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Overall signature of the metric and the cosmological constant
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abstract
We consider a little known aspect of signature change, where the overall sign of the metric is allowed to change, with physical implications. We show how, in different formulations of general relativity, this type of classical signature change across boundaries with a degenerate metric can be made consistent with a change in sign (and value) of the cosmological constant $\Lambda$. In particular, the separate "mostly plus" and "mostly minus" signature sectors of Lorentzian gravity are most naturally associated with different signs of $\Lambda$. We show how this general phenomenon allows for classical solutions where the open dS patch can arise from a portion of AdS space time. These can be interpreted as classical "imaginary space" extensions of the usual Lorentzian theory, with $a^2<0$.
Forward citations
Cited by 6 Pith papers
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Background-level reconstruction of scalar-field potentials from dark-energy histories and comparison with analytic potential families
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Complex degenerate metrics in general relativity: a covariant extension of the Moore-Penrose algorithm
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