Universe critical density

An inventory of the Universe Critical density = 10 gcm density of luminous matter/critical density = 0.005% density of gravitating matter/critical density = 10-30% density of nuclear matter/critical density = 2-5% total density of the Universe/critical density = 1. 

The primordial Li abundance was sought primarily because of its ability to constrain the baryon to photon ratio in the Universe, or equivalently the baryon contribution to the critical density. In this way, Li was able to complement estimates from 4He, the primordial abundance of which varied only slightly with baryon density. Li also made up for the fact that the other primordial isotopes, 2H (i.e. D) and 3He, were at that time difficult to observe and/or interpret. During the late 1990 s, however, measurements of D in damped Lyman alpha systems (high column-density gas believed to be related to galaxy discs) provided more reliable constraints on the baryon density than Li could do (e.g. [19]). Even more recently, the baryon density has been inferred from the angular power spectrum of the cosmic microwave background radiation, for example from the WMAP measurements [26]. We consider the role of Li plateau observations post WMAP. 

The critical density is traditionally dehned as that density which separates the closed (finite) universe from the open (infinite) universe in the simplest model available, i.e. in a universe without cosmological constant or quintessence. It corresponds to a universe with zero total energy, where the kinetic energy due to expansion is exactly balanced by gravitational potential energy. The value of the critical density is 10 gcm, which amounts to very httle when compared to a chunk of iron ... 

Quantitatively speaking, the density of nuclear matter in the Universe is estimated to be between 2% and 5% of the critical density as defined above. The density of visible... 

By comparing calculated values with the actual content of these various elements in the oldest astronomical objects, we deduce that the density of nuclear matter cannot exceed 5% of the critical density. Now it so happens that the best cosmological theory to date, the theory of cosmological inflation, predicts that the Universe has exactly the critical density. This conclusion is supported by recent observations of remote supernovas and the relic background radiation. 

Let us examine this situation in more detail. It is quite clear that the density of matter in clusters of galaxies is significantly higher than the density of nuclear matter as deduced from primordial nucleosynthesis (2-5% of the critical density). If we assume that these structures are representative of the Universe as a whole, then in order to make up the difference, we are forced to resort to clouds of exotic elementary particles left over from the Big Bang. The fate of the Universe then lies in the hands of non-nuclear matter of unknown but not unknowable nature (e.g. neutralinos). 

On the other hand, we must somehow close the Universe, or more precisely, find some way of giving it the critical density, since this is what inflation demands. Indeed, it is required not only by inflationary theory, but also by close scrutiny of the leopard skin p attern that constitutes the microwave background, radiative relic from the B ig B ang. We... 

In spite of the constant density of the gel, the friction of the poly(N-isopropylacrylamide) gel reversibly decreases by three orders of magnitude and appears to diminish as the gel approaches a certain temperature. This phenomenon should be universal and may be observed in any gel under optimal experimental conditions of the solvent composition and the temperature because the unique parameter describing the friction is the correlation length which tends to diverge in the vicinity of the volume phase transition point of gels. The exponent v for the correlation length obtained from the frictional experiment is far from the theoretical value. It will, therefore, be important to study a poly(N-isopropylacrylamide) gel prepared at the critical isochore where the frictional property of gel may be governed by the critical density fluctuations of the gel. 

Considering the inflation, we assume a universe with a critical density Qo = 1, k = 0 and qo = The universe is assumed to be matter dominated during all the epoch of interest. Then the scale factor Rit) of the universe expands as ... 

In the following years main attention was devoted to detailed elaboration of the concept of the cold dark matter dominated Universe. Here a central issue was the amount of dark matter. Initially opinions varied from a moderate density of the order of 0.2 critical density up to the critical density. Only a few years ago it was clarified that dark matter constitutes only 0.25 of the critical density, and the rest is mostly dark energy, characterized by the cosmological constant or the U A-term. 

Figure 15 shows the lifetime as a function of temperature at the critical density of carbon dioxide. With CO2 as the solvent there is no inverted region in which the lifetime becomes longer as the temperature is increased. Instead, the lifetime decreases approximately linearly. Thus the inverted behavior is not universal but is specific to the properties of the particular solvent. The fact that the nature of the temperature dependence changes fundamentally when the solvent is changed from ethane to C02 demonstrates the sensitivity of the vibrational relaxation to the details of the solvent properties. The solid line is the theoretically calculated curve. The calculation of the temperature dependence is done with no adjustable... 

Although, in general, a, H, and f are all time-dependent, eq. 2.11 reveals that if ever Q < 1, then it will always be < 1 and in this case the universe is open (k < 0). Similarly, if ever Q > 1, then it will always be > 1 and in this case the universe is closed (re > 0). For the special case of Q = ]. where the density is equal to the critical density Pent = 3H2/8itG, Q is always unity and the universe is flat (Euclidean 3-space sections re = 0). 

Figure 10. The various contributions to the present universal mass/energy density, as a fraction of the critical density (Q), as a function of the Hubble parameter (Ho). The curve labelled Luminous Baryons is an estimate of the upper bound to those baryons seen at present (z ( 1) either in emission or absorption (see the text). The band labelled BBN represents the D-predicted SBBN baryon density. The band labelled by M (Om = 0.3 0.1) is an estimate of the current mass density in nonrelativistic particles ( Dark Matter ).

The ratio between the actual energy density at any given moment in the cosmic expansion and the critical density at that moment is designated by the Greek letter Q. This is a pure number and must be close to unity for the universe to be flat i.e. the actual density at any moment must be close to the critical density at that moment. The energy density itself is, of course, constantly decreasing as the universe expands. 

Other anthropic explanations for the value of the cosmological constant and the why now problem have been suggested in the context of maximally extended (N = 8) supergravity (Kallosh and Linde, 2003 Linde, 2003). In particular, the former authors found that the universe can have a suffciently long lifetime only if the scalar field satisfies initially (j) Mp and if the value of the potential V(0), which plays the role of the cosmological constant, does not exceed the critical density po 10 "/Wj,. 

As Fig. 3 illustrates, this is really a parameter-free potential in the sense that if V R) is expressed in units of Dg, and R in units of a, then there is only one universal Lennard-Jones (12, 6) potential. Such universality appears in the Law of Corresponding States, the relation in which all the characteristic properties of any gas, including its condensation and critical behavior, depend only on its critical temperature Tg, critical pressure Pg and critical density pc (or specific volume i/g). While this law is only approximate for real gases, it would be strictly true for a gas whose particle interact... 

Research into the future of the universe is clearly speculative. Whether the universe will continue to expand indefinitely depends on its mean density. Below a critical level (the critical density), gravitational attraction will not be enough to stop the expansion. However, if the mean density is above the critical density the universe is bound and an eventual contraction will occur resulting in a big crunch. This may precede another big bang initiating the whole cycle again. 

Analysis of the density of the substance which the Universe consists of has shown that its value sharply falls upon transition from small objects to big ones it is lO g/cm in atomic nuclei and in neutron stars, about 1 g/cm in planets and many stars, about 10 " g/cm in the Galaxy, and over the whole observable Universe the average density of substance is close to the so-called critical density estimated as 10" g/cm ... 

Also the simplest version of the field-theoretical realization of inflation predicts a total energy density very close to the critical density p, which separates the parameter region of a recollapsing Universe from the region where a non-accelerating expansion continues forever. Such a Universe is spatially flat. In the apparently relevant case of accelerated expansion, the borderline is shifted and universes somewhat above the critical densities might expand with no return. It is customary to measure the density of a specific constituent of the Universe in proportion to the critical density 13, = Pilpc-... 

The parameter 77 also depends on fij, = /tb IPo i-C-> the ratio of the baryon density to the critical density Pc needed for a flat Universe. 

Question by G. J. Van Wylen, University of Michigan Is the difference in the results from the various methods due to the fact that the various equations of state for the pure components give different accuracies in the region of the critical density ... 

Densities. It is well known that the SRK equation tends to predict liquid molal volumes that are too high, and that this is particularly noticeable in the vicinity of the critical point. The fact that the PR equation gives a universal critical compressibility factor of 0.307 compared to 0.333 for the SRK equation has improved the ability of the PR equation to predict liquid densities. 

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