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In this paper a framework is introduced to remove the huge discrepancybetween the empirical value of the cosmological constant and the contributionto the cosmological constant predicted from the vacuum energy of quantumfields. An extra dimensional space with metric reversal symmetry and $R^2$gravity is considered to this end. The resulting 4-dimensional energy-momentumtensor (obtained after integration over extra dimensions) consists of termsthat contain off-diagonally coupled pair of Kaluza-Klein modes. This, in turn,generically results in vanishing of the vacuum expectation value of theenergy-momentum tensor for quantum fields, and offers a way to solve theproblem of huge contribution of quantum fields to the vacuum energy density.

A way to get rid of cosmological constant and zero point energy problems of quantum fields through metric reversal symmetry