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Loop quantum cosmology is a symmetry reduced quantization of cosmological spacetimes based on loop quantum gravity. While it has been successful in resolution of various cosmological singularities and connecting Planck scale physics to phenomenology, its connection with loop quantum gravity has remained elusive. It is therefore important to integrate more and more features of the full theory into this framework and understand the reliability of physical predictions. In particular, if one wishes to connect the effective Hamiltonian in loop quantum cosmology to an expectation value of the scalar constraint operator in suitable coherent states for the full theory, one has to go beyond the standard setting of loop quantum cosmology. One possibility is to introduce gauge-covariant fluxes, which become necessary because the presence of a finite regularization parameter causes functions built out of the standard discretized variables to be in general not gauge invariant. Following the construction of gauge-covariant fluxes pioneered by Thiemann [Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories, Classical Quantum Gravity 18, 3293 (2001)CQGRDG0264-938110.1088/0264-9381/18/17/301], we show that the physics of loop quantum cosmology is affected in a nontrivial way. The bounce turns out to be generically asymmetric with a rescaling of Newton's constant in the prebounce branch. Gauge-covariant fluxes result in a higher order quantum difference equation in comparison to loop quantum cosmology. Even the behavior of matter, which behaves innocuously in loop quantum cosmology, is enriched resulting in an effective nonminimal coupling. These effects are shown to be common to different choices of regularization parameters.

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Physical Review D