Jordan-Brans-Dicke theory

Jordan-Brans-Dicke theory
Name	Jordan–Brans–Dicke theory
Field	Theoretical physics
Introduced	1950s
Contributors	Pascual Jordan; Carl H. Brans; Robert H. Dicke

Jordan-Brans-Dicke theory is a scalar–tensor theory of gravitation that generalizes General relativity by introducing a dynamical scalar field coupled to the metric, providing a varying effective gravitational "constant" and alternative explanations for cosmological phenomena. It was proposed to incorporate Machian ideas and to provide a testable rival to Albert Einstein's theory, influencing observational programs and theoretical work in cosmology and gravitational physics. The theory has played a central role in debates over scalar fields, cosmological evolution, and experimental tests such as solar-system experiments, binary-pulsar timing, and cosmological observations.

Introduction

Jordan–Brans–Dicke theory was formulated to modify General relativity by promoting Newton's constant to a field, thereby coupling a scalar degree of freedom to the spacetime metric; early proponents included Pascual Jordan and later Carl H. Brans and Robert H. Dicke. The theory's parameter ω (the Brans–Dicke coupling) controls the scalar's influence, with the ω → ∞ limit recovering Einstein field equations under certain conditions; proponents argued links to Mach's principle and to varying-constant ideas explored by Paul Dirac and contemporaries. The theory motivated observational programs at institutions such as Princeton University and collaborations with observatories and laboratories including Mount Wilson Observatory and Bell Labs.

Historical development

Development began with Pascual Jordan's work in the 1950s on scalar extensions motivated by unified-field efforts and by discussions at meetings involving figures like Albert Einstein and Arthur Eddington. In 1961 Carl H. Brans and Robert H. Dicke published the modern scalar–tensor formulation, catalyzing experimental tests by groups including Clifford M. Will's collaborators and researchers at Harvard University. The theory influenced research programs at institutions such as California Institute of Technology, Massachusetts Institute of Technology, and observatories like Kitt Peak National Observatory and Arecibo Observatory where tests of light deflection and time delay were planned. Debates over cosmological implications engaged theorists from Princeton University and Institute for Advanced Study, and later work connected the theory to developments in string theory research spearheaded by figures at Institute for Advanced Study and CERN.

Theoretical formulation

The Brans–Dicke action supplements the Einstein–Hilbert action with a scalar field φ and a dimensionless coupling ω, leading to field equations that mix φ, the metric, and the matter stress–energy tensor; the formalism was analyzed by authors at Princeton University, Cambridge University, and University of Chicago. Solutions depend on ω and on boundary conditions often discussed in the literature by researchers at Stanford University and Yale University; conservation laws and the weak equivalence principle were examined by researchers connected to NASA and laboratories at Jet Propulsion Laboratory. The scalar couples nonminimally in the Jordan frame often used in the original presentation, while conformal transformations relate this to the Einstein frame studied by groups at University of Oxford and Brown University. Mathematical techniques from work by Roger Penrose and Stephen Hawking on singularities and global structure have been applied to analyze causal structure and energy conditions in scalar–tensor theories.

Solutions and cosmological models

Exact solutions include static, spherically symmetric metrics analogous to the Schwarzschild solution and cosmological solutions generalizing Friedmann–Lemaître–Robertson–Walker models; these were investigated by researchers affiliated with Max Planck Society, University of Tokyo, and Imperial College London. Brans–Dicke cosmologies permit varying effective gravitational coupling with implications for primordial nucleosynthesis studied by teams at Brookhaven National Laboratory and Lawrence Berkeley National Laboratory and for structure formation explored by researchers at NASA Goddard Space Flight Center and European Space Agency. Inflationary and late-time acceleration scenarios in extended scalar–tensor frameworks have been modeled by groups at Princeton University, Harvard University, and University of Cambridge, and comparisons with observational programs such as Wilkinson Microwave Anisotropy Probe and Planck constrained parameter space.

Experimental tests and constraints

Solar-system tests—perihelion precession, light deflection, Shapiro time delay—performed by teams at MIT Lincoln Laboratory, Jet Propulsion Laboratory, and observatories including Palomar Observatory provided tight lower bounds on ω, following analyses by researchers like Clifford M. Will and experimental groups at NASA. Lunar laser ranging at McDonald Observatory and Apache Point Observatory has constrained temporal variation in the effective gravitational coupling, while timing of binary pulsars such as PSR B1913+16 by groups at Arecibo Observatory and Green Bank Observatory placed additional limits. Cosmological probes including Big Bang nucleosynthesis analyses by teams at Oak Ridge National Laboratory and cosmic microwave background studies by Planck and WMAP collaborations further restricted models, and laboratory tests of the inverse-square law at institutions like Stanford University and University of Washington explored short-range departures.

Extensions and related theories

Brans–Dicke theory spawned extensions and connections to varied frameworks, including Bergmann–Wagoner scalar–tensor models developed by researchers at Columbia University, f(R) gravity proposals studied at Max Planck Institute for Gravitational Physics and Perimeter Institute, and low-energy limits of string theory investigated by groups at CERN and Institute for Advanced Study. Chameleon and screening mechanisms examined by teams at University of California, Berkeley and University of Cambridge were proposed to reconcile scalar fields with local tests, while Horndeski and generalized Galileon theories developed by researchers at University of Geneva and University of Tokyo expanded the landscape of viable scalar–tensor dynamics. Applications to dark energy, modified gravity phenomenology pursued at Kavli Institute for Cosmological Physics and observational programs at Large Hadron Collider and Vera C. Rubin Observatory link the theory to contemporary efforts in theoretical and experimental physics.

Category:Gravitation