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A reconstruction of modified gravity is proposed by establishing acorrespondence between the effective density of the modified gravity and theholographic density. The non-homogeneous term in the modified Friedmannequation, generated by the vacuum (holographic) energy density, lead toreconstructed models that contain explicitly, as part of the solution, theEinstein-Hilbert term. It was shown that the $\Lambda$CDM-type cosmic historiesallow the general relativity Lagrangian with cosmological constant as aparticular reconstructed solution. The Starobinsky term appears in somereconstructed solutions, and an approximate reconstruction of the Chaplygin gascosmology was performed in terms of elementary functions of curvature.

Reconstructing modified gravity with holographic vacuum energy density