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The starting point of standard cosmology is the so-called cosmological principle, which considers the universe on a large scale to be homogeneous and isotropic. According to this principle, the space-time structure of the universe is described by the Robertson-Walker metric: where R(t) is the cosmological scale factor, which is a constant, which can take +1, -1, and 0. When k = -1, 0, The universe is open and infinite; when k = +1, it is closed and limited.
With R(t), two parameters can be defined: where t0 represents the current universe, H0 is the Hubble constant, and q0 is the deceleration parameter.
Measuring cosmological parameters is the basic method for determining the age of cosmology. It can be seen from Hubble's law U=H0D that if the expansion rate of the universe is constant, the time required for any two points in the universe to be infinitely close (the big bang start time) to today's distance D is D/U=1/H0, ie It is exactly the reciprocal of the Hubble constant H0. This is the case if there is no substance in the universe. However, we know that there are indeed substances in the universe. Many of the galaxies, stars, and even our own human beings we see are formed by these substances. In addition, the observational evidence also indicates that there are probably a large number of so-called "dark matter" in the universe that are different from the usual substances. During the expansion of the universe, the gravitational pull between substances will prevent the expansion of the universe, thus slowing down the expansion of the universe. In cosmology, people use the cosmological parameter q0 to represent this deceleration. Q0 is called the cosmic deceleration parameter. Obviously, q0 is related to the average density of matter in the universe. The q. value is generally considered to be between 0 and 1. When H. is given, the age of the universe obtained for different q. values ​​is different. When q0 = 0, t is about 0.67 (1/H); and when q0 = 1, t is about 0.57 (1/). It can be seen that, in any case, q0 and H0 are quantities that are closely related to the age of the universe to determine the time scale. Accurately determining q0 and H0 is critical to determining the age of the universe and deepening our understanding of the evolution of the universe.
2 The energy of the universe We use the statistical point of view to regard the collection of the entire galaxy as the fluctuation density field of the random motion relative to the Hubble flow. We should look for the relationship between the potential energy W and the dynamic kinetic energy T in the density fluctuation. .
Let the density field be described by the two-point galaxies related function, U represents the component of the motion in a given direction, then there is: the equation gives a well-known form of 3 (13) where <5 port> is The average density within the ruler is "increased". Substituting (8) and G=pj/pct(14) (where PG is the density of the galaxies and Pt is the critical density) into (13): g=H0GV<5p>/2PG(15) where V=H0R is R Hubble speed. After a Hubble, the current motion caused by g is v=gH0-1(16)(15) and (16) we have: g=2(v/V)/5(17)16 where stone 1" It is usually assumed that there is a power law and Davis et al. use the survey data to obtain Y=2.0, rc=3h-1Mpc. For the convergence of the integral U, corresponding to the scale of the galaxies, the lower limit is 4h-Xpc, and for r>2rc, the hypothesis is The curve has a gradient of y = 3. Geller and Davis apply the cosmological energy theorem to all samples of the star that is brighter than 13 m, and one difficulty in applying the formula (9) is that U is a non-observation, and two can be observed. The radial velocity difference between galaxies U. In order to make more direct use of U, Peebles obtains the so-called "second universe virial theorem", which is in the form of the above formula and the relative velocity of the given two galaxies at a distance r. The mean square, a is the normalization constant, which depends on the relationship between the two-point and three-point correlation functions. Peebles was obtained from 166 galaxy data, but this statistical method does not give a contribution to the density of a uniformly distributed material background.
3 Supergalactic galaxies consider a larger system than the Abell galaxies - super galaxies, whose center is in the Virgo Cluster, and its own group of galaxies outside of 10h-1Mpc is also a member of it. On such a large scale, we cannot ignore the Hubble expansion.
Consider a spherically symmetric mass "increasing the additional acceleration from the center R as: where 5 < 5p > / Pg is the average density contrast within R.
Some basic data were obtained by measuring the dynamics of the galaxies in the direction of the Virgo. Yahil, DeVaucouleurs used the traditional method% and Aaronson et al. used infrared measurement; Smoot and Rubin used the anisotropy measurement of microwave background radiation, and their results are listed in Table 1. The local galaxies are relative to the virgin cluster. If the Bo speed V is 1050kms-1, then U/V-0.3. Table 1 to the Virgo's movement v (km/s) Yahil et al. In 1998, the average density contrast is obtained from the distribution of galaxies located within the local group of galaxies. 3.5, this value and the above UV value is substituted into (17), then 04.2. Davis et al. made the motion correction before the density distribution, and got a smaller 5屮. 2, and using a more in-depth analysis than (17), this result shows that the contribution of invisible matter to the total density has continued to rise to the scale of 10h-1Mpc, which implies that the invisible matter is not as good as the galaxy. If the inhomogeneous scale of the invisible material is larger than the super galaxies, then 幺0.3
In the standard cosmological model, the finite infinity depends only on the magnitude of the deceleration parameter q, and the finite infinite argument has actually become the determination of q.
Graphically express this situation. The ordinate in the figure is the Hubble constant H... The two horizontal dotted lines represent the currently accepted range of H. possible values. The abscissa is the q value, and the generally acceptable range is ... 1-1.0. The three curves in the figure correspond to the age of the universe of 1.20 billion, 1.40 billion and 1.60 billion years respectively. As mentioned earlier, the age of the universe derived from the determination of stellar age should be greater than 140-16. billion years.