Singularities in Graviton - Dilaton System : Their Implications on the PPN Parameters and the Cosmological Constant

Alternatives to Einstein’s theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters β and γ, equal to one in Einstein theory, can be obtained from static spherically symmetric solutions. For the graviton-dilaton system, as in Brans-Dicke or low energy string theory, we find that if γ 6= 1 for a charge neutral point star, then there exist naked singularities. Thus, if γ is measured to be different from one, then it cannot be explained by these theories, without implying naked singularities. We also couple a cosmological constant Λ to the graviton-dilaton system, a la string theory. We find that static spherically symmetric solutions in low energy string theory, which describe the gravitational field of a point star in the real universe atleast upto a distance r∗ ≃ O(pc), always lead to curvature singularities. These singularities are stable and much worse than the naked ones. Requiring their absence upto a distance r∗ implies a bound |Λ| < 10−102( r∗ pc )−2 in natural units. If r∗ ≃ 1Mpc then |Λ| < 10−114, and if r∗ extends all the way upto the edge of the universe (10cm) then |Λ| < 10−122 in natural units.