In a multi-fold universe, gravity emerges from Entanglement through the multi-fold mechanisms. As a result, gravity-like effects appear in between entangled particles that they be real or virtual. Long range, massless gravity results from entanglement of massless virtual particles. Entanglement of massive virtual particles leads to massive gravity contributions at very smalls scales. Multi-folds mechanisms also result into a spacetime that is discrete, with a random walk fractal structure and non-commutative geometry that is Lorentz invariant and where spacetime nodes and particles can be modeled with microscopic black holes. All these recover General relativity at large scales and semi-classical model remain valid till smaller scale than usually expected. Gravity can therefore be added to the Standard Model. This can contribute to resolving several open issues with the Standard Model without new Physics other than gravity. These considerations hints at a even stronger relationship between gravity and the Standard Model. Besides having multi-folds, and gravitons, living in AdS(5) tangent to the multi-fold universe spacetime, spacetime points and particles or field locally encounter additional 3D spatial dimensions due to the multi-folds used by paths of entangled particles. It provides an apparent local 7D manifold embedding the multi-fold universe spacetime. Modern unconstrained 5+D Kaluza-Klein (KK) empty (flat) space models, i.e. without compactification constraints of the additional spatial dimensions in 7D, allow the recovery from the 7D vacuum of gravity and electromagnetism as well as Yang Mills and the symmetries needed for strong and weak interactions. They also provide geometrical sources for masses, charges, wave functions, equations, quantum behavior and quantum vacuum. Unfortunately, limitations in terms of lack of chirality and chiral fermions, as well as apparition 5th or higher order forces, have tampered the enthusiasm just as what happened with earlier KK models. Within a multi-fold universe, we can recover chiral fermion and chiral symmetry breaking, due to gravity, of Electroweak and Strong interactions, while avoiding 5th (and more) forces, magnetic monopoles (because not relying on compactification), undue precessions, loss of conservation laws or supersymmetry. Such considerations do not work in conventional induced space-time-matter theories. In other words, the Standard Model seems to be induced purely from gravity and spacetime geometries in a multi-fold universe. Explanations for masses, charges and quantum behaviors (wave functions, equations QFT loops and of course entanglement and quantum gravity emerging from entanglement) can be hinted, albeit not (yet) quantified, in multi-fold universes. This is quite an achievement putting multi-fold mechanisms, themselves also physically clarified in terms of mapping, on par with, if not ahead of, other Quantum Gravity, GUTs and ToEs candidates of Unification of Physics. The analysis of 7D empty universes vs. AdS(5) both surrounding any spacetime points, in a multi-fold universe, also illustrates the implications of dualities and the differences between multi-fold universes with additional dimensions vs. the universe where superstrings, supersymmetry, supergravity and M-theory seem to live and matter [Truncated to <400 words by Admin]

/pdf/tracking-down-the-standard-model-with-gravity-in-multi-fold-okrreegjs8.pdf

Tracking Down the Standard Model with Gravity in Multi-Fold Universes

Recently, it has been shown that a four-dimensional (4D) Brans–Dicke (BD) theory with an effective matter field and a self-interacting potential can be achieved from the vacuum 5D BD field equations, where we refer to as a modified Brans–Dicke theory (MBDT). We investigate a generalized Bianchi type I anisotropic cosmology in 5D BD theory, and by employing the obtained formalism, we derive the induced matter on any 4D hypersurface in the context of the MBDT. We illustrate that if the usual spatial scale factors are functions of the time while the scale factor of extra dimension is constant, and the scalar field depends on the time and the fifth coordinate, then, in general, one will encounter inconsistencies in the field equations. Then, we assume that the scale factors and the scalar field depend on the time and the extra coordinate as separated variables in the power-law forms. Hence, we find a few classes of solutions in 5D spacetime through which we probe the one which leads to a generalized Kasner relation among the Kasner parameters. The induced scalar potential is found to be in the power law or in the logarithmic form; however, for a constant scalar field and even when the scalar field only depends on the fifth coordinate, it vanishes. The conservation law is indeed valid in this MBDT approach for the derived induced energy–momentum tensor (EMT). We proceed our investigations for a few cosmological quantities, where for simplicity we assume that the metric and the scalar field are functions of the time. Hence, the EMT satisfies the barotropic equation of state, and the model indicates that the constant mean Hubble parameter is not allowed. Thus, by appealing to the variation of the Hubble parameter, we assume a fixed deceleration parameter, and set the evolution of the quantities with respect to the fixed deceleration, the BD coupling and the state parameters. The WEC allows a shrinking extra dimension for a decelerating expanding universe that, in the constant scalar field, evolves the same way as the flat FRW spacetime in GR. The quantities for the stiff fluid and the radiation-dominated universe indicate an expanding universe commenced with a big bang. There is a horizon for each of the fluids, and the rate of expansion slows down by the time. The allowed ranges of the deceleration and the BD coupling parameters have been obtained, and the model gives an empty universe when the time goes to infinity.

http://iopscience.iop.org/article/10.1088/0264-9381/28/15/155004/pdf

An anisotropic cosmological model in a modified Brans–Dicke theory

We discuss how embeddings in connection with the Campbell–Magaard (CM) theorem can have a physical interpretation. We show that any embedding whose local existence is guaranteed by the CM theorem can be viewed as a result of the dynamical evolution of initial data given in a four-dimensional spacelike hypersurface. By using the CM theorem, we establish that for any analytical spacetime, there exist appropriate initial data whose Cauchy development is a five-dimensional vacuum space into which the spacetime is locally embedded. We shall see also that the spacetime embedded is Cauchy stable with respect to the initial data.

Dynamically generated embeddings of spacetime

The extension of the Campbell–Magaard embedding theorem to general relativity with minimally coupled scalar fields is formulated and proven The result is applied to the case of a self-interacting scalar field for which new embeddings are found, and to Brans–Dicke theory The relationship between the Campbell–Magaard theorem and the General Relativity Cauchy and initial value problems is outlined

Embeddings in space-times sourced by scalar fields

We revisit Weyl geometry in the context of recent higher-dimensional theories of space-time. After introducing the Weyl theory in a modern geometrical language we present some results that represent extensions of Riemannian theorems. We consider the theory of local embeddings and submanifolds in the context of Weyl geometries and show how a Riemannian space-time may be locally and isometrically embedded in a Weyl bulk. We discuss the problem of classical confinement and the stability of motion of particles and photons in the neighborhood of branes for the case when the Weyl bulk has the geometry of a warped product space. We show how the confinement and stability properties of geodesics near the brane may be affected by the Weyl field. We construct a classical analog of quantum confinement inspired in theoretical-field models by considering a Weyl scalar field which depends only on the extra coordinate.

On the embedding of space-time in five-dimensional Weyl spaces

We extend Campbell-Magaard embedding theorem by proving that any n-dimensional semi-Riemannian manifold can be locally embedded in an (n+1)-dimensional Einstein space. We work out some examples of application of the theorem and discuss its relevance in the context of modern higher-dimensional spacetime theories.

C. Romero

Papers

The embedding of the spacetime in five dimensions: an extension of Campbell-Magaard theorem