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

TL;DR

This paper investigates singularities in graviton-dilaton systems, showing that deviations in PPN parameters imply naked singularities, and derives bounds on the cosmological constant based on the stability of solutions.

Contribution

It demonstrates that non-standard PPN parameters lead to naked singularities in graviton-dilaton theories and establishes extremely tight bounds on the cosmological constant from solution stability.

Findings

Naked singularities occur if PPN parameter gamma differs from one.

Stable solutions with a cosmological constant imply bounds |Lambda| < 10^-102 to 10^-122.

Curvature singularities are unavoidable in low energy string theory solutions.

Abstract

Alternatives to Einstein's theory of general relativity can be distinguished by measuring the parametrised post Newtonian parameters. Two such parameters $\beta$ and $\gamma$, 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 $\gamma \ne 1$ for a charge neutral point star, then there exist naked singularities. Thus, if $\gamma$ 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 $\Lambda$ 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 $r_* \simeq {\cal O} ({\rm pc})$, 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 $| \Lambda | < 10^{- 102} (\frac{r_*}{{\rm pc}})^{- 2}$ in natural units. If $r_* \simeq 1 {\rm Mpc}$ then $| \Lambda | < 10^{- 114}$, and if $r_*$ extends all the way upto the edge of the universe ($10^{28} {\rm cm}$) then $| \Lambda | < 10^{- 122}$ in natural units.