A STRATIFIED FRAMEWORK FOR SCALAR-TENSOR THEORIES OF MODIFIED DYNAMICS

Although the modified Newtonian dynamics (MOND) proposed by Milgrom su ccessfully accounts for the systematics of galaxy rotation curves and cluster dynamics without invoking dark matter, the idea remains a larg ely ad hoc modification of Newtonian dynamics with no basis in deeper theory. Nonstandard scalar-tensor theories have been suggested as a th eoretical basis for MOND; however, any such theory with the usual conf ormal relation between the Einstein and physical metrics fails to pred ict the degree of light deflection observed in distant clusters of gal axies. The prediction is that there should be no discrepancy between t he detectable mass in stars and gas and the lensing mass, in sharp con tradiction to the observations (Bekenstein & Sanders). In the present paper, I demonstrate that one can write down a framework for scalar-te nsor theories that predict the MOND phenomenology for the low-velocity (upsilon much less than c) dynamics of galaxies and clusters of galax ies and are consistent with observations of extragalactic gravitationa l lenses, provided that one drops the requirement of the Lorentz invar iance of gravitational. dynamics. This leads to ''preferred-frame'' th eories characterized by a nonconformal relation between the two metric s. I describe a toy theory in which the local environment (the solar s ystem, binary pulsars) is protected from detectable preferred-frame ef fects by the very same nonstandard (aquadratic) scalar Lagrangian that gives rise to the MOND phenomenology. Although this particular theory is also contrived, it represents a limiting case for two-field theori es of MOND and is consistent with a wide range of gravitational phenom ena. Moreover, it is a cosmological effective theory which may explain the near numerical coincidence between the MOND acceleration paramete r and the present value of the Hubble parameter multiplied by the spee d of light.