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4.8 Isotropy: Intuitive meaning of higher power corrections

Higher-power corrections represent an independent implication of the discreteness of quantum geometry. It is thus interesting to compare their possible effects with those of effective densities and to see if they support each other or act antagonistically. A basic observation indicates supportive behavior because higher-power corrections can also be associated with repulsive contributions to the gravitational force at small scales. The origin is not as intuitive as with effective densities because higher powers of c or ˙a cannot be understood in analogy to classical mechanics, in which the emergence of new forces would be imminent.

Instead, one can understand the repulsive behavior directly as a consequence of the discreteness of quantum geometry. Rather than providing an infinite reservoir of a continuous spacetime medium, quantum geometry as a discrete structure has only finite storage space for energy. When energy densities become too high, e.g., near a classical singularity, they can no longer be supported by quantum geometry, while classical geometry easily allows an infinite increase of energy densities. Like a sponge, which when fully soaked repels further water, quantum spacetime reacts to high energy densities with repulsive forces. This expectation is also borne out by specific phenomenological and effective analysis of higher-power models.


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