Cosmological Dynamics from Modified $f(R)$ Gravity in Einstein Frame

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In this paper, we investigate and analyze the cosmological dynamics of the universe, with an effect of modified $f(R)$ gravity emerging at cosmological scale. We choose the Einstein frame as a physical frame. We consider phase portraits of the universe at the late time from modified $f(R)$ gravity model. This result gives our universe an acceleration phase expansion without introducing existence of dark energy dominating our universe.
12 pages, 2 figures, added detail analysis, discussions and references

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