The fundamental constants and their variation: observational status and theoretical motivations

Abstract

This article describes the various experimental bounds on the variation of the fundamental constants of nature. After a discussion on the role of fundamental constants, of their definition and link with metrology, the various constraints on the variation of the fine structure constant, the gravitational, weak and strong interactions couplings and the electron to proton mass ratio are reviewed. This review aims (1) to provide the basics of each measurement, (2) to show as clearly as possible why it constrains a given constant and (3) to point out the underlying hypotheses. Such an investigation is of importance to compare the different results, particularly in view of understanding the recent claims of the detections of a variation of the fine structure constant and of the electron to proton mass ratio in quasar absorption spectra. The theoretical models leading to the prediction of such variation are also reviewed, including Kaluza-Klein theories, string theories and other alternative theories and cosmological implications of these results are discussed. The links with the tests of general relativity are emphasized.

56 pages, l7 figures, submitted to Rev. Mod. Phys

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• Effects of the U-boson on the inner edge of neutron star crusts
• Scale-Dependent Newton's Constant G in the Conformal Newtonian Gauge
• Transitions in Zr, Hf, Ta, W, Re, Hg, Ac and U ions with high sensitivity to variation of the fine-structure constant
• Reappraisal of the limit on the variation in $\alpha$ implied by Oklo
• Oklo reactors and implications for nuclear science
• Tachyon with an inverse power-law potential in a braneworld cosmology
• Rippled Cosmological Dark Matter from Damped Oscillating Newton Constant
• Cosmological Density Perturbations with a Scale-Dependent Newton's G
• A 5% measurement of the gravitational constant in the Large Magellanic Cloud
• Gravitational Higgs Mechanism in Neutron Star Interiors
• Properties of condensed matter from fundamental physical constants
• Viscosity and diffusion in life processes and tuning of fundamental constants
• Does the Newton's gravitational constant vary sinusoidally with time? Orbital motions say no
• Scalar-tensor cosmologies without screening
• Sisyphus Optical Lattice Decelerator
• Sensitivity to alpha-variation in ultracold atomic-scattering experiments
• Do the fundamental constants change with time ?
• Newtonian approximation and possible time-varying $G$ in nonlocal gravities
• Fractal Approach to Large-Scale Galaxy Distribution
• A Machian Solution of the Hierarchy Problem
• Constraining fundamental constants of physics with quasar absorption line systems
• The local dark sector. Probing gravitation's low-acceleration frontier and dark matter in the Solar System neighborhood
• Dimensionless cosmology
• Time Variation of Fine Structure Constant and Proton-Electron Mass Ratio with Quintessence
• Microwave spectroscopy of Lambda-doublet transitions in the ground state of CH
• Cosmic Variation of Proton to Electron Mass Ratio with an interacting Higgs Scalar Field
• The value of the fine structure constant over cosmological times
• Constraining a possible time-variation of the speed of light along with the fine-structure constant using strong gravitational lensing and Type Ia supernovae observations
• Observational constraints on varying fundamental constants in a minimal CPC model
• Probing the time variation of fine structure constant using galaxy clusters and quintessence model
• Relativistic energy shifts in Ge II, Sn II and Pb II and search for cosmological variation of the fine structure constant
• Does the Hubble Redshift Flip Photons and Gravitons?
• Variation of the fine structure constant in the light of recent helium abundance measurement
• Chameleonic dilaton, nonequivalent frames, and the cosmological constant problem in quantum string theory
• The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey: constraints on the time variation of fundamental constants from the large-scale two-point correlation function
• Constraints on fundamental physical constants from bio-friendly viscosity and diffusion
• Variations of nuclear binding with quark masses
• Halting eternal acceleration with an effective negative cosmological constant
• Interpretation of geodesy experiments in non-Newtonian theories of gravity
• Varying-Alpha and K-Essence
• The Geometrical Origin of Dark Energy
• Generalized nonconservative gravitational field equations from Herglotz action principle
• Redshift space distortions in the presence of non-minimally coupled dark matter
• uGMRT search for cold gas at z~1-1.4 towards red quasars
• Stellar Helium Burning in Other Universes: A solution to the triple alpha fine-tuning problem
• Solar chameleons: Novel channels
• Constraints of the variation of fundamental couplings and sensitivity of the equation of state of dense matter
• Non-minimally coupled varying constants quantum cosmologies
• The role of unit systems in expressing and testing the laws of nature
• Transition from decelerated to accelerated cosmic expansion in braneworld universes
• Let's talk about varying G
• Cosmic strings in Bekenstein-type models
• Gluon condensate, modified gravity, and the accelerating Universe
• Efficient and robust photo-ionization loading of beryllium ions
• The Phase Space Elementary Cell in Classical and Generalized Statistics
• Varying fine structure "constant" and charged black holes
• Laser spectroscopy of cold molecules
• SeD Radical: A probe for measurement of time variation of Fine Structure Constant($\alpha$) and Proton to Electron Mass Ratio($\mu$)
• A back-reaction approach to dark energy
• Non-adiabatic quantum effects from a Standard Model time-dependent Higgs vev
• Scalar charges and pulsar-timing observables in the presence of nonminimally coupled scalar fields
• Hubble tension as a window on the gravitation of the dark matter sector: Exploration of a family of models
• 2d Stringy Black Holes and Varying Constants
• Quantum fields, cosmological constant and symmetry doubling
• Varying fundamental constants: a full covariant approach and cosmological applications
• Transiting planets as a precision clock to constrain the time variation of the gravitational constant
• Accelerated expansion from braneworld models with variable vacuum energy
• Violation of the Weak Equivalence Principle in Bekenstein's theory
• Shadows of black holes at cosmological distances in the co-varying physical couplings framework
• Black Hole-Wormhole transition in (2+1) Einstein -- anti-de Sitter Gravity Coupled to Nonlinear Electrodynamics
• The variation of the fine structure constant: testing the dipole model with thermonuclear supernovae
• Review on the minimally extended varying speed of light model
• Covariant formulation of refracted gravity
• Observational constraints on spatial anisotropy of G from orbital motions
• A search for the fine-structure constant evolution from fast radio bursts and type Ia supernovae data
• Probe the gravitational constant variation via the propagation of gravitational waves
• Two-branes with variable tension model and the effective Newtonian constant
• Effects of a scalar fifth force on the dynamics of a charged particle as a new experimental design to test chameleon theories
• Prospects for high-resolution microwave spectroscopy of methanol in a Stark-deflected molecular beam
• The effect of the gravitational constant variation on the propagation of gravitational waves
• Mirror Dark Sector Solution of the Hubble Tension with Time-varying Fine-structure Constant
• Recent developments in premetric classical electrodynamics
• Can homogeneous extra dimensions be stabilized during matter domination?
• Constraining Coupling Constants' Variation with Supernovae, Quasars, and GRBs
• Constraining the fundamental interactions and couplings with Eötvös experiments
• Tests of Relativistic Gravity in Space: Recent Progress and Future Directions
• Scenario of Accelerating Universe from the Phenomenological Λ- Models
• Nonclassical effects in geodesic motion
• Variational Vibrational States of Methanol (12D)
• A matter-dominated cosmological model with variable $G$ and $\Lambda$. Confrontation of theoretical predictions with observational data
• Time delay of photons of different energies in multi-dimensional cosmological models
• 1/R multidimensional gravity with form-fields: stabilization of extra dimensions, cosmic acceleration and domain walls
• Solving nonlinear Klein-Gordon equations on unbounded domains via the Finite Element Method
• Kinematical Conformal Cosmology: fundamental parameters from astrophysical observations
• Asymptotic bound on slow-roll parameter in stringy quintessence model
• Angular momentum sensitivities in scalar-tensor theories
• Speed of light in the extended gravity theories
• Effects of a Late Gravitational Transition on Gravitational Waves and Anticipated Constraints
• Scaling solution for field-dependent gauge couplings in quantum gravity
• Zeldovich Lambda and Weinberg Relation: An Explanation for the Cosmological Coincidences
• Detecting Ultralight Dark Matter with Matter Effect
• One possible mechanism for massive neutron star supported by soft EOS
• Dirac Cosmology and the Acceleration of the Contemporary Universe
• Gauss-Bonnet brane-world cosmology without $Z_2$-symmetry
• Chameleon gravity on cosmological scales
• Dynamics of the self-interacting chameleon cosmology
• Measuring the speed of light with cosmological observations: current constraints and forecasts
• Is Gravity an Interaction?
• Solar System planetary tests of \dot c/c
• Non-parametric reconstruction of the fine structure constant with galaxy clusters
• Charge non-conservation, dequantisation, and induced electric dipole moments in varying-alpha theories
• How strongly does dating meteorites constrain the time-dependence of the fine-structure constant?
• Few Body Reserch - Summary
• Constraints on the minimally extended varying speed of light model using the Pantheon+ dataset
• The momentum constraint equation in Parameterised Post-Newtonian Cosmology
• Evolution of the Universe with Flat Extra Dimensions
• Metrological constraints on the variability of the fundamental constants $e$, $\hslash$, and $c$
• Cosmological Model with Cosmic transit behaviour in Brans-Dicke Theory
• Hyperfine structure of the ${\mathbf{A}}^1\mathbf{\Pi }$ state of AlCl and its relevance to laser cooling and trapping
• Constraints on Field Theoretical Models for Variation of the Fine Structure Constant
• Time varying $\alpha$ in N=8 extended Supergravity
• Constraining an Expanding Locally Anisotropic metric from the Pioneer anomaly
• Big bang nucleosynthesis as a probe of fundamental "constants"
• Internal heating and thermal emission from old neutron stars: Constraints on dense-matter and gravitational physics
• Is Quintessence an Indication of a Time-Varying Gravitational Constant?
• Bloch-Siegert shift in application to the astrophysical determination of the fundamental constants variation
• Varying constants driven baryogenesis
• Physical dimensions/units and universal constants: their invariance in special and general relativity
• Notes on several phenomenological laws of quantum gravity
• Hidden Symmetries in Deformed Very Special Relativity
• On cosmologically induced hierarchies in string theory
• Implication of Spatial and Temporal Variations of the Fine-Structure Constant
• Is there any evidence for extra-dimensions or quantum gravity effects from the delayed MeV-GeV photons in GRB 940217?
• A Locally Anisotropic Metric for Matter in an Expanding Universe: I. The Ansatz and the Modified Newton Law
• Thermodynamics in variable speed of light theories
• Transition frequencies, isotope shifts, and hyperfine structure in $4s\to 4p$ transitions of Ti${}^{+}$ ions
• How to Create Universes with Internal Flux
• Probing nuclear observables via primordial nucleosynthesis
• Dark Energy, scalar-curvature couplings and a critical acceleration scale
• Addressing the DESI DR2 Phantom-Crossing Anomaly and Enhanced $H_0$ Tension with Reconstructed Scalar-Tensor Gravity
• Relativistic configuration-interaction calculations of U I hyperfine constants
• Some boundary effects in quantum field theory
• Sensitivity of the energy levels of singly ionized cobalt to the variation of the fine structure constant
• Estimations of the cosmological parameters from the observational variation of the fine structure constant
• The establishment of the Standard Cosmological Model through observations
• The Future Evolution of White Dwarf Stars Through Baryon Decay and Time Varying Gravitational Constant
• Energy production in varying α theories
• Observable Effects of Scalar Fields and Varying Constants
• Effect of the Chameleon Scalar Field on Brane Cosmological Evolution
• Cosmological Behavior of a Parity and Charge-Parity Violating Varying Alpha Theory
• THESEUS$-$BTA cosmological tests using Multimessenger Gamma-Ray Bursts observations
• Einstein's Geometrical Versus Feynman's Quantum-Field Approaches to Gravity Physics: Testing by Modern Multimessenger Astronomy
• 5-Dimensional Kaluza-Klein Theory with a Source
• Non-minimal coupling inspires the Dirac cosmological model
• Accelerating universe with time variation of $G$ and $\Lambda$
• Anthropic Selection of Physical Constants, Quantum Entanglement, and the Multiverse Falsifiability
• Sympathetically cooled molecular ions: from principles to first applications
• Extrinsic and intrinsic effects setting viscosity in complex fluids and life processes: the role of fundamental physical constants
• Future constraints on variations of the fine structure constant from combined CMB and weak lensing measurements
• Constants of extended Standard Model and search for their temporal variations
• Constraining PCP Violating Varying Alpha Theory Through Laboratory Experiments
• Improved Constraints on the Variation of the Weak Scale from Big Bang Nucleosynthesis
• Galaxies as Rotating Buckets - a Hypothesis on the Gravitational Constant Based on Mach's Principle
• Speed Limit on the brane
• Variations of the Fine Structure Constant in Space and Time
• Effects of Variable Newton Constant During Inflation
• An investigation of a varying G through Strong Lensing and SNe Ia observations
• Single barium ion spectroscopy: light shifts, hyperfine structure, and progress on an optical frequency standard and atomic parity violation
• Reconstruction of Cosmological Evolution in the Presence of Extra Dimensions
• Time Variation of the Fine Structure Constant in the Spacetime of a Domain Wall
• Dilaton-induced variations in Planck constant and speed of light: An alternative to Dark Energy
• An interstellar mission to test astrophysical black holes
• Cosmological evolution of the proton-to-electron mass ratio in an extended Brans-Dicke theory
• Confining Boundary conditions from dynamical Coupling Constants
• Variation of the Fine-Structure Constant from the de Sitter Invariant Special Relativity
• Limits on the Time Evolution of Space Dimensions from Newton's Constant
• B-L-symmetric Baryogenesis with Leptonic Quintessence
• Measuring the Time Variation of the Fine-structure Constant with Quasars Detected by LAMOST
• Search of High-Frequency Variations of Fundamental Constants Using Spin-based Quantum Sensors
• Planck's Constant as a Dynamical Field & Path Integral
• A possible probe of the new fifth force
• Fundamental physical constants, operation of physical phenomena and entropy increase
• Cosmological Constraints on Radion Evolution in the Universal Extra Dimension Model
• New analysis of SNeIa Pantheon Catalog: Variable speed of light as an alternative to dark energy
• Search for Variations of Fundamental Constants
• The Primordial Helium Abundance
• A mechanism to generate varying speed of light via Higgs-dilaton coupling: Theory and cosmological applications
• Riemann Tensor of the Ambient Universe, the Dilaton and the Newton's Constant
• Late-time Cosmology without Dark Sector but with Closed String Massless Sector
• Accelerated expansion in a stochastic self-similar fractal Universe
• Discrete Cosmological Models in the Brans-Dicke Theory of Gravity
• Constraining Co-Varying Coupling Constants from Globular Cluster Age
• Planetary motion on an expanding locally anisotropic background
• Primordial He4 Abundance Constrains the Possible Time Variation of the Higgs Vacuum Expectation Value
• Time-varying Quark Masses and Cosmological Axion Energy
• Time variation of the fine structure constant in decrumpling or TVSD model
• On Maximal-Acceleration, Strings and the Group of Minimal Planck-Area Relativity Theory
• Self-acceleration in scalar-bimetric theories
• Low Duty Cycle Pulsed UV Technique for Spectroscopy of Aluminum Monochloride
• Gravitationally-Induced Quantum Superpopsition Reduction with Large Extra Dimensions
• On the Difference between Physics and Biology: Logical Branching and Biomolecules
• Several Action and Action Deformation Proposals in f(R) Variable G Modified Gravities and a Brief Expose on Variable G Ontology
• Unified presentation of four fundamental inequalities
• Brane Cosmology from Heterotic String Theory
• Dynamical dark energy from extra dimensions
• Confining Boundary conditions from dynamical Coupling Constants for Abelian and non Abelian symmetries
• A theory of evolving natural constants embracing Einstein's theory of general relativity and Dirac's large number hypothesis
• A Solar System Test of Mach's Principle with Gravimetric Data
• Measurement of the Electric Dipole Moment of AlCl by Stark Level Spectroscopy
• New constraints on the values of the fundamental constants at a look-back time of 7.3 Gyr
• CMB Constraint on Radion Evolution in the Brane World Scenario
• System parameters and measurement instrument parameters are not separately observable: Relational mass is observable while absolute mass is not
• Consistent gauge interaction involving dynamical coupling and anomalous current
• On Generalized Theories of Varying Fine Structure Constant
• Notes on the compatibility of type Ia supernovae data and varying--$G$ cosmology
• Lumpy cosmic strings
• Optimizing Pulsed-Laser Ablation Production of AlCl Molecules for Laser Cooling
• A model-independent test of speed of light variability with cosmological observations
• State-Relevant Maxwell's Equation from Kaluza-Klein Theory
• Gauge invariance and non-constant gauge couplings
• Engineering the sensitivity of macroscopic physical systems to variations in the fine-structure constant
• Very Light Cosmological Scalar Fields from a Tiny Cosmological Constant
• The motion of stars in galaxies and the gravitational time dilatation
• Investigating a Possible Variation of the Gravitational Constant Through Gas Mass Fraction Measurements and Type Ia Supernovae Observations
• Stable exponential cosmological solutions with three factor spaces of dimensions $m=3$, $k_1=k$ and $k_2=k$ in the Einstein-Gauss-Bonnet model with a $\Lambda$-term
• Non-Newtonian gravity in finite nuclei
• NuAncestor: an artificial satellite-borne star for accurate frequency calibration of ground-based EPRV spectrographs
• Analysing the Effect on CMB in a Parity and Charge Parity Violating Varying Alpha Theory
• Mach's Principle and a Variable Speed of Light
• Disentangling the Cosmic/Comoving Duality: The Cognitive Stability and Typicality Tests
• From primordial ${}^4$He abundance to the Higgs field
• Cosmological solutions of Tensor-Vector theories of gravity with varying the space-time-matter coupling constant