1 v 2 1 9 A ug 2 00 1 SELF - TUNING SOLUTIONS OF THE COSMOLOGICAL CONSTANT ∗

It is generally believed that the cosmological constant problem is the most severe hierarchy problem in particle physics. The hierarchy problem has been formulated since 1975 in connection with grand unified theories(GUTs). GUTs introduce two scales which differ by a factor of 10. At the classical Lagrangian level, there appear parameters which are of order 10 GeV. But loop corrections and spontaneous symmetry breaking enter and after the dust settles down we require to have an electroweak vacuum expectation value(VEV) of order 100 GeV. This implies that the parameter of the Higgs boson mass must satisfy M H + ∆M 2 H = O(10 −28)M2 GUT , which is a fine-tuning problem known as the so-called gauge hierarchy problem. When we consider different scales in the same Lagrangian, in general we encounter this kind of hierarchy problem. Gravity is described by metric gμν . Then the metric theory of gravity is given by the action