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We develop the general scheme for modified $f(R)$ gravity reconstruction fromany realistic FRW cosmology. We formulate several versions of modified gravitycompatible with Solar System tests where the following sequence of cosmologicalepochs occurs: a. matter dominated phase (with or without usual matter),transition from decceleration to acceleration, accelerating epoch consistentwith recent WMAP data b. $\Lambda$CDM cosmology without cosmological constant.As a rule, such modified gravities are expressed implicitly (in terms ofspecial functions) with late-time asymptotics of known type (for instance, themodel with negative and positive powers of curvature). In the alternativeapproach, it is demonstrated that even simple versions of modified gravity maylead to the unification of matter dominated and accelerated phases at the priceof the introduction of compensating dark energy.Comment: LaTeX file, 12 pages, discussion is extended, version to appear  Physical review

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Modified<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity consistent with realistic cosmology: From a matter dominated epoch to a dark energy universe

Modifiedf(R)gravity consistent with realistic cosmology: From a matter dominated epoch to a dark energy universe