Advances in atomic physics, such as cooling and trapping of atoms and molecules and developments in frequency metrology, have added orders of magnitude to the precision of atom-based clocks and sensors. Applications extend beyond atomic physics and this article reviews using these new techniques to address important challenges in physics and to look for variations in the fundamental constants, search for interactions beyond the standard model of particle physics, and test the principles of general relativity.

Search for New Physics with Atoms and Molecules

Over recent decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f (T) gravity, where f (T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f (T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f (T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, alternative to a cosmological constant, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, for a certain class of f (T) models, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations-or, alternatively, the Big Bang singularity can be avoided at even earlier moments due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f (T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f (T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f (R) gravity, trying to illuminate the subject of which formulation, or combination of formulations, might be more suitable for quantization ventures and cosmological applications.

f(T) teleparallel gravity and cosmology

Over the past decades, the role of torsion in gravity has been extensively investigated along the main direction of bringing gravity closer to its gauge formulation and incorporating spin in a geometric description. Here we review various torsional constructions, from teleparallel, to Einstein-Cartan, and metric-affine gauge theories, resulting in extending torsional gravity in the paradigm of f(T) gravity, where f(T) is an arbitrary function of the torsion scalar. Based on this theory, we further review the corresponding cosmological and astrophysical applications. In particular, we study cosmological solutions arising from f(T) gravity, both at the background and perturbation levels, in different eras along the cosmic expansion. The f(T) gravity construction can provide a theoretical interpretation of the late-time universe acceleration, and it can easily accommodate with the regular thermal expanding history including the radiation and cold dark matter dominated phases. Furthermore, if one traces back to very early times, a sufficiently long period of inflation can be achieved and hence can be investigated by cosmic microwave background observations, or alternatively, the Big Bang singularity can be avoided due to the appearance of non-singular bounces. Various observational constraints, especially the bounds coming from the large-scale structure data in the case of f(T) cosmology, as well as the behavior of gravitational waves, are described in detail. Moreover, the spherically symmetric and black hole solutions of the theory are reviewed. Additionally, we discuss various extensions of the f(T) paradigm. Finally, we consider the relation with other modified gravitational theories, such as those based on curvature, like f(R) gravity, trying to enlighten the subject of which formulation might be more suitable for quantization ventures and cosmological applications.

Physical aspects of the space-time torsion

Torsion balance experiments: A low-energy frontier of particle physics

Known data are used to place an upper bound on new coupling constants that arise in gravitation with torsion that is derived as the exterior derivative of a potential. The form of the quantum-mechanical interaction is deduced from the classical theory and verified by the nonrelativistic reduction of the Dirac equation. Both minimal and nonminimal coupling is considered. \textcopyright{} 1995 The American Physical Society.

Upper limit on the torsion coupling constant.

A theory of gravitation with torsion that is derived from a potential is developed. An explicit material action is presented that gives rise to the correct conservation laws and equations of motion. It is shown that the Noether identities yield the same conservation laws as the Bianchi identities, and the Papapetrou method is used to develop the propagation equations and the force law. The equations are put in the nonrelativistic limit and the 3-vector formulation is displayed.

Spin, torsion, forces

The problem of radiation reaction and the self force is the oldest unsolved mystery in physics. At times it is considered a minor issue, a malefactor born of classical electrodynamics, while at other times it is public enemy number one, a major inconsistency and unsolved problem. This work derives some of the basic and most important results while reviewing some of the other known approaches to the problem. Some historical notes are given, and yet another approach is discussed that accounts for radiation reaction without the unphysical behavior that plagues so many theories. c

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Relativistic Particle Motion and Radiation Reaction in Electrodynamics

Intensities of ${10}^{22}$ W ${\mathrm{cm}}^{\ensuremath{-}2}$ have been reached and it is expected that this will be increased by two orders of magnitude in the near future. At these intensities the radiation reaction force is important, especially in calculating the terminal velocity of an electron. The following briefly describes some of the problems of the existing most well-known equations and describes an approach based on conservation of energy. The resulting equation is compared to the Landau Lifshitz and Ford O'Connell equations, and laboratory tests are proposed.

Radiation reaction at ultrahigh intensities

A term bilinear in the derivative of the torsion is added to the Lagrangian of general relativity to produce torsion that propagates. Using standard variational techniques, field equations are derived with the torsion being interpreted as the electromagnetic potential and the antisymmetric part of the Ricci tensor as the electromagnetic field tensor. The equation of motion is derived from the field equations, and the results are compared to the Einstein-Maxwell formulation.

Richard T. Hammond

Papers

Upper limit on the torsion coupling constant.

Spin, torsion, forces

Relativistic Particle Motion and Radiation Reaction in Electrodynamics

Radiation reaction at ultrahigh intensities

Gravitation, torsion, and electromagnetism