Abstract
By adding a matter-coupled dark energy field to Einstein's general relativity, this paper proves that the dynamical dark energy field can change the frequency of photons from distant galaxies as well as from background radiation of remote Universe. Therefore, when the observed frequency shift of the photons is entirely attributed to the temporal variation of the cosmic scale factor, the calculated expansion rate of the Universe will be slightly greater than its actual value. The predicted values of the temperature of the cosmic blackbody radiation in the past (future) of the Universe are slightly larger (gradually smaller and smaller) than those in the standard cosmology. Since the blackbody radiation becomes the present cosmic microwave background and its present-day temperature is directly estimated according to the Planck's law of blackbody radiation, the measured value of the cosmic microwave background temperature is independent of whether to consider the scalar field or not.
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