The key fact is that the matter density anywhere in the universe is also a function of redshift. This fraction is itself a function of the redshift of the object (symbol: z): Where = is the radial velocity of the object, as a fraction of the speed of light. The integral of the above equation, expressed in dimensionless numbers, is: Specifically,, where is the critical mass density, above which the universe would be closed and destined to collapse. Where is the mass-energy density fraction of the universe. Where r is the distance of the object from earth (or more properly, our galaxy).Īn observation of a far-off object is typically made at a given moment and from a given place, and so ds=dt=0. Īdding this dimension requires adding a new term to the classic space-time interval, and so: Where is a constant (evaluated at 4.28 * 10 17 s) that is the reciprocal of the Hubble factor H 0 in weak gravity. This radial velocity is related to the distance of the object by this equation: Briefly, Hartnett begins with Moshe Carmeli's relativity model, which adds a dimension of the radial velocity of a far-off object to the Einsteinian dimensions of space and time.
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The full derivation of Hartnett's field equation that describes the motion of far-off objects is included in Appendix 2 of his book. This included the assumption that the matter density of the universe is at the critical level for a "coasting" universe. Hartnett extended Carmeli's model and discarded several assumptions that Carmeli initially had thought were safe. In making this prediction, Carmeli did not invoke either dark energy or dark matter. He made this prediction in 1996, two years before the publication of the Type Ia supernova data and the introduction of the idea of "dark energy" into cosmological discussions. John Hartnett, in Starlight, Time and the New Physics, reminds his readers that Moshe Carmeli first formed a new model, called cosmological relativity, and through this model predicted that the universe would in fact appear to be accelerating.
In conclusion dark energy is not been observed nor reproduced in a lab. More recent surveys have shown that the discrepancy persists. (The symbol z stands for redshift in this context.) The findings of an accelerated universe came as a profound surprise to all interested observers and commentators. A competing group, the High-Z Supernova Search Team, reported similar results from their observations of 14 other supernovae.
(Type Ia supernovae are objects of easily discernible brightness and thus are favorite objects for standardization of redshift and hence of the speed of expansion.) These supernovae were actually much dimmer than expected, a finding that indicated an acceleration of expansion, not the deceleration that gravitational attraction would produce. In 1998, the Supernova Cosmology Project observed 42 Type Ia supernovae, most of these from the ground, in an effort to measure the rate of deceleration of the expansion of the universe.
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