Thus in a uniform and constant field the velocity is a linear function of time. The expression obtained for v shows that the particle moves in the plane defined by the force vector F and the initial velocity vector v0. Let us take this as the xy plane, and the y axis in the ...
In the case of an arbitrary mass distribution, the gravitational force acting on a particle at a given point can be expressed as the product of the mass of the particle and the vector g, which is called the gravitational field strength at the given point. The larger the absolute value of...
According to linear perturbation theory, scalar, vector, and tensor modes do not interact. Now, let us calculate the gravitational waves generated by second-order gravitational interactions resulting from first-order curvature perturbations [71,72,73,74]. Using the Newtonian gauge, the perturbed ...
We replaced the original Gothic letters with their Latin counterparts and added the vector symbol. We changed the superscripts of the electric and magnetic versors into subscripts. The scalar product between \( \vec{k} \) and \( \vec{x} \) in the original paper was implied. In our trans...
Sensitivity down to gravitational strength forces accesses the natural scale7 for a wide class of cosmologically motivated scalar field models8,9 of modified gravity and dark energy. We improve the limits on two such models, chameleons9 and symmetrons10,11, by over two orders of magnitude. We ...
Expanding the action 104 to leading order in the field strength F and ignoring non-scalar couplings between the various sectors, the generic expression 104 reduces to eq. 47 which is general enough to discuss all the important physical feature of the holographic axion model. Self-consistency of ...
Additionally, the background of coupled vector ULDM particles can induce dark “electric” fields, which cause periodic displacements between the Earth and any given pulsar [196], [197]. Through these mechanisms, Afzal et al. [189] set stringent upper limits on the coupling constant between UL...
From the observations, quantities that can be modeled have been removed, so that an element of the vector is given by: where: and yp is the mean value of xk over the area involved in the prediction, so that the residual observations involved in the prediction are centered. Δgkt(SH)...
A comparison of lens-finding algorithms, including conventional methods (e.g., arc finders and visual inspection), and machine learning methods, such as support vector machines (SVM, e.g., Hartley et al. 2017) and convolutional neural networks (CNNs), was presented in the ‘strong ...
Due to the gauge freedom Au → Au+∇uθ and Pu → Pu+∇uθ , where θ = Avdv and θ = Pvdv, the only non-zero four-vector components are Au and Pu. They are functions of retarded and advanced time. The equation of motion for the phantom scalar field (2.4) in the chosen ...