THE SCALAR-TENSOR THEORY OF GRAVITATION

By SUSAN JACKSON

CONTENTS INTRODUCTION WHAT IS THE SCALAR–TENSOR THEORY OF GRAVITATION? WHERE DOES THE SCALAR ?ELD COME FROM? 1 2 1 THE SCALAR ?ELD ARISING FROM THE SIZE OF COMPACTI?ED INTERNAL SPACE 1 2 2 THE DILATON FROM STRING THEORY 1 2 3 THE SCALAR ?ELD IN A BRANE WORLD 1 2 4 THE SCALAR ?ELD IN THE ASSUMED TWO-SHEETED STRUCTURE OF SPACE-TIME COMMENTS 1 3 1 THE WEAK EQUIVALENCE PRINCIPLE 1 3 2 THE VALUE OF ? AND MASS OF THE SCALAR ?ELD 1 3 3 CONFORMAL TRANSFORMATION 1 3 4 MACH’S PRINCIPLE AND DIRAC’S SUGGESTION FOR TIME-DEPENDENT G 1 3 5 DOES THE SCALAR–TENSOR THEORY HAVE ANY ADVANTAGE OVER SIMPLE SCALAR THEORIES? THE PROTOTYPE BRANS–DICKE MODEL THE LAGRANGIAN FIELD EQUATIONS THE WEAK-?ELD APPROXIMATION THE PARAMETERIZED POST-NEWTONIAN APPROXIMATION A SPINOR ?ELD AS MATTER THE MECHANISM OF MIXING CONFORMAL TRANSFORMATION WHAT IS A CONFORMAL TRANSFORMATION? NONMINIMAL COUPLING COUPLING TO MATTER THE GEODESIC IN THE E FRAME COSMOLOGY WITH ? HOW HAS THE COSMOLOGICAL CONSTANT RE-EMERGED? THE STANDARD THEORY WITH ? THE PROTOTYPE BD MODEL WITHOUT ? THE PROTOTYPE BD MODEL WITH ? 4 4 1 SOLUTION IN THE J FRAME 4 4 2 SOLUTION IN THE E FRAME 4 4 3 A PROPOSED REVISION AND REMARKS MODELS OF AN ACCELERATING UNIVERSE DARK ENERGY QUINTESSENCE QUINTESSENCE IN THE BRANE WORLD 5 3 1 A SCALAR ?ELD IN THE BRANE WORLD 5 3 2 QUINTESSENCE IN THE BRANE WORLD SCALAR–TENSOR THEORY 5 4 1 HESITATION BEHAVIOR 5 4 2 A TWO-SCALAR MODEL 5 4 3 QUALITATIVE FEATURES UNIQUE TO THE TWO-SCALAR MODEL QUANTUM E?ECTS SCALE INVARIANCE THE DILATON AS A NAMBU–GOLDSTONE BOSON THE CONTRIBUTION FROM LOOPS 6 3 1 THE COUPLING TO MATTER OF ?, A SELF-COUPLED SCALAR ?ELD 6 3 2 THE COUPLING TO MATTER OF ?, SCALAR QED NON-NEWTONIAN GRAVITY A CONSEQUENCE OF THE SUSPECTED OCCURRENCE OF THE SCALAR ?ELD IN THE MAXWELL TERM TIME-VARIABILITY OF THE ?NE-STRUCTURE CONSTANT 6 6 1 ELECTROMAGNETIC COUPLING OF ?? 6 6 2 THE BEHAVIOR OF THE SCALAR ?ELD