Universe, expansion

In the next section each light nuclide is considered in turn, its post-BBN evolution briefly reviewed along with identification of a few of the potential challenges to accurately inferring the primordial abundances from the observational data. Then, having established that the current data - taken at face value - are not entirely consistent with SBBN, I investigate whether changes in the early universe expansion rate can reconcile them. 

There are many different extensions of the standard model of particle physics which result in modifications of the early universe expansion rate (the time -temperature relation). For example, additional particles will increase the energy density (at fixed temperature), resulting in a faster expansion. In such situations it is convenient to relate the extra energy density to that which would have been contributed by an additional neutrino with the ordinary weak interactions [19]. Just prior to e annihilation, this may be written as... 

If more relativistic particles are present, gef f increases and the universe would expand faster so that, at fixed T, the universe would be younger. Since the synthesis of the elements in the expanding universe involves a competition between reaction rates and the universal expansion rate, gef j will play a key role in determining the BBN-predicted primordial abundances. 

As time goes by and the universe cools, the lighter protons are favored over the heavier neutrons and the neutron-to-proton ratio decreases, initially as n/p oc exp(—Am/T), where Am = 1.29 MeV is the neutron-proton mass difference. As the temperature drops below roughly 0.8 MeV, when the universe is roughly one second old, the rate of the two-body collisions in eq. 3.24 becomes slow compared to the universal expansion rate and deviations from equilibrium occur. This is often referred to as freeze-out , but it should be noted that the n/p ratio continues to decrease as the universe expands, albeit at a slower rate than if the ratio tracked the exponential. Later, when the universe is several... 

The primordial abundances of D, 3He, and 7Li(7Be) are rate limited, depending sensitively on the competition between the nuclear reactions rates and the universal expansion rate. As a result, these nuclides are potential baryometers since their abundances are sensitive to the universal density of nucleons. As the universe expands, the nucleon density decreases so it is useful to compare the nucleon density to that of the CMB photons r) = n /n7. Since this ratio will turn out to be very small, it is convenient to introduce... 

In contrast to the other light nuclides, the primordial abundance of 4He (mass fraction Y) is relatively insensitive to the baryon density, but since virtually all neutrons available at BBN are incorporated in 4He, it does depend on the competition between the weak interaction rate (largely fixed by the accurately measured neutron lifetime) and the universal expansion rate (which depends on geff)- The higher the nucleon density, the earlier can the D-bottleneck be breached. At early times there are more neutrons and, therefore, more 4He will be synthesized. This latter effect is responsible for the very slow (logarithmic) increase in Y with rj. Given the standard model relation between time and temperature and the nuclear and weak cross sections and decay rates measured in the laboratory, the evolution of the light nuclide abundances may be calculated and the frozen-out relic abundances predicted as a function of the one free parameter, the nucleon density or rj. These are shown in Fig. 1. 

It is clear from Fig. 16 that for a large range in r], a combination of ANv and e can be found so that the BBN-predicted abundances will lie within our adopted primordial abundance ranges. However, there are constraints on 77 and ANv from the CMB temperature fluctuation spectrum (see KSSW for details and further references). Although the CMB temperature fluctuation spectrum is insensitive to e, it will be modified by any changes in the universal expansion rate. While SBBN (ANv = 0) is consistent with the combined constraints from BBN and the CMB (see 5.5) for 7710 5.8 (Qb 2 0.021), values of ANv as large as ANv 6 are also allowed (KSSW). 

If further observational and associated theoretical work should confirm the current tension among the SBBN-predicted and observed primordial abundances of D, 4He, 7Li, what physics beyond the standard models of cosmology and particle physics has the potential to resolve the apparent conflicts Are those models which modify the early, radiation-dominated universe expansion rate consistent with observations of the CMB temperature fluctuation spectrum If neutrino degeneracy is invoked, is it consistent with the neutrino properties (masses and mixing angles) inferred from laboratory experiments as well as the solar and cosmic ray neutrino oscallation data ... 

The linear law, cz = Hr, relating the redshift 2 to distance r through c and the constant H, is known as Hubble s law and H is Hubble s constant. This relationship is of the same form as (6.5), which describes the rate of universal expansion according to de Sitter, rearranged to read ... 

Assume that the big bang happened at a time T in the past at space coordinates (0,0,0). This means that primeval radiation has travelled a distance d = cT hy now. An absorber, which interacts with the same radiation on Earth today, must have moved the same distance at a velocity v = d/T from the big-bang coordinates where it came into being. The only transport mechanism of moving the absorber to its present coordinates, at velocity v, is the universal expansion. 

Troitskij s analysis is based on more than 37 000 galactic and quasar redshifts. By comparison, the meagre sample that originally established the linear Hubble law is rather crude. However, as defenders of universal expansion freely use data conditioned by Hubble s law, further debate of the issue becomes pointless. 

Infons that originate at stars that move towards earth, arrive with velocities c + v and there is no device to slow them down to the observable velocity of c. Such stars remain invisible and hence, all galactic objects appear to be redshifted. The light from several near-by galaxies, including M31 in Andromeda, is actually blue shifted. Like universal expansion the infon model cannot account for this observation, but without relative motion in the local group no spectral shift is predicted and the blue shift could be induced by statistical optics. 

Before one can seriously consider an alternative plasma cosmology the ideas of Alfven and others need to be integrated with a sensible alternative to universal expansion and the topology of space-time. Instead of chasing after non-baryonic dark matter the role of hydrogen in that regard should be explored and the interaction between matter and antimatter, an important argument in the current theories (Lerner, 1991), must be rationalized. 

The elastic lateral stiffness of a bellows decreases linearly with increasing pressure (EJMA, 1993 Newland, 1964 Snedden, 1985) and, upon sufficient increase, the beUows can become unstable, usually resulting in very rapid (10 to 50 ms) gross lateral deflection or squirm. The lateral stiffness and response of a universal expansion joint, i.e., two bellows interconnected by a straight length of pipe or spool piece, has been considered by Newland (1964). The lateral stiffness for two bellows connected by an offset spool piece, such as here, was undertaken by Newland (1976). No determination appears to exist for the determination of natural frequency with an offset spool piece. 

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