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| Brans–Dicke | |
|---|---|
| Name | Brans–Dicke theory |
| Authors | Carl H. Brans; Robert H. Dicke |
| Year | 1961 |
| Field | Theoretical physics; General Relativity alternatives; Gravitation |
Brans–Dicke is a scalar–tensor theory of gravitation proposing that gravitation is mediated by both a tensor field and a scalar field, developed to incorporate Machian ideas and variable effective gravitational coupling. The theory was introduced by Carl H. Brans and Robert H. Dicke as an alternative to Einstein's general relativity and has been influential in discussions involving Dirac-inspired large number hypotheses, Eddington's ideas, and scalar fields in cosmology. Brans–Dicke has informed work in Schwarzschild solutions, Dicke's experiments, and later scalar–tensor frameworks connected to Brans–Dicke-inspired models in inflation, string theory, and Kaluza–Klein reductions.
Brans–Dicke sets out a scalar field φ coupled to the metric g_{μν} with a dimensionless coupling parameter ω, aiming to satisfy Machian notions advocated by Mach and pursued by Sciama. The theory was presented in the early 1960s within the context of debates involving Einstein, Feynman, and Wheeler on foundational aspects of gravity, and it catalyzed observational programs by Dicke, Taylor, and Will. Brans–Dicke influenced subsequent proposals by Zel'dovich, Sakharov, and researchers at institutions like Princeton University, MIT, and Caltech.
The action functional of Brans–Dicke modifies the Einstein–Hilbert action by replacing Newton's constant with 1/φ and adding a kinetic term for φ with coefficient ω, an approach discussed alongside scalar actions used by Pascual Jordan in the Jordan framework and by researchers like Thiry. Field equations couple φ to the Ricci scalar R and to the stress–energy tensor T_{μν}, producing modified geodesic and conservation relations examined by Weyl and compared to formulations by Levi-Civita and Cartan. Gauge choices and conformal frames (Jordan frame vs. Einstein frame) create relationships to transformations studied by Weyl and by Dicke in equivalence principle discussions. The parameter ω determines the scalar's influence and connects to limits explored by Nordtvedt and by parameterized post-Newtonian analyses by Will.
Cosmological solutions of Brans–Dicke were applied to Big Bang models, FLRW cosmologies, and CMB predictions evaluated against data from COBE, WMAP, and Planck. Scalar dynamics alter expansion histories considered by Friedmann, Lemaître, and Robertson, and have been used in alternative inflationary scenarios following ideas from Guth and Linde. Astrophysical applications include stellar structure modifications relevant to Chandrasekhar limits, compact object models connected to Schwarzschild and Kerr geometries, and gravitational lensing predictions compared with tests by Chandrasekhar groups and lens surveys from Hubble Space Telescope and Sloan Digital Sky Survey.
Post-Newtonian parameters in Brans–Dicke map to the PPN parameters measured in solar-system tests by Cassini, lunar laser ranging by Apollo, and deflection measurements by Eddington-style experiments updated by VLBI. Constraints from the perihelion precession of Mercury, time delay of Shapiro, and frame-dragging measurements by Gravity Probe B limit ω to high values, pushing the theory toward GR limits; analyses by Will, Damour, and Nordtvedt quantified bounds. Cosmological datasets from Type Ia supernovae surveys by High-Z Team and Supernova Cosmology Project, together with BAO results from BOSS, place complementary constraints on evolving φ scenarios studied by Faraoni and Clifton.
Brans–Dicke inspired scalar–tensor families such as the Bergmann–Wagoner class, Nordtvedt variants, and generalized Horndeski and beyond-Horndeski actions linked to Horndeski's work. Connections to string theory effective actions, dilaton fields in bosonic string and superstring contexts, and to f(R) theories have been explored by researchers at CERN, Perimeter Institute, and Institute for Advanced Study. Chameleon screening mechanisms invoked by Khoury and Weltman and Galileon models by Nicolis relate to environment-dependent scalar couplings studied in laboratory tests at CERN and in astrophysical probes by LIGO and Virgo. Quantum corrections and renormalization-group approaches discussed by Weinberg and 't Hooft inform attempts to embed Brans–Dicke-like scalars in effective field theory frameworks.
Exact solutions include scalarized analogues of the Schwarzschild and Kerr spacetimes, static spherically symmetric configurations investigated by Morris-type and wormhole analyses informed by Thorne and Visser, and cosmological exacts such as power-law FLRW models related to work by Friedmann and McVittie. Solution-generating techniques utilize conformal transformations developed by Weyl and canonical methods analogous to those in Hamiltonian mechanics by Hamilton. Mathematical properties like Cauchy problem well-posedness, singularity theorems extending Hawking and Penrose results, and stability analyses were pursued by Choquet-Bruhat and Christodoulou.
Introduced in 1961 by Brans and Dicke at institutions including Princeton University and Cornell University, the theory stimulated experimental programs by Dicke and theoretical critiques from Wheeler, Einstein-inspired communities, and proponents of Pauli-style uniqueness arguments. During the 1960s and 1970s it influenced work by Jordan, Thiry, Brans, and Dicke and later engaged researchers such as Will, Damour, and Nordtvedt in precision tests. Interest revived with connections to string theory in the 1980s and with observational tensions in cosmology evaluated by teams at NASA, ESA, and major observatories, securing Brans–Dicke's place in the archive of alternative gravitational theories.
Category:Gravity theories