By J. A. Peacock
Gravitation and relativity -- Classical cosmology -- fundamentals of quantum fields -- The early universe -- Observational cosmology -- Galaxy formation and clustering
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Extra info for Cosmological physics
This is not surprising, since we have seen that both this phenomenon and spacetime curvature are consequences of the equivalence principle. g. Hehl et al. 1976). This is a theory with non-zero torsion, in which the connection is not symmetric, deﬁning a tensor S: μ = Γμαβ − Γμβα . 89) Now, we saw earlier that the application of the equivalence principle generated a connection that was automatically symmetric. In a local inertial frame, the equivalence principle asserts that Γ = 0 and the torsion therefore vanishes in this frame; a tensor that vanishes in one frame is zero in all, as may be seen by transforming components to a diﬀerent frame.
Since the metric tensor has zero covariant divergence, it is possible to write a modiﬁed set of ﬁeld equations that are also consistent with the conservation laws: energy density of the vacuum Gμν + Λg μν = − 8πG μν T . 86) Λ is a new constant of nature: the cosmological constant. We will see that this modiﬁcation allows the construction of a static universe. However, it is ad hoc; when the expansion of the universe was established, the Λ term was repudiated by Einstein. Despite this condemnation from its creator, the cosmological constant has refused to die and has assumed a central role in modern cosmology.
Apart from this restriction, there are no obvious areas of incompleteness: general relativity has plugged the gaps in Newtonian theory that were known to exist in the regime of strong ﬁelds and high velocities. Nevertheless, although general relativity has fared better than Newtonian theory in matching observations, it is possible that more accurate experiments will reveal discrepancies. Over the years, this possibility has motivated many suggestions of alternatives to general relativity. Sometimes these ideas can be rather subtle, but three main approaches can be distinguished.
Cosmological physics by J. A. Peacock