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Within the framework of loop quantum cosmology, there exists a semi-classicalregime where spacetime may be approximated in terms of a continuous manifold,but where the standard Friedmann equations of classical Einstein gravityreceive non-perturbative quantum corrections. An approximate, analyticalapproach to studying cosmic dynamics in this regime is developed for bothspatially flat and positively-curved isotropic universes sourced by aself-interacting scalar field. In the former case, a direct correspondencebetween the classical and semi-classical field equations can be establishedtogether with a scale factor duality that directly relates different expandingand contracting universes. Some examples of non-singular, bouncing cosmologiesare presented together with a scaling, power-law solution.Comment: 14 pages, In Press, JCA

Early universe dynamics in semi-classical loop quantum cosmology