code-128 maker toget code 128c with .net Code 128 Code Set C The visible mass density con visual .net ANSI/AIM Code 128 tributes a fraction vis = 0.005 of the critical density.

By itself, the visible mass density could not stop the expansion of the Universe. We saw in 14 that there is a lot of missing mass. We shall see in 25 that some of it perhaps four times as much as the visible mass is in the form of hydrogen and helium gas that has never formed stars.

Much more than this is hidden dark matter, in a form that astronomers have not yet identi ed. The best estimates of the amount of dark matter on the cosmological scale give densities a factor of three lower than the critical density: M = 0.3.

If the Universe at the present time were matter-dominated, then it would have less than the critical density, and it would expand forever. We calculate the actual deceleration of such a model in Investigation 24.3, where we address an important detail of principle: we show that the deceleration is also proportional to distance, so that the Hubble law (Equation 24.

8 on page 360) remains true for all time. The result is the important equation:. / acosmol = -4 3 G d. (24.12). The fact that the inward acc eleration increases in proportion to d implies that the Hubble law will hold for all time. Cosmologists usually write this equation in a slightly different way, de ning the dimensionless deceleration parameter q by q= so that a = -qH2 d. The value of the deceleration parameter today, q0 , is related to the dimensionless density parameter of the Universe, de ned in Equation 24.

11 on the preceding page, by = 2q0 . (24.14) The expansion of the Universe at present appears to be accelerating, so that means it cannot be matter-dominated.

To include pressure, one simply replaces by the density of active gravitational mass, + 3p/c2 , in Equation 24.12. In particular, the dark energy must be added to other mass densities when comparing with the critical density of the Universe.

Since the dark energy behaves like a cosmological constant, astronomers denote its density relative to the critical density by the symbol . As Figure 24.4 on page 352 shows, the density associated with the dark energy is just enough, when added to the density of the dark matter, to give the critical density, within the observational errors.

This result is borne out by measurements of the cosmic microwave background radiation as well, as illustrated in Figure 27.2 on page 403. This is an unexpected result that many physicists want to see explained.

As we will see in 27, it is predicted by the theory of in ation. However, when pressure is important the evolution of the Universe will of course be different. In particular, the work done by the pressure as the Universe expands will affect the mass-energy density .

Moreover, the pressure itself can change. Normally, to decide whether a particular model Universe will expand forever or re-collapse requires a computer calculation. 4 G , 3H2 (24.

13). The cosmological scale-factor Investigation 24.3. Cosmological gravity A key question is, does the VS .NET barcode 128 expansion of the Universe maintain the Hubble law Hubble discovered the expansion in the rst place by nding that the speed of recession of a galaxy is proportional to its distance, v = Hd, (24.15) where H is Hubble s constant.

If this describes the velocity of matter in the Universe now, then will the expansion of the Universe change it After billions of years, will the expansion law look di erent, say with speed depending on the square of the distance We don t expect it to, since the Hubble law is the only one that a homogeneous Universe can satisfy. But we need to check that the law of gravity does indeed maintain this. Otherwise, we have a logical inconsistency in our model of the Universe.

Now, the expansion of the Universe must be slowing down or speeding up, due to gravity, so Hubble s constant is generally not constant in time. If the Hubble law is preserved, then it follows that the acceleration (or deceleration) must also be proportional to the distance. Therefore, we expect to nd, at least near to our Galaxy, a = Kd, (24.

16) Reassuringly, the acceleration increases in proportion to d, just as we expected: our model of an expanding homogeneous universe governed by the known laws of gravity is self-consistent. The constant of proportionality in Equation 24.16 is then K = -4 G /3.

Cosmologists do not usually deal with K directly. Instead, they de ne a dimensionless measure of the deceleration, called the deceleration parameter. Here is how it is de ned.

We have already noted that the Hubble constant has dimensions of 1/time, and that 1/H is a measure of the age of the Universe. Now look at the proportionality constant K. Its dimensions are those of acceleration divided by distance, which works out to be 1/(time)2 .

So the ratio K/H 2 is dimensionless. It is, to within a sign, what cosmologists call the deceleration parameter q: q=K 4 G = . H2 3H 2 (24.

18). where K is a di erent const ant , a number that is independent of position but can change with time. Because, as we have seen in the text, the acceleration depends only on the mass closer to us than d, we can calculate this in the same manner as we calculated the escape speed. The mass closer to us than the galaxy is M = 4 d 3 /3, and the acceleration it produces is -GM/d 2 .

This gives the cosmological acceleration: acosmol = GM 4 G d 3 4 G ==d. d2 3d 2 3 (24.17).

We can thus write the cosmol barcode 128 for .NET ogical acceleration in Equation 24.12 as 2 a = -qH d.

The present values of all these constants are denoted by a subscript 0 : H0 , q0 , 0 , and p0 . Starting from Equation 24.17, it is possible to calculate the expected evolution of the Universe.

We show how to do this with the help of a computer in Investigation 24.4 on the next page. If pressure is not negligible, say because of radiation in the early Universe or because of a cosmological constant, then we just replace by the relativistic + 3p/c 2 everywhere in this calculation.

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