Extra dimensions

In the present thesis we have found constraints on the fundamental Planck scale within extra dimensional models, by analyzing the torsion induced four-fermion interaction and the LHC data. Additionally, such an interaction induces corrections to the one-loop observables within the Standard Model (SM) of particle physics, which was used to obtain more stringent constraints on the fundamental Planck scale through the SM precision measurements. Further, it was argued that the Yukawa sector of the SM may arise from the condensation of a fourth family of heavy quarks, through the four-fermion interaction in gravity with torsion. This approach gives rise to a composite Higgs boson. Finally, we considered two different scenarios of torsion-descended axions and demonstrated that they are equivalent from the effective theory point of view. We studied the solution to the strong CP problem using such kind of torsion-descended axions and examined some of their cosmological implications.

The scale dimension discovered in the theory of infinite nesting of matter is studied from the perspective of physical implementation of well-studied four-and n-dimensional geometric objects. Adding the scale dimension to Minkowski four-dimensional space means the necessity to use the five-dimensional spacetime.

Consciousness is considered as a fundamental property of the universe in quantum theories of consciousness. We consider our physical universe as appeared by the phase-like transition of the energy waves, unfolded from 10 dimensions. The human brain and its mental aspects are associated with classical brain physiology and are also part of a quantum physical universe. We consider the whole universe being multi-dimensional, of (4 + D)-dimensional Friedmann-Robertson-Walker-type (FRW), with complex scale factor “R + i RI”, where “R” is the scale factor corresponding to the usual 4-dimensional universe, and “i RI” is that of D-dimensional space-time. It is found that for D = 6 (i.e. in 10 dimensions), the Wheeler-DeWitt equation is symmetric under the exchange RI ↔ R. Mathematically, when D = 6, it is RI = R and the physical universe starts. The universe starts with the symmetry breaking of group SU(11). We assume that the extra-dimensions “D” are associated with a mental-consciousness or that of the individual mind-consciousness is (partly) an expression of a universal mind-consciousness through holonomic communication with quantum fields. “Consciousness” is created by the electromagnetic force in the framework of SU(6) U(1), whereas “mind” is created by the framework of SU(2)  U(1). The human brain is conceived as an interfacing organ that not only produces mind and consciousness, but also receives information. The brain or parts of it are conceived as an “interference hologram” of incoming data and already existing ones (a “personal universe”), equivalent to the subject’s memory. If properly analyzed, information about the outer world can be distilled, with the analyzer being cerebral electrophysiology.

We investigate a point-like massive source in non-linear f(R) theories in the case of arbitrary number of spatial dimensions D\geq 3. If D>3 then extra dimensions undergo toroidal compactification. We consider a weak-field approximation with Minkowski and de Sitter background solutions. In both these cases point-like massive sources demonstrate good agreement with experimental data only in the case of ordinary three-dimensional (D=3) space. We generalize this result to the case of perfect fluid with dust-like equations of state in the external and internal spaces. This perfect fluid is uniformly smeared over all extra dimensions and enclosed in a three-dimensional sphere. In ordinary three dimensional (D=3) space, our formulas are useful for experimental constraints on parameters of f(R) models.

This article discusses the motion of particles in multiple time dimensions and in multiple space dimensions. Transformations are presented for the transfer from one inertial frame of reference to another inertial frame of reference for the case of multidimensional time. The implications are indicated of the existence of a large number of time dimensions on physical laws like the Lorentz covariance, CPT symmetry, the principle of invariance of the speed of light, the law of addition of velocities, the energy-momentum conservation law, etc. The Doppler effect is obtained for the case of multidimensional time. Relations are derived between energy, mass, and momentum of a particle and the number of time dimensions in which the particle is moving. The energy-momentum conservation law is formulated for the case of multidimensional time. It is proven that if certain conditions are met, then particles moving in multidimensional time are as stable as particles moving in one-dimensional time. This result differs from the view generally accepted until now [J. Dorling, Am. J. Phys. 38, 539 (1970)]. It is proven that luxons may have nonzero rest mass, but only provided that they move in multidimensional time. The causal structure of space-time is examined. It is shown that in multidimensional time, under certain circumstances, a particle can move in the causal region faster than the speed of light in vacuum. In the case of multidimensional time, the application of the proper orthochronous transformations at certain conditions leads to movement backwards in the time dimensions. It is concluded that the number of different antiparticles in the k-dimensional time is equal to 3^k − 2^k. Differences between tachyons and particles moving in multidimensional time are indicated. It is shown that particles moving faster than the speed of light in vacuum can have a real rest mass (unlike tachyons), provided that they move in multidimensional time.

We consider the ADM splitting of the Einstein-Hilbert action in five dimensions in the presence of matter that can be either a “point particle”, or a set of scalar fields. The Hamiltonian, being a linear superposition of constraints, is equal to zero. Upon quantization, we obtain the Schr¨odinger equation for a wave functional, $\Psi$, that depends on the matter degrees of freedom, and on the 5D gravity degrees of freedom. After the Kaluza-Klein splitting, the
functional Schr¨odinger equation decomposes so that it contains a part due to 4D gravity, a part due to electrodynamics, and a part due to matter. Depending on choice of the matter term, we obtain two different versions of a modified quantum electrodynamics. In one version, time automatically appears, and there is no problem with infinite vacuum energy density of matter fields, whereas in the other version such problems exist.

Mathematical physics relies foundationally on symbols, for expressing e.g. hypothetical relationships between various natural phenomena. Curiously, to date, both mathematical physics and science more generally have lacked an explicit symbolism for conscious experience. Consequently, physical theory has simply overlooked a number of acute problems with standard theories of the brain-experience relationship – as well as overlooking a number of problems and opportunities for physics itself, and for science-as-a-whole!
This paper remedies the notational gap in current physical theory, by defining a new symbol class for conscious experience. Of course, it could be that new symbols are trivial. But this paper refutes that possibility directly, uncovering new and fundamentally-interesting content in six experience-related topic-areas (emergence, experiments, evolution, spatiotemporal relationships, theories-of-everything, and the foundations of science). Ten specific puzzles are identified as future research directions.

It has long been expected that a consistent theory of quantum gravity will eventually unify gravitation with particle interactions. However, there is an alternative way – explaining all four types of interactions with vacuum geometry. The General Principle of Interaction (GPI) presents a philosophical concept that extends Einstein's understanding of the geometrically deformed vacuum (spacetime) in order to explain particle interactions. Surprisingly, this simple concept remained undeveloped to this day. If spacetime includes three separate " compartments " : 4D ordinary spacetime (OST), " electromagnetic space " (EMS) with one extra dimension and " nuclear space " (NS) with three extra dimensions, then each type of interaction is governed by spacetime geometrical alterations in one of these " compartments ". Consequently, any fundamental interacting field (gravitational, electromagnetic, or strong) is governed by geometrical deformations originating in one of the three spacetime " compartments " (OST, EMS or NS). The weak interaction should be understood as a type of electromagnetic interaction. Thus, a future GPI-based unified theory might be able to describe all four types of interaction with the " pure geometry " of 8D spacetime. The theory should be developed as a minimal extension of Einstein-Cartan theory taking into the account both metric and torsion tensors. It is expected that elementary particles will be described as quantized curvature/torsion wave-like vacuum deformations originating in the extra dimensions with certain secondary effects in 4D (mass, electromagnetic and strong fields). Unlike gravitation, the electromagnetic and strong fields cannot be described by a classical theory, as those fields originate in the extra dimensions, which are " unmeasurable ". Hence, it is likely that the new theory will adopt (to a certain extent) quantum field methodology while remaining background-independent and avoiding any virtual particles or gauge bosons and neutrinos. This concept not only promises full unification solely based on spacetime geometry but also drastically simplifies the descriptions of particle interactions by reducing the elementary particle set and the total number of interacting fields.

Why should the concept of Imperatively Hidden Elements (IHE) become common knowledge, especially in machine learning and feature selection? Did everyone, except for me, knew all along that our scientific progress-rate limiting bottlenecking factor is proper feature selection but not the lack of advances in improving our machine learning algorithms? I assumed that this could not be the case because most publications present improvements in machine learning algorithms, but neglect to even mention that lack of progress in better feature selection is preventing us from making any significant progress but not poorly performing machine learning algorithms. I thought that if I did not know that until my defense, then most others, especially those who don't know much about machine learning yet, i.e. most of our wet-lab biologists, who need to design their experiments accordingly, are not aware of this problem either. Then I thought I must tell them or else they keep mistakenly misinterpreting unpredictable outcomes as unavoidable noise instead of correctly realizing that still imperatively hidden elements (IHE) affect our predicted outcome in manner, which we cannot yet explain, unless we start observing the last temporal visible object/observation/event, after which we can no longer correctly predict the chain of subsequent events or observations, from many different perspectives and angles in order to really scrutinize it legitimacy, because most likely, it is composed of more than a single visible object (VO), of which we are already aware, because an undetermined number of distinctly different, but yet still imperatively hidden; thus inevitably for us still imperceptible, but nevertheless fully legitimate and truly existing yet invisible objects look too similar to our only visible object, which tricks us into the illusion of erroneously believing that it's only a single object. But the truth is that it is actually 2 or more objects, between which we cannot yet distinguish. Nevertheless, the number of possible outcomes depends on the number of truly existing objects, regardless whether or not we can distinguish them from their background. For example, until this morning, I was not aware of the difference between Python and Cython. Cython was for me in imperatively hidden object, which to me looked exactly like Python, because Cython is almost identical to Python, except for, that its variables must be of a specified type, e.g. string, vector, list, numeric, data frame, etc., which is not the case in Python. This led to my observation that some Python packages run fine on Windows whereas other never worked. Since the PyAffy.py library must have been written in Cython, it tricked me into the illusion that the only way to use a Python package, which fails to run under Windows, is to use Linux. It took us 3 months to set up a Linux laptop I could see. Now I discovered that we could have copied the Cython code and save it as a Python file by omitting specifying the variable type and run it just like a Python file. If we had used machine learning to discover the reason for some Python packages, specifically the PyAffy-package not running under Windows, could machine learning figure out that the feature " variable type selection " , which is a Boolean of present or absent, can be used to distinguish between Python and Cython? If we just gave the programming code of Python libraries and the outcome of running and not running as training data for supervised machine learning, could it figure out without any prior knowledge about Cython, that a programming language other than Python is causing problems under Windows? Can machine learning learn programming? Can it learn to conceptually understand the differences between variable types, If the concept of IHE is true, then most graduates are not well prepared to deal with imperatively hidden elements (IHE), because they appear to be totally left in the dark about this dangerously unnecessarily very time-consuming temporary progress-preventing nettlesome barrier, which can halt progress for many years, because nobody ever shared with them (i.e. our future wet-lab scientists, who must choose wisely, which data they collect for the computational analysts, to reach valid conclusions) the concept that the risk for misinterpreting poor outcome predictability as unavoidable background noise instead of getting alerted that a still imperatively hidden element (IHE), which we cannot perceive yet, creates a much bigger and more dangerous obstacle, than any visible element, which has at least one feature that causes it

In Kaluza-Klein models with an arbitrary number of toroidal internal spaces, we investigate soliton solutions which describe the gravitational field of a massive compact object. We single out the physically interesting solution corresponding to a point-like mass. For the general solution we obtain equations of state in the external and internal spaces. These equations demonstrate that the point-like mass soliton has dust-like equations of state in all spaces. We also obtain the PPN parameters, which give the possibility to obtain the formulas for perihelion shift, deflection of light and time delay of radar echoes. Additionally, the gravitational experiments lead to a strong restriction on the parameter of the model: τ = -(2.1± 2.3)× 10^-5. The point-like mass solution contradicts this restriction. The condition τ=0 satisfies the experimental limitation and defines a new class of solutions which are indistinguishable from general relativity. We call such solutions latent solitons. B...

In this article, I have studied the cosmoparticle constraints on a generic class of large field ($|\Delta\phi|>M_{p}$) and small field ($|\Delta\phi|<M_{p}$) models of brane inflationary
magnetogenesis {\it aka} ``braneflamagnetogenesis'' from: (1) tensor-to-scalar ratio ($r$), (2) reheating, (3) leptogenesis
and (4) baryogenesis in case of Randall-Sundrum single braneworld gravity (RSII) framework. I also establish
a direct connection between the magnetic field at the present epoch ($B_{0}$) and primordial gravity waves
($r$), which give a precise estimate of non-vanishing CP asymmetry ($\epsilon_{CP}$) in leptogenesis and baryon
asymmetry ($\eta_{B}$) in baryogenesis scenario respectively. Further assuming the conformal invariance to be restored
after inflation in the framework of RSII, I have explicitly shown that the requirement of the sub-dominant feature
of large scale coherent magnetic field after inflation gives two fold non-trivial characteristic
constraints- on equation of state parameter ($w$) and the corresponding energy scale during reheating ($\rho^{1/4}_{rh}$) epoch. Hence giving the proposal for avoiding the contribution
of back-reaction from the magnetic field I have established a bound on the generic reheating
characteristic parameter ($R_{rh}$) and its rescaled version ($R_{sc}$), to achieve large scale magnetic field within the prescribed setup and further apply the CMB constraints as obtained from recently observed Planck 2015 data and Planck+BICEP2+Keck Array joint constraints. Using all these
derived results I have shown that it is possible to put further stringent constraints on various classes of large and small field inflationary models to break the degeneracy between various cosmophenomenological parameters within the framework of RSII. Finally, I have studied the consequences from two specific models of brane inflation- monomial and hilltop, after applying all the constraints obtained from ``braneflamagnetogenesis''.

This  paper  presents  an  evaluation  of  the  discovery  potential  of  Supersymmetry  and  Universal
Extra Dimensions for channels with jets, leptons and missing transverse energy. The LHC running
scenario at a center-of-mass energy of 10 TeV, delivering an integrated luminosity of 200 pb-1, is
investigated. This paper focuses on the discovery reach, and provides references to more detailed
studies.

In this paper we study the role of the 5D Gauss-Bonnet corrections and two loop higher genus contribution to the gravity action in type IIB string theory inspired low energy supergravity theory in the light of gravidilatonic interactions on the lightest Kaluza-Klein graviton mass spectrum. From the latest constraints on the lightest Kaluza-Klein graviton mass as obtained from the ATLAS dilepton search in 7 TeV proton-proton collision, we have shown that due to the presence of Gauss-Bonnet and string loop corrections, the warping solution in an AdS_5 bulk is quite distinct from Randall-Sundrum scenario. We discuss the constraints on the model parameters to fit with present ATLAS data.

We propose a framework of modulus stabilization in two brane warped geometry scenario in presence of higher curvature gravity and dilaton in bulk space-time. In the prescribed setup we study various features of the stabilized potential for the modulus field, generated by a bulk scalar degrees of freedom with quartic interactions localized on the two 3-branes placed at the orbifold fixed points. We determine the parameter space for the gravidilaton and Gauss-Bonnet required to stabilize the modulus in such higher curvature dilaton gravity setup.

The scale dimension discovered in the theory of infinite nesting of matter is studied from the perspective of physical implementation of well-studied four-and n-dimensional geometric objects. Adding the scale dimension to Minkowski four-dimensional space means the necessity to use the five-dimensional spacetime.

In this paper we consider a multidimensional Kaluza-Klein (KK) model with a Ricci-flat internal space, e.g., a Calabi-Yau manifold. We perturb this background metrics by a system of gravitating masses, e.g., astrophysical objects such as our Sun. We suppose that these masses are pressureless in the external space but they have relativistic pressure in the internal space. We show that metric perturbations do not depend on coordinates of the internal space and gravitating masses should be uniformly smeared over the internal space. This means, first, that KK modes corresponding to the metric fluctuations are absent and, second, particles should be only in the ground quantum state with respect to the internal space. In our opinion, these results look very unnatural. According to statistical physics, any nonzero temperature should result in fluctuations, i.e. in KK modes. We also get formulae for the metric correction terms which enable to calculate the gravitational tests: the deflection of light, the time-delay of the radar echoes and the perihelion advance.

We put to the test an effective three-dimensional electrostatic potential, obtained effectively by considering an electrostatic source inside a (5+p)-dimensional braneworld scenario with p compact and one infinite spacial extra dimensions in the RS II-p model, for p=1 and p=2. This potential is regular at the source and matches the standard Coulomb potential outside a neighborhood. We use variational and perturbative approximation methods to calculate corrections to the ground energy of the Helium atom modified by this potential, by making use of a 6 and 39-parameter trial wave function of Hylleraas type for the ground state. These corrections to the ground-state energy are compared with experimental data for Helium atom in order to set bounds for the extra dimensions length scale. We find that these bounds are less restrictive than the ones obtained by Morales et. al. through a calculation using the Lamb shift in Hydrogen.

In this paper we argue the possibility that fermion masses, in particular quarks, originate through the condensation of a fourth family that interacts with all of the quarks via a contact four-fermion term coming from the existence of torsion on the spacetime. Extra dimensions are considered to avoid the hierarchy problem.

It is well known that inclusion of torsion in the gravitational formalism, leads to four-fermion interactions. Although the coupling constant of this interaction is strongly suppressed in four dimensions, its value is enhanced in models with n extra dimensions. In this context, we reinterpret the recent limits established by LHC experiments to four-fermion contact interactions, to set bounds on the size of the extra dimensions. For n = 2, the limits are comparable to those in the literature, while for n ≥ 3 the volume of the extra dimensions is strongly constrained.

We investigate the possibility of obtaining non-singular black-hole solutions in the brane world model by solving the effective field equations for the induced metric on the brane. The Reissner-Nordstrom solution on the brane was obtained by Dadhich etal by imposing the null energy condition on the 3-brane for a bulk having non zero Weyl curvature. In this work, we relax the condition of vanishing scalar curvature R, however, retaining the null condition. We have shown that it is possible to obtain class of static non-singular spherically symmetric brane space-times admitting horizon. We obtain one such class of solution which is a regular version of the Reissner-Nordstrom solution in the standard general relativity.

The minisuperspace model in 3+d spatial dimensions with matter described by the bag model is considered with the aim of estimating the probability of creation of compactified extra dimensions in nuclear collisions. The amplitude of transition from three- to (3+d)-dimensional space has been calculated both in the case of completely confined matter, when the contribution of radiation is ignored, and in the case of radiation domination, when the bag constant is negligible. It turns out that the number of additional dimensions is limited in the first regime, while it is infinite in the second one. It is shown that the probability of creation of extra dimensions is finite in the both regimes.

We study the possibility of testing some generic properties of Brane-World scenarios at the LHC. In particular, we pay attention to KK-graviton and branon production. Both signals can be dominant depending on the value of the brane tension. We analyze the differences between these two signatures. Finally, we use recent data in the single photon channel from the ATLAS collaboration to constraint the parameter space of both phenomenologies.

Following a recent approach, complete and analytic solutions (brane and bulk) of regular black holes are shown in a brane context. The metrics are regular both on the four-dimensional brane and in the five-dimensional bulk. Like many brane world scenarios, the bulk spacetime is asymptotically anti-de Sitter. On the other hand, a de Sitter core on the brane avoids the singularity inside the event horizon, providing then well-known regular black holes on the brane. From the bulk perspective, the regular black holes are five-dimensional objects, with the event horizon extending to the extra dimension, but the de Sitter core is entirely on the four-dimensional brane.

We investigate the consequences of one extra compactified dimension for the energy spectrum of the non-relativistic hydrogen atom with a potential defined by Gauss' law, i.e. proportional to 1/|x| 2 in non-compactified 4d space. The calculations were performed numerically by diagonalizing the Hamiltonian in two different sets of basis vectors. The energy levels and electron probability density are plotted as a function of the compactification radius. The occurrence of several physical effects is discussed and interpreted.

We propose a framework of modulus stabilization in two brane warpedgeometry scenario in presence of higher curvature gravity and dilaton in bulk space-time. In the prescribed setup we study various features of the stabilized potentialfor the modulus field, generated by a bulk scalar degrees of freedom with quarticinteractions localized on the two 3-branes placed at the orbifold fixed points. Wedetermine the parameter space for the gravidilaton and Gauss-Bonnet required tostabilize the modulus in such higher curvature dilaton gravity setup.

Fermion localization in a braneworld model in presence of dilaton coupled higher curvature Gauss-Bonnet bulk gravity is discussed. It is shown that the lowest mode of left handed fermions can be naturally localized on the visible brane due to the dilaton coupled higher curvature term without the necessity of any external localizing bulk field.