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Loop Quantum Cosmology, Modified Gravity and Extra Dimensions
universe Review Loop Quantum Cosmology, Modified Gravity and Extra Dimensions Xiangdong Zhang Department of Physics, South China University of Technology, Guangzhou 510641, China; [email protected] Academic Editor: Jaume Haro Received: 24 May 2016; Accepted: 2 August 2016; Published: 10 August 2016 Abstract: Loop quantum cosmology (LQC) is a framework of quantum cosmology based on the quantization of symmetry reduced models following the quantization techniques of loop quantum gravity (LQG). This paper is devoted to reviewing LQC as well as its various extensions including modified gravity and higher dimensions. For simplicity considerations, we mainly focus on the effective theory, which captures main quantum corrections at the cosmological level. We set up the basic structure of Brans–Dicke (BD) and higher dimensional LQC. The effective dynamical equations of these theories are also obtained, which lay a foundation for the future phenomenological investigations to probe possible quantum gravity effects in cosmology. Some outlooks and future extensions are also discussed. Keywords: loop quantum cosmology; singularity resolution; effective equation 1. Introduction Loop quantum gravity (LQG) is a quantum gravity scheme that tries to quantize general relativity (GR) with the nonperturbative techniques consistently [1–4]. Many issues of LQG have been carried out in the past thirty years. In particular, among these issues, loop quantum cosmology (LQC), which is the cosmological sector of LQG has received increasing interest and has become one of the most thriving and fruitful directions of LQG [5–9]. It is well known that GR suffers singularity problems and this, in turn, implies that our universe also has an infinitely dense singularity point that is highly unphysical. -
Quantum Vacuum Energy Density and Unifying Perspectives Between Gravity and Quantum Behaviour of Matter
Annales de la Fondation Louis de Broglie, Volume 42, numéro 2, 2017 251 Quantum vacuum energy density and unifying perspectives between gravity and quantum behaviour of matter Davide Fiscalettia, Amrit Sorlib aSpaceLife Institute, S. Lorenzo in Campo (PU), Italy corresponding author, email: [email protected] bSpaceLife Institute, S. Lorenzo in Campo (PU), Italy Foundations of Physics Institute, Idrija, Slovenia email: [email protected] ABSTRACT. A model of a three-dimensional quantum vacuum based on Planck energy density as a universal property of a granular space is suggested. This model introduces the possibility to interpret gravity and the quantum behaviour of matter as two different aspects of the same origin. The change of the quantum vacuum energy density can be considered as the fundamental medium which determines a bridge between gravity and the quantum behaviour, leading to new interest- ing perspectives about the problem of unifying gravity with quantum theory. PACS numbers: 04. ; 04.20-q ; 04.50.Kd ; 04.60.-m. Key words: general relativity, three-dimensional space, quantum vac- uum energy density, quantum mechanics, generalized Klein-Gordon equation for the quantum vacuum energy density, generalized Dirac equation for the quantum vacuum energy density. 1 Introduction The standard interpretation of phenomena in gravitational fields is in terms of a fundamentally curved space-time. However, this approach leads to well known problems if one aims to find a unifying picture which takes into account some basic aspects of the quantum theory. For this reason, several authors advocated different ways in order to treat gravitational interaction, in which the space-time manifold can be considered as an emergence of the deepest processes situated at the fundamental level of quantum gravity. -
Aspects of Loop Quantum Gravity
Aspects of loop quantum gravity Alexander Nagen 23 September 2020 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London 1 Contents 1 Introduction 4 2 Classical theory 12 2.1 The ADM / initial-value formulation of GR . 12 2.2 Hamiltonian GR . 14 2.3 Ashtekar variables . 18 2.4 Reality conditions . 22 3 Quantisation 23 3.1 Holonomies . 23 3.2 The connection representation . 25 3.3 The loop representation . 25 3.4 Constraints and Hilbert spaces in canonical quantisation . 27 3.4.1 The kinematical Hilbert space . 27 3.4.2 Imposing the Gauss constraint . 29 3.4.3 Imposing the diffeomorphism constraint . 29 3.4.4 Imposing the Hamiltonian constraint . 31 3.4.5 The master constraint . 32 4 Aspects of canonical loop quantum gravity 35 4.1 Properties of spin networks . 35 4.2 The area operator . 36 4.3 The volume operator . 43 2 4.4 Geometry in loop quantum gravity . 46 5 Spin foams 48 5.1 The nature and origin of spin foams . 48 5.2 Spin foam models . 49 5.3 The BF model . 50 5.4 The Barrett-Crane model . 53 5.5 The EPRL model . 57 5.6 The spin foam - GFT correspondence . 59 6 Applications to black holes 61 6.1 Black hole entropy . 61 6.2 Hawking radiation . 65 7 Current topics 69 7.1 Fractal horizons . 69 7.2 Quantum-corrected black hole . 70 7.3 A model for Hawking radiation . 73 7.4 Effective spin-foam models . -
The Large Hadron Collider Lyndon Evans CERN – European Organization for Nuclear Research, Geneva, Switzerland
34th SLAC Summer Institute On Particle Physics (SSI 2006), July 17-28, 2006 The Large Hadron Collider Lyndon Evans CERN – European Organization for Nuclear Research, Geneva, Switzerland 1. INTRODUCTION The Large Hadron Collider (LHC) at CERN is now in its final installation and commissioning phase. It is a two-ring superconducting proton-proton collider housed in the 27 km tunnel previously constructed for the Large Electron Positron collider (LEP). It is designed to provide proton-proton collisions with unprecedented luminosity (1034cm-2.s-1) and a centre-of-mass energy of 14 TeV for the study of rare events such as the production of the Higgs particle if it exists. In order to reach the required energy in the existing tunnel, the dipoles must operate at 1.9 K in superfluid helium. In addition to p-p operation, the LHC will be able to collide heavy nuclei (Pb-Pb) with a centre-of-mass energy of 1150 TeV (2.76 TeV/u and 7 TeV per charge). By modifying the existing obsolete antiproton ring (LEAR) into an ion accumulator (LEIR) in which electron cooling is applied, the luminosity can reach 1027cm-2.s-1. The LHC presents many innovative features and a number of challenges which push the art of safely manipulating intense proton beams to extreme limits. The beams are injected into the LHC from the existing Super Proton Synchrotron (SPS) at an energy of 450 GeV. After the two rings are filled, the machine is ramped to its nominal energy of 7 TeV over about 28 minutes. In order to reach this energy, the dipole field must reach the unprecedented level for accelerator magnets of 8.3 T. -
Introduction to Loop Quantum Gravity
Introduction to Loop Quantum Gravity Abhay Ashtekar Institute for Gravitation and the Cosmos, Penn State A broad perspective on the challenges, structure and successes of loop quantum gravity. Addressed to Young Researchers: From Beginning Students to Senior Post-docs. Organization: 1. Historical & Conceptual Setting 2. Structure of Loop Quantum Gravity 3. Outlook: Challenges and Opportunities – p. 1. Historical and Conceptual Setting Einstein’s resistance to accept quantum mechanics as a fundamental theory is well known. However, he had a deep respect for quantum mechanics and was the first to raise the problem of unifying general relativity with quantum theory. “Nevertheless, due to the inner-atomic movement of electrons, atoms would have to radiate not only electro-magnetic but also gravitational energy, if only in tiny amounts. As this is hardly true in Nature, it appears that quantum theory would have to modify not only Maxwellian electrodynamics, but also the new theory of gravitation.” (Albert Einstein, Preussische Akademie Sitzungsberichte, 1916) – p. • Physics has advanced tremendously in the last 90 years but the the problem of unification of general relativity and quantum physics still open. Why? ⋆ No experimental data with direct ramifications on the quantum nature of Gravity. – p. • Physics has advanced tremendously in the last nine decades but the the problem of unification of general relativity and quantum physics is still open. Why? ⋆ No experimental data with direct ramifications on the quantum nature of Gravity. ⋆ But then this should be a theorist’s haven! Why isn’t there a plethora of theories? – p. ⋆ No experimental data with direct ramifications on quantum Gravity. -
Anomalous Muon Magnetic Moment, Supersymmetry, Naturalness, LHC Search Limits and the Landscape
OU-HEP-210415 Anomalous muon magnetic moment, supersymmetry, naturalness, LHC search limits and the landscape Howard Baer1∗, Vernon Barger2†, Hasan Serce1‡ 1Homer L. Dodge Department of Physics and Astronomy, University of Oklahoma, Norman, OK 73019, USA 2Department of Physics, University of Wisconsin, Madison, WI 53706 USA Abstract The recent measurement of the muon anomalous magnetic moment aµ ≡ (g − 2)µ=2 by the Fermilab Muon g − 2 experiment sharpens an earlier discrepancy between theory and the BNL E821 experiment. We examine the predicted ∆aµ ≡ aµ(exp) − aµ(th) in the context of supersymmetry with low electroweak naturalness (restricting to models which give a plausible explanation for the magnitude of the weak scale). A global analy- sis including LHC Higgs mass and sparticle search limits points to interpretation within the normal scalar mass hierarchy (NSMH) SUSY model wherein first/second generation matter scalars are much lighter than third generation scalars. We present a benchmark model for a viable NSMH point which is natural, obeys LHC Higgs and sparticle mass constraints and explains the muon magnetic anomaly. Aside from NSMH models, then we find the (g − 2)µ anomaly cannot be explained within the context of natural SUSY, where a variety of data point to decoupled first/second generation scalars. The situation is worse within the string landscape where first/second generation matter scalars are pulled arXiv:2104.07597v2 [hep-ph] 16 May 2021 to values in the 10 − 50 TeV range. An alternative interpretation for SUSY models with decoupled scalar masses is that perhaps the recent lattice evaluation of the hadronic vac- uum polarization could be confirmed which leads to a Standard Model theory-experiment agreement in which case there is no anomaly. -
Loop Quantum Gravity Alejandro Perez, Centre De Physique Théorique and Université Aix-Marseille II • Campus De Luminy, Case 907 • 13288 Marseille • France
features Loop quantum gravity Alejandro Perez, Centre de Physique Théorique and Université Aix-Marseille II • Campus de Luminy, case 907 • 13288 Marseille • France. he revolution brought by Einstein’s theory of gravity lies more the notion of particle, Fourier modes, vacuum, Poincaré invariance Tin the discovery of the principle of general covariance than in are essential tools that can only be constructed on a given space- the form of the dynamical equations of general relativity. General time geometry.This is a strong limitation when it comes to quantum covariance brings the relational character of nature into our descrip- gravity since the very notion of space-time geometry is most likely tion of physics as an essential ingredient for the understanding of not defined in the deep quantum regime. Secondly, quantum field the gravitational force. In general relativity the gravitational field is theory is plagued by singularities too (UV divergences) coming encoded in the dynamical geometry of space-time, implying a from the contribution of arbitrary high energy quantum processes. strong form of universality that precludes the existence of any non- This limitation of standard QFT’s is expected to disappear once the dynamical reference system—or non-dynamical background—on quantum fluctuations of the gravitational field, involving the dynam- top of which things occur. This leaves no room for the old view ical treatment of spacetime geometry, are appropriately taken into where fields evolve on a rigid preestablished space-time geometry account. But because of its intrinsically background dependent (e.g. Minkowski space-time): to understand gravity one must definition, standard QFT cannot be used to shed light on this issue. -
MIT at the Large Hadron Collider—Illuminating the High-Energy Frontier
Mit at the large hadron collider—Illuminating the high-energy frontier 40 ) roland | klute mit physics annual 2010 gunther roland and Markus Klute ver the last few decades, teams of physicists and engineers O all over the globe have worked on the components for one of the most complex machines ever built: the Large Hadron Collider (LHC) at the CERN laboratory in Geneva, Switzerland. Collaborations of thousands of scientists have assembled the giant particle detectors used to examine collisions of protons and nuclei at energies never before achieved in a labo- ratory. After initial tests proved successful in late 2009, the LHC physics program was launched in March 2010. Now the race is on to fulfill the LHC’s paradoxical mission: to complete the Stan- dard Model of particle physics by detecting its last missing piece, the Higgs boson, and to discover the building blocks of a more complete theory of nature to finally replace the Standard Model. The MIT team working on the Compact Muon Solenoid (CMS) experiment at the LHC stands at the forefront of this new era of particle and nuclear physics. The High Energy Frontier Our current understanding of the fundamental interactions of nature is encap- sulated in the Standard Model of particle physics. In this theory, the multitude of subatomic particles is explained in terms of just two kinds of basic building blocks: quarks, which form protons and neutrons, and leptons, including the electron and its heavier cousins. From the three basic interactions described by the Standard Model—the strong, electroweak and gravitational forces—arise much of our understanding of the world around us, from the formation of matter in the early universe, to the energy production in the Sun, and the stability of atoms and mit physics annual 2010 roland | klute ( 41 figure 1 A photograph of the interior, central molecules. -
An Introduction to Loop Quantum Gravity with Application to Cosmology
DEPARTMENT OF PHYSICS IMPERIAL COLLEGE LONDON MSC DISSERTATION An Introduction to Loop Quantum Gravity with Application to Cosmology Author: Supervisor: Wan Mohamad Husni Wan Mokhtar Prof. Jo~ao Magueijo September 2014 Submitted in partial fulfilment of the requirements for the degree of Master of Science of Imperial College London Abstract The development of a quantum theory of gravity has been ongoing in the theoretical physics community for about 80 years, yet it remains unsolved. In this dissertation, we review the loop quantum gravity approach and its application to cosmology, better known as loop quantum cosmology. In particular, we present the background formalism of the full theory together with its main result, namely the discreteness of space on the Planck scale. For its application to cosmology, we focus on the homogeneous isotropic universe with free massless scalar field. We present the kinematical structure and the features it shares with the full theory. Also, we review the way in which classical Big Bang singularity is avoided in this model. Specifically, the spectrum of the operator corresponding to the classical inverse scale factor is bounded from above, the quantum evolution is governed by a difference rather than a differential equation and the Big Bang is replaced by a Big Bounce. i Acknowledgement In the name of Allah, the Most Gracious, the Most Merciful. All praise be to Allah for giving me the opportunity to pursue my study of the fundamentals of nature. In particular, I am very grateful for the opportunity to explore loop quantum gravity and its application to cosmology for my MSc dissertation. -
Accelerators and Beams
Accelerators AND Beams TOOLS Of DiSCOVERy anD innOVATION 4th Edition Published by the Division of Physics of Beams of the American Physical Society Accelerators AND Beams Introduction Why care about accelerators? .................................. 1 What are accelerators for? ..................................... 2 What is an accelerator? ........................................ 3 The invention of particle accelerators. ........................... 4 How accelerators work ......................................... 6 Applications of accelerators .................................... 8 Advancing the frontiers of knowledge ........................... 9 Accelerators for diagnosing illness and fighting cancer ............ 10 Accelerators to beat food-borne illness ......................... 11 An accelerator makes our band-aids safe ........................ 12 Accelerators and national security .............................. 13 Accelerators validate nuclear weapons readiness ................ 14 Beams of light from beams of particles .......................... 15 Accelerators energize a new kind of laser ........................ 18 Free-electron laser applications ................................. 19 Accelerators for improving materials’ surfaces ................... 20 Accelerator-based neutron science yields payoffs ................ 21 Multiple uses for portable accelerators ......................... 22 Accelerators boost international cooperation .................... 23 Why is an accelerator under the Louvre museum? ................ 24 Accelerators -
Emergence of Time in Loop Quantum Gravity∗
Emergence of time in Loop Quantum Gravity∗ Suddhasattwa Brahma,1y 1 Center for Field Theory and Particle Physics, Fudan University, 200433 Shanghai, China Abstract Loop quantum gravity has formalized a robust scheme in resolving classical singu- larities in a variety of symmetry-reduced models of gravity. In this essay, we demon- strate that the same quantum correction which is crucial for singularity resolution is also responsible for the phenomenon of signature change in these models, whereby one effectively transitions from a `fuzzy' Euclidean space to a Lorentzian space-time in deep quantum regimes. As long as one uses a quantization scheme which re- spects covariance, holonomy corrections from loop quantum gravity generically leads to non-singular signature change, thereby giving an emergent notion of time in the theory. Robustness of this mechanism is established by comparison across large class of midisuperspace models and allowing for diverse quantization ambiguities. Con- ceptual and mathematical consequences of such an underlying quantum-deformed space-time are briefly discussed. 1 Introduction It is not difficult to imagine a mind to which the sequence of things happens not in space but only in time like the sequence of notes in music. For such a mind such conception of reality is akin to the musical reality in which Pythagorean geometry can have no meaning. | Tagore to Einstein, 1920. We are yet to come up with a formal theory of quantum gravity which is mathematically consistent and allows us to draw phenomenological predictions from it. Yet, there are widespread beliefs among physicists working in fundamental theory regarding some aspects of such a theory, once realized. -
Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara Min [email protected]
Supersymmetry Min Raj Lamsal Department of Physics, Prithvi Narayan Campus, Pokhara [email protected] Abstract : This article deals with the introduction of supersymmetry as the latest and most emerging burning issue for the explanation of nature including elementary particles as well as the universe. Supersymmetry is a conjectured symmetry of space and time. It has been a very popular idea among theoretical physicists. It is nearly an article of faith among elementary-particle physicists that the four fundamental physical forces in nature ultimately derive from a single force. For years scientists have tried to construct a Grand Unified Theory showing this basic unity. Physicists have already unified the electron-magnetic and weak forces in an 'electroweak' theory, and recent work has focused on trying to include the strong force. Gravity is much harder to handle, but work continues on that, as well. In the world of everyday experience, the strengths of the forces are very different, leading physicists to conclude that their convergence could occur only at very high energies, such as those existing in the earliest moments of the universe, just after the Big Bang. Keywords: standard model, grand unified theories, theory of everything, superpartner, higgs boson, neutrino oscillation. 1. INTRODUCTION unifies the weak and electromagnetic forces. The What is the world made of? What are the most basic idea is that the mass difference between photons fundamental constituents of matter? We still do not having zero mass and the weak bosons makes the have anything that could be a final answer, but we electromagnetic and weak interactions behave quite have come a long way.