Tensor-multi-scalar theories of gravitation

Abstract

A generic class of theories where gravity is mediated by one tensor field together with an arbitrary number of scalar fields is considered. The predictions of these theories are worked out in four different observationally relevant regimes: (i) quasi-stationary weak fields (solar system conditions); (ii) rapidly varying weak fields (gravitational wave experiments); (iii) quasi-stationary strong fields (motion of systems of compact bodies, i.e. neutron stars or black holes); and (iv) the mixing of strong and radiative field effects in the gravitational radiation of N-compact-body systems. Moreover, the authors derive several significant relations between the theoretical quantities entering these predictions. They show how strong-field-gravity effects in the motion and gravitational radiation of N-compact-body systems can be parametrized by a set of theory parameters that generalize the usual post-Newtonian parameters ( gamma , beta ,. . .) introduced in the context of quasi-stationary weak gravitational fields. These new parameters ( beta 2, beta ', beta 3, beta ",. . .) provide a chart for the yet essentially unexplored domain of strong-gravitational-field effects, and thereby suggest new directions for testing relativistic gravity. This is illustrated by studying in detail a specific two-parameter tensor-bi-scalar theory T( beta ', beta ") which has the same post-Newtonian limit as general relativity but leads to new nonEinsteinian predictions for the various observables that can be extracted from binary pulsar data.