Constante gravitationnelle | EPFL Graph Search

En physique, la constante gravitationnelle, aussi connue comme la constante universelle de gravitation, notée , est la constante de proportionnalité de la loi universelle de la gravitation d'Isaac Newton. Cette constante physique fondamentale apparaît dans des lois de l'astronomie classique qui en découlent (gravité à la surface d'un corps céleste, troisième loi de Kepler), ainsi que dans la théorie de la relativité générale d'Albert Einstein. La constante est aussi connue comme : la constante de Newton en l'honneur d'Isaac Newton (-) car elle intervient dans l'expression de la loi que le savant britannique a proposée en ; la constante de Cavendish en l'honneur de Henry Cavendish (-) qui a réalisé, en , une expérience permettant d'estimer la valeur de la constante ; le grand G en raison de son symbole usuel . D'après Newton, la gravitation est une force d'attraction entre deux corps massifs qui, d'une part, est directement proportionnelle au produit de leur masse et, d'autre part, est inversement proportionnelle au carré de la distance qui sépare leur centre de masse respectif : L'analyse dimensionnelle permet de comparer la dimension d'une force : et la dimension de : où est la dimension d'une masse, celle d'une longueur et celle d'un temps. Les deux termes n'étant pas de même dimension, la relation de proportionnalité permet de définir un facteur de sorte que : Ce facteur est donc de dimension : Dans le système international d'unités, il s'exprime donc en . On distingue parfois les masses inertes des masses graves. Les masses reliées aux forces par l'équation fondamentale de la dynamique sont des masses inertes, les masses à l'origine du champ gravitationnel sont des masses graves. En physique classique, la loi de l'action et de la réaction implique que la force d'attraction est symétrique entre deux corps de masses respectives et , et donc que masse grave et masse inerte sont identiques. En mécanique relativiste, l'identité entre masse inerte et masse grave fait l'objet du principe d'équivalence.

Scale-Invariant Models of Gravity and Particle Physics and their Cosmological Implications

Daniel Zenhäusern

Currently, the best theoretical description of fundamental matter and its gravitational interaction is given by the Standard Model (SM) of particle physics and Einstein's theory of General Relativity (GR). These theories contain a number of seemingly unrelated scales. While Newton's gravitational constant and the mass of the Higgs boson are parameters in the classical action, the masses of other elementary particles are due to the electroweak symmetry breaking. Yet other scales, like ΛQCD associated to the strong interaction, only appear after the quantization of the theory. We reevaluate the idea that the fundamental theory of nature may contain no fixed scales and that all observed scales could have a common origin in the spontaneous break-down of exact scale invariance. To this end, we consider a few minimal scale-invariant extensions of GR and the SM, focusing especially on their cosmological phenomenology. In the simplest considered model, scale invariance is achieved through the introduction of a dilaton field. We find that for a large class of potentials, scale invariance is spontaneously broken, leading to induced scales at the classical level. The dilaton is exactly massless and practically decouples from all SM fields. The dynamical break-down of scale invariance automatically provides a mechanism for inflation. Despite exact scale invariance, the theory generally contains a cosmological constant, or, put in other words, flat spacetime need not be a solution. We next replace standard gravity by Unimodular Gravity (UG). This results in the appearance of an arbitrary integration constant in the equations of motion, inducing a run-away potential for the dilaton. As a consequence, the dilaton can play the role of a dynamical dark-energy component. The cosmological phenomenology of the model combining scale invariance and unimodular gravity is studied in detail. We find that the equation of state of the dilaton condensate has to be very close to the one of a cosmological constant. If the spacetime symmetry group of the gravitational action is reduced from the group of all diffeomorphisms (Diff) to the subgroup of transverse diffeomorphisms (TDiff), the metric in general contains a propagating scalar degree of freedom. We show that the replacement of Diff by TDiff makes it possible to construct a scale-invariant theory of gravity and particle physics in which the dilaton appears as a part of the metric. We find the conditions under which such a theory is a viable description of particle physics and in particular reproduces the SM phenomenology. The minimal theory with scale invariance and UG is found to be a particular case of a theory with scale and TDiff invariance. Moreover, cosmological solutions in models based on scale and TDiff invariance turn out to generically be similar to the solutions of the model with UG. In usual quantum field theories, scale invariance is anomalous. This might suggest that results based on classical scale invariance are necessarily spoiled by quantum corrections. We show that this conclusion is not true. Namely, we propose a new renormalization scheme which allows to construct a class of quantum field theories that are scale-invariant to all orders of perturbation theory and where the scale symmetry is spontaneously broken. In this type of theory, all scales, including those related to dimensional transmutation, like ΛQCD, appear as a consequence of the spontaneous break-down of the scale symmetry. The proposed theories are not renormalizable. Nonetheless, they are valid effective theories below a field-dependent cut-off scale. If the scale-invariant renormalization scheme is applied to the presented minimal scale-invariant extensions of GR and the SM, the goal of having a common origin of all scales, spontaneous breaking of scale invariance, is achieved.

EPFL2011

Scale-Invariant Models of Gravity and Particle Physics and their Cosmological Implications

Daniel Zenhäusern

EPFL2011