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First-order quantum-gravitational correction to Friedmannian cosmology from covariant, holomorphic spinfoam cosmology

The first-order loop quantum gravity correction of the simplest, classical general-relativistic Friedmann Hamiltonian constraint, emerging from a holomorphic spinfoam cosmological model peaked on homogeneous, isotropic geometries, is studied. The quantum Hamiltonian constraint, satisfied by the EPRL transition amplitude between the boundary cosmological coherent states, includes a contribution of the order of the Planck constant $\hbar$ that also appears in the corresponding semiclassical symplectic model. The analysis of this term gives a quantum-gravitational correction to the classical Friedmann dynamics of the scale factor yielding a small decelerating expansion (small accelerating contraction) of the universe. The robustness of the physical interpretation is established for arbitrary refinements of the boundary graphs. Also, mathematical equivalences between the semiclassical cosmological model and certain classical fluid and scalar field theories are explored.