Einstein cosmological model

Einstein develops first relativistic cosmological model and introduces concepts of transition probabilities and stimulated emission. 

The paper is organized as follows in section 2, we briefly review the geometry and dynamics of the Universe and then give the Einstein-Friedman-Lemaitre (hereafter EEL) equations section 3 introduces some important quantities needed for observations in section 4, we rapidly present some solutions of the EEL equations, i.e. some cosmological models in section 5, the Standard Big Bang Nucleosynthesis Model is described while section 6 shows a statement of observations of primordial abundances in section 7, we confront the predictions of the Standard Big Bang Nucleosynthesis (hereafter SBBN) model to the observations of the primordial abundances a brief conclusion is... 

Cosmological models obtained through the simplifying assumption of an affine-connected manifold must, by definition, be no more than a crude approximation. The one feature in common to all possible models is the balance between a curvature tensor and a stress tensor, as specified by Einstein s field... 

In order to avoid the problem of boundary conditions at infinity Einstein, in his original cosmological model, based on general relativity, assumed space to be closed, in which case there is no infinity. As a working model he selected what is known as a topological 3-sphere, which is the 3-surface of the four-dimensional hypersphere of radius Rq, defined by the set of points in Euclidean space that satisfies the equation... 

The question of the world invariance was discussed since Einstein who believed the Universe to be invariable and static. But in 1917, having applied his general relativity theory to cosmology, Einstein unexpectedly found that the cosmological model created by him did not confirm the eternity, invariance, and static character of the Universe. To save his ideas of the static character and invariance of the Universe,... 

Alexandr Alexandrovitch Friedmann (1888-1925), Russian mathematician and physicist, in his articie in Zeit. Phys., 10, 377 (1922), proved on the basis of Einstein s general theory of relativity that the curvature of the Universe must change, which became the basis of cosmological models of the expanding Universe. During World War I, Friedman was a pilot in the Russian army and made bombing raids over my beloved Przemysl. 

All of these effects are included in codes like CMBFAST (Seljak and Zal-darriaga 1996 Zaldarriaga and Seljak, 2000, http //www.cmbfast.org/) and CAMB (Lewis et al., 2000, http //camb.info/) which solve the combined Boltzmann and linearized Einstein equations in an expanding Universe. These codes allow one to calculate the CMB temperature power spectrum for a given model. A sample of spectra for various input cosmological parameters is shown in Figure 10.2. 

Figure 12.1. Hubble diagram of nearby Type la supernovae. The distances are derived from light curve shape corrected luminosities (data from Tonry et al. 2003). The solid line is for an empty universe (Qa = Ojh = 0), the dotted line for an Einstein-de Sitter model (Qa = 0, Hm = 1) and the dashed line for a model with no matter and all cosmological constant (Qa = 1,0 1 = 0). The concordance model (Qa = 0.7, Qaj = 0.3) is shown as the line fitting the data best. The bottom panel shows all distances relative to the empty universe model.

To keep the record straight, what is generally known as standard cosmology refers to the model proposed by Einstein and de Sitter (1932). It consists of a Ftiedmann solution with A = 0, A = 0 and zero pressure, without reference to Friedmann or Lemaitre. The space-time is topologically like M and... 

In all of these statements the emphasis is on unified fields and not on cosmology. As a matter of fact, the equivalence of the projective unified model to five-dimensional spaces in general, and to that of Einstein and Mayer in particular, was first demonstrated by Veblen himself (Monograph Chapter Vlll). The crucial observation is that this equivalence mapping is done in the tangent space, without implying the equivalence of the Einstein-Mayer five-dimensional construct with four-dimensional projective space-time. The five-dimensional spaces are not projective, but affine spaces. 

Cosmology in its present form developed as a by-product of Einstein s gravitational field equations, based on the astronomical data of the previous millenium, which established the heliocentric model of the solar system. The struggle against the authority of Ptolemy, Aristotle and the Inquisition, the rivalry between Kepler and Galileo, and the intrigue between Newton and his contemporaries, Descartes, Leibniz, Hooke and others, overshadow the important theoretical advances that produced the mechanical clockwork model of Laplace. 

---