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| scalar–tensor theories of gravity | |
|---|---|
| Name | Scalar–tensor theories of gravity |
| Field | Theoretical physics |
| Originated | 20th century |
| Key people | Carl H. Brans, Robert H. Dicke, Albert Einstein, Yakov Zeldovich, Alexander Friedmann, Georges Lemaître, Andrei Sakharov, Paul Dirac, Willy Hermann Kottler, Hermann Weyl, Max Planck, Erwin Schrödinger, Arthur Eddington, Subrahmanyan Chandrasekhar, Roger Penrose, Stephen Hawking, Kip S. Thorne, John Archibald Wheeler, Leonard Susskind, Gerard 't Hooft, Alexander Vilenkin, Alan Guth, Andrei Linde, David Bohm, Richard Feynman, John von Neumann, Emmy Noether, Niels Bohr, Paul Dirac (physicist), Wolfgang Pauli, Pascual Jordan, Jordan, P., Carl Gustav Jacob Jacobi, Hermann Minkowski, J. Robert Oppenheimer, Lev Landau, Igor Novikov, James Peebles, Viatcheslav Mukhanov, Yakov B. Zel'dovich, Bruce Allen, Clifford M. Will, Sean M. Carroll, Thomas P. Sotiriou, Valerio Faraoni, Tomi Koivisto, Tsvi Piran, Eugene Parker, Alan H. Guth, Jim Hartle, Stephen Weinberg |
scalar–tensor theories of gravity Scalar–tensor theories of gravity are a class of alternative gravitational models in which the gravitational interaction is mediated by both a tensor field, typically the metric of general relativity, and one or more scalar fields. They extend the framework of Albert Einstein's field equations by introducing dynamical scalar degrees of freedom that couple to curvature and matter, and have been applied to cosmology, astrophysics, and tests of fundamental physics. These theories connect to research by figures such as Carl H. Brans, Robert H. Dicke, Pascual Jordan, and have influenced studies in inflationary cosmology, dark energy, and modified gravity.
Scalar–tensor frameworks generalize Albert Einstein's General relativity by adding scalar fields that alter the effective gravitational "constant" and interact with the metric tensor; early proponents include Pascual Jordan, Yukawa, and the Brans–Dicke program of Carl H. Brans and Robert H. Dicke. The approach intersects with work on cosmological inflation by Alan Guth, Andrei Linde, and A. D. Linde, and with quantum gravity, semiclassical gravity, and attempts by Stephen Hawking and Roger Penrose to reconcile gravitation with quantum field theory. Scalar–tensor models serve as a unifying language for phenomenology explored by researchers such as Clifford M. Will, Tsvi Piran, and Sean M. Carroll.
The genesis traces to proposals by Pascual Jordan in the 1950s, a motivation from variable gravitational "constant" ideas related to Paul Dirac's large numbers hypothesis and earlier scalar ideas from Hermann Weyl and Arthur Eddington. The Brans–Dicke theory (1961) by Carl H. Brans and Robert H. Dicke formalized a minimal scalar coupling and stimulated experimental programs at institutions including Princeton University and Caltech. Later developments incorporated lessons from Stephen Hawking's work on black holes, Alan Guth's inflationary scenario, and insights from Andrei Sakharov on induced gravity. Renewed interest in the 1990s and 2000s linked scalar–tensor models to dark energy research by James Peebles, Viatcheslav Mukhanov, Alexander Vilenkin, and string-inspired studies by Leonard Susskind and Gerard 't Hooft.
A prototypical action for scalar–tensor models generalizes the Einstein–Hilbert action with a scalar field φ and functions F(φ), Z(φ), V(φ); early canonical form appears in the Brans–Dicke action of Carl H. Brans and Robert H. Dicke. Field equations derive from variational principles akin to methods used by Noether and John Archibald Wheeler, producing modified Einstein equations with additional stress-energy contributions from φ and a scalar wave equation sourced by curvature and matter. Conformal transformations between the Jordan frame and the Einstein frame are standard tools used by theorists like Clifford M. Will and Valerio Faraoni to analyze couplings and energy conditions, and canonical quantization attempts reference techniques developed by Paul Dirac and Richard Feynman.
Notable examples include the Brans–Dicke theory of Carl H. Brans and Robert H. Dicke; scalar-tensor inflaton models associated with Alan Guth and Andrei Linde; Damour–Esposito-Farèse scalarization models by Thibault Damour and G. Esposito-Farèse; chameleon models explored by Justin Khoury and Amanda Weltman; symmetron models developed by Philippe Brax and collaborators; and Horndeski theories originally by Gregory Horndeski and revived in modern contexts by Claudia de Rham and Andrew J. Tolley. Extensions informed by String theory researchers like Gabriele Veneziano and Michael Green include dilaton couplings and moduli stabilization studied in the context of compactification scenarios explored by Edward Witten and Cumrun Vafa.
Scalar degrees of freedom modify gravitational wave emission, black hole structure, neutron star equilibrium, and cosmological evolution—subjects investigated by Kip S. Thorne, Eanna Flanagan, Luc Blanchet, and Nils Andersson. Effects include variations in the effective gravitational constant relevant to solar-system tests by teams at Jet Propulsion Laboratory and NASA, modifications to the parametrized post-Newtonian (PPN) parameters used by Clifford M. Will, and potential signatures in the cosmic microwave background studied by Pieter G. van Dokkum and Max Tegmark. Phenomena such as spontaneous scalarization in compact objects were predicted by Thibault Damour and G. Esposito-Farèse and explored with numerical relativity methods by Miguel Alcubierre and Carsten Gundlach.
Solar-system constraints from missions and observatories associated with Stanford University, Caltech, European Space Agency, and NASA place tight bounds on Brans–Dicke parameter ω via light-deflection and time-delay experiments influenced by work at Harvard–Smithsonian Center for Astrophysics and MIT. Binary pulsar timing by groups around Russell Hulse and Joseph Taylor provides limits on scalar dipole radiation, while gravitational-wave observations by LIGO Scientific Collaboration, VIRGO, and KAGRA test deviations in waveform phasing linked to scalar modes. Cosmological surveys led by Planck, Sloan Digital Sky Survey, Dark Energy Survey, and teams like Supernova Cosmology Project and High-Z Supernova Search Team constrain scalar dynamics relevant to dark energy and inflationary predictions from Alan Guth-style scenarios.
Scalar–tensor theories overlap with and complement f(R) gravity (often recast as scalar-tensor models), effective field theories considered by Claudia de Rham and Arkani-Hamed, and low-energy limits of String theory studied by Joseph Polchinski and Michael Green. They contrast with metric theories developed in the tradition of Albert Einstein and with vector-tensor frameworks explored by Jacob Bekenstein and Ted Jacobson. Connections to quantum gravity programs by Carlo Rovelli, Lee Smolin, and holographic perspectives from Juan Maldacena enrich comparative studies, while phenomenological bridges link to modified Newtonian dynamics investigated by Mordehai Milgrom.