Abstract
We describe a spacetime endowed with a non-metricity tensor which effectively serves as a model of a spacetime foam. We explore the consequences of the non-metricity in several f(R) theories.
Highlights
It has been argued by Wheeler [1, 2] that the spacetime may have a nontrivial structure over small scales
This nontrivial structure is characterized by uctuations of the metric and the topology
We have proposed an effective description of the spacetime foam in terms of the non-metricity tensor
Summary
It has been argued by Wheeler [1, 2] that the spacetime may have a nontrivial structure over small scales. The topological changes are usually referred to as spacetime defects (or spacetime foam). It is not dif cult to convince oneself that a spacetime with changing topology over small scales is hard to describe or even intractable. It seems, natural to take an effective perspective, where the spacetime foam is described by an intrinsic geometrical property of the spacetime manifold. We add one appendix with technical details about the stability of the solutions
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