DOCSLIB.ORG

Cosmological Evolution of a Tachyon-Quintom Model of Dark

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Cosmological Evolution of a Tachyon-Quintom Model of Dark Cosmological Evolution of a Tachyon-Quintom Model of Dark Energy Shang-Gang Shi1, Yun-Song Piao1 and Cong-Feng Qiao1,2 1College of Physical Sciences,Graduate University of CAS, YuQuan Road 19A, Beijing 100049, China 2Theoretical Physics Center for Science Facilities (TPCSF), CAS., Beijing 100049, China Abstract In this work we study the cosmological evolution of a dark energy model with two scalar fields, i.e. the tachyon and the phantom tachyon. This model enables the equation of state w to change from w > 1 to w < 1 in the evolution of the universe. The phase-space − − analysis for such a system with inverse square potentials shows that there exists a unique stable critical point, which has power-law solutions. In this paper, we also study another form of tachyon-quintom model with two fields, which voluntarily involves the interactions between both fields. arXiv:0812.4022v2 [astro-ph] 7 Mar 2009 1 I. INTRODUCTION Recent observational data [1, 2, 3] strongly indicate that the Universe is spatially flat and accelerating at the present time. Within the framework of general relativity, cosmic acceleration can be sourced by an energy-momentum tensor which has a large negative pressure called dark energy (See Ref. [4] for a recent review). The simplest candidate for dark energy seems to be a small positive cosmological constant, but it suffers from difficulties associated with the fine tuning and coincidence problem. This problem can be alleviated in models of dynamically evolving dark energy called quintessence [5], which have tracker like properties where the energy density in the fields track those of the background energy density before dominating today. The phantom, whose kinetic energy term has the reverse sign, has been also proposed as a candidate of dynamical dark energy [6]. There has been the enormous variety of DE models suggested in the literature, see Ref. [7] for reviews. The analysis of the properties of dark energy from recent observations mildly favor models with ω crossing 1 in the near past [8, 9]. But, neither quintessence nor phantom can fulfill − this transition. The quintom scenario of dark energy is designed to understand the nature of dark energy with ω across 1. The first model of quintom scenario of dark energy is given − in Ref. [9] with two scalar fields, where one is quintessence and the other is phantom. This model has been studied in detail later on [10, 11, 12, 13, 14, 15], and recently a new type of quintom model inspired by the string theory has also been proposed, which only have a single scalar field [16]. The role of the rolling tachyon [17] in string theory has been widely studied in cos- mology, see Refs.[18, 19], and especially Refs.[20, 21, 22, 23] for dark energy. Some sort of tachyon condensate may described by effective field theory with a Lagrangian density = V (φ) 1+ gµν∂ φ∂ φ. It can act as a source of dark matter or inflation field. Mean- L − µ ν while the tachyonp can also act as a source of dark energy depending upon the form of the tachyon potential. However, as compared to canonical quintessence, tachyon models require more fine-tuning to agree with observations. In Ref. [24], the authors consider the Born- Infeld type Lagrangian with negative kinetic energy term. The Lagrangian density they choose is = V (ϕ) 1 gµν∂ ϕ∂ ϕ. It is clear that for the spatially homogeneous scalar L − − µ ν field, the equation ofp state ω = 1 ϕ˙ 2 will be less than 1 unless the kinetic energy term − − − ϕ˙ 2 = 0. This field is called phantom tachyon, see for example [25]. In principle, we can consider the multi-fields model including multiple tachyon and mul- tiple phantom tachyon. However, without loss of generality, we only consider the case of one tachyon and one phantom tachyon, since it is the simplest one to realize that the equation of state w cross 1 during the evolution of the universe and it shows most of the central ideas − of such model. Because of the quintom-like behavior it shows, we call it tachyon-quintom for the convenience. This paper is organized as follows: in section II we study in detail the tachyon-quintom model with inverse square potentials. The numerical analysis shows this model is not sensitive to the initial kinetic energy density of tachyon and phantom tachyon, and we give the reason in detail. Then the phase-space analysis of the spatially flat FRW models shows that there exist a unique stable critical point, and we compare it 2 with tachyon model; in section III we present another two-field model which include the interaction between two fields; the section IV is summary. II. THE TACHYON-QUINTOM MODEL A. The tachyon-quintom model We assume a four-dimensional, spatially-flat Friedmann-Robertson-Walker Universe filled by a homogeneous tachyon φ with potential V (φ), a homogeneous phantom tachyon ϕ with potential V (ϕ) and a fluid with barotropic equation of state p =(γ 1)ρ ,0 <γ 2, such γ − γ ≤ as radiation (γ =4/3)or dust matter (γ = 1). In this section, we turn our attention to the possibility of the tachyon and phantom tachyon as a source of the dark energy. The action for such a system is given by 2 4 Mp S = d x√ g R + φ + ϕ + m (1) Z − 2 L L L where M is the reduced Planck mass, is the scalar curvature, represents the p R Lm Lagrangian density of matter fields and = V (φ) 1+ gµν∂ φ∂ φ (2) Lφ − µ ν p = V (ϕ) 1 gµν∂ ϕ∂ ϕ. (3) Lϕ − − µ ν p We now restrict to spatially homogeneous time dependent solutions for which ∂iφ = ∂iϕ = 0. Thus the energy densities and the pressure of the field φ and ϕ are given, respectively, by V (φ) ρ = , p = V (φ) 1 φ˙2, (4) φ φ − − 1 φ˙2 q q − V (ϕ) 2 ρϕ = , pϕ = V (ϕ) 1 +ϕ ˙ (5) 2 1 +ϕ ˙ − p p Here a dot is derivation with respect to synchronous time. The background equations of motion are φ¨ 1 dV (φ) +3Hφ˙ + =0 (6) 1 φ˙2 V (φ) dφ − ϕ¨ 1 dV (ϕ) +3Hϕ˙ =0 (7) 1 +ϕ ˙ 2 − V (ϕ) dϕ ρ˙ = 3γHρ (8) γ − γ 1 H˙ = 2 (ρφ + pφ + ρϕ + pϕ + ργ + pγ ) − 2Mp 2 2 (9) 1 φ˙ V (φ) ϕ˙ V (ϕ) = 2 + γργ 2Mp √1 φ˙2 √1+ϕ ˙ 2 − − − 3 together with a constraint equation for the Hubble parameter: 2 1 V (φ) V (ϕ) H = + + ργ (10) 3M 2 2 p 1 φ˙2 1 +ϕ ˙ q − p The potentials we considered are inverse square potentials: 2 2 2 2 V (φ)= Mφ φ− , V (ϕ)= Mϕϕ− (11) Those potentials allow constructing a autonomous system [26, 27] using the evolution equations, and give power-law solutions. The cosmological dynamics of the tachyon field with inverse square potential was studied in Ref. [20, 22, 23]. Interestingly, the inverse square potential plays the same role for tachyon fields as the exponential potential does for standard scalar fields. We define the following dimensionless quantities : ˙ V (φ) V (ϕ) ργ xφ φ, yφ 2 2 , xϕ ϕ,˙ yϕ 2 2 , z 2 2 (12) ≡ ≡ 3H Mp ≡ ≡ 3H Mp ≡ 3H Mp Now the Eqs. (10) and (9) can be rewrite as follow: y y 1= φ + ϕ + z Ω + z (13) 2 DE 2 1+ xϕ ≡ 1 xφ q − p 2 2 H 3 yφ(γ x ) yϕ(γ + x ) ′ = − φ ϕ + γ (14) 2 H −2 − 2 − 1+ xϕ 1 xφ q − p where ΩDE measure the dark energy density as a fraction of the critical density, a prime denotes a derivative with respect to the logarithm of the scale factor,N = ln a. Then the evolution Eqs. (6) and (7) can be written to an autonomous system: 2 x′ = 3(x β y )(1 x ) (15) φ − φ − φ φ − φ p 2 2 yφ(γ xφ) yϕ(γ + xϕ) y′ =3y − β y x + γ (16) φ φ 2 φ φ φ − 2 − 1+ xϕ − 1 xφ p q − p 2 x′ = 3(x + β y )(1 + x ) (17) ϕ − ϕ ϕ ϕ ϕ p 2 2 yφ(γ xφ) yϕ(γ + xϕ) y′ =3y − β y x + γ (18) ϕ ϕ 2 ϕ ϕ ϕ − 2 − 1+ xϕ − 1 xφ p q − p where 2 2 4Mp 4Mp βφ = 2 , βϕ = 2 (19) 3Mφ 3Mϕ The equation of state of the dark energy is 2 2 2 2 V (φ) 1 φ˙ V (ϕ) 1 +ϕ ˙ yφ 1 xφ yϕ 1+ xϕ ω = − q − − = − q − − (20) V (φ) V (ϕ) p yφ yϕp 2 + 2 2 + 2 1 x √1 φ˙ √1+ϕ ˙ √ φ √1+xϕ − − 4 -8 -6 -4 -2 0 -8 -6 -4 -2 0 0.8 0.8 0.0 0.0 0.7 0.7 a a a b -0.2 b -0.2 0.6 0.6 c c 0.5 0.5 -0.4 -0.4 0.4 0.4 -0.6 -0.6 w DE 0.3 0.3 -0.8 -0.8 0.2 0.2 b 0.1 0.1 -1.0 -1.0 c 0.0 0.0 -1.2 -1.2 -0.1 -0.1 -8 -6 -4 -2 0 -8 -6 -4 -2 0 N N FIG. 1: Evolution of the equation of state (ω)and density parameters(ΩDE) as a function of N for the dark energy model with β = β = 1/3, γ = 1.
Load more

Recommended publications
  • On Dark Energy Models of Single Scalar Field
    Home Search Collections Journals About Contact us My IOPscience On dark energy models of single scalar field This content has been downloaded from IOPscience. Please scroll down to see the full text. JCAP04(2012)003 (http://iopscience.iop.org/1475-7516/2012/04/003) View the table of contents for this issue, or go to the journal homepage for more Download details: IP Address: 140.112.101.4 This content was downloaded on 06/11/2014 at 07:57 Please note that terms and conditions apply. ournal of Cosmology and Astroparticle Physics JAn IOP and SISSA journal On dark energy models of single scalar field JCAP04(2012)003 Mingzhe Li,a,f Taotao Qiu,b,c Yifu Caid and Xinmin Zhange aDepartment of Physics, Nanjing University, Nanjing 210093, P.R. China bDepartment of Physics and Center for Theoretical Sciences, National Taiwan University, Taipei 10617, Taiwan cLeung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 106, Taiwan dDepartment of Physics, Arizona State University, Tempe, AZ 85287, U.S.A. eInstitute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918-4, Beijing 100049, P.R. China f Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing University — Purple Mountain Observatory, Nanjing 210093, P.R. China E-mail: [email protected], [email protected], [email protected], [email protected] Received January 2, 2012 Accepted March 7, 2012 Published April 2, 2012 Abstract. In this paper we revisit the dynamical dark energy model building based on single scalar field involving higher derivative terms. By imposing a degenerate condition on the higher derivatives in curved spacetime, one can select the models which are free from the ghost mode and the equation of state is able to cross the cosmological constant boundary smoothly, dynamically violate the null energy condition.
    [Show full text]
  • Cosmología De Tiempo Tardío Para Un Campo Escalar Con
    Cosmolog´ıa de Tiempo Tard´ıo para un Campo Escalar con Acoplamientos Cinetico´ y de Gauss-Bonnet Edwin Loaiza Acuna˜ Tesis doctoral presentada como requisito parcial para optar al t´ıtulo de Doctor en Ciencias - F´ısica Director: Luis Norberto Granda Velasquez´ Universidad del Valle Facultad de Ciencias Naturales y Exactas Programa Academico´ de postgrado en F´ısica Julio 2016 Abstract In this thesis we study late-time cosmological solutions for a scalar field model with kinetic coupling to curvature and the scalar field coupled to the Gauss-Bonnet inva- riant, in order to explain the late-time accelerated expansion of the universe. Initially, exact cosmological solutions that show the phases of decelerated expansion, accelera- ted expansion and transition to the phantom phase have been found. These phases are necessary for the satisfactory explanation of the early inflation, and the current acce- lerated (super accelerated) expansion of the universe. These solutions have been found by imposing appropriate restrictions on the Gauss-Bonnet and kinetic couplings, ba- sed on the asimptotic limits of the Friedmann equations. Solutions with Big Rip and without Big Rip singularities have been studied. An especific choice of the Gauss- Bonnet coupling, where the squared of the Hubble parameter is proportional to the kinetic term, allows the reconstruction of the model for an appropriate cosmological evolution. The new found solution can describe the three cosmological phases that go from the power-law expansion, that describes a matter dominated universe, to the scalar field dominated phantom phase. For this solution and according to the values of the equation of state parameter during di↵erent epochs, the parameters of the solution can be adjusted in order to obtain di↵erent scenarios with and without Big Rip singularities.
    [Show full text]
  • Spinor Quintom Cosmology with Intrinsic Spin
    Hindawi Publishing Corporation Advances in High Energy Physics Volume 2016, Article ID 3740957, 10 pages http://dx.doi.org/10.1155/2016/3740957 Research Article Spinor Quintom Cosmology with Intrinsic Spin Emre Dil DepartmentofPhysics,SinopUniversity,Korucuk,57000Sinop,Turkey Correspondence should be addressed to Emre Dil; [email protected] Received 5 October 2016; Revised 5 November 2016; Accepted 7 November 2016 Academic Editor: Dandala R. K. Reddy Copyright © 2016 Emre Dil. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3. We consider a spinor quintom dark energy model with intrinsic spin, in the framework of Einstein-Cartan-Sciama-Kibble theory. After constructing the mathematical formalism of the model, we obtain the spin contributed total energy-momentum tensor giving the energy density and the pressure of the quintom model, and then we find the equation of state parameter, Hubble parameter, deceleration parameter, state finder parameter, and some distance parameter in terms of the spinor potential. Choosing suitable potentials leads to the quintom scenario crossing between quintessence and phantom epochs, or vice versa. Analyzing three quintom scenarios provides stable expansion phases avoiding Big Rip singularities and yielding matter dominated era through the stabilization of the spinor pressure via spin contribution. The stabilization in spinor pressure leads to neglecting it as compared to the increasing energy density and constituting a matter dominated stable expansion epoch. 1. Introduction which is also named as a ghost [17].
    [Show full text]
  • Dark Energy (De) and Expanding Universe(Eu) an Augmentation -Detrition Model
    International Journal of Scientific and Research Publications, Volume 2, Issue 6, June 2012 1 ISSN 2250-3153 DARK ENERGY (DE) AND EXPANDING UNIVERSE(EU) AN AUGMENTATION -DETRITION MODEL 1DR K N PRASANNA KUMAR, 2PROF B S KIRANAGI AND 3 PROF C S BAGEWADI ABSTRACT: A system of dark energy-expanding universe is investigated. It is shown that the time independence of the contributions portrays another system by itself and constitutes the equilibrium solution of the original time independent system. With the methodology reinforced and revitalized with the explanations, we write the governing equations with the nomenclature for the systems in the foregoing. Further papers extensively draw inferences upon such concatenation process, ipso facto,fait accompli desideratum. INDEX TERMS: Dark Energy, Expanding Universe ,Empty Space, Repulsive Force INTRODUCTION: In physical cosmology, astronomy and celestial mechanics, dark energy is a hypothetical form of energy that permeates all of space and tends to accelerate the expansion of the universe. Dark energy is the most accepted hypothesis to explain observations since the 1990s that indicate that the universe is expanding at an accelerating rate. In the standard model of cosmology, dark energy currently accounts for 73% of the total mass-energy of the universe. At the UK-Germany National Astronomy Meeting NAM2012, the Baryon Oscillation Spectroscopic Survey (BOSS) team has just announced the most accurate measurement yet of the distribution of galaxies between five and six billion years ago. This was the key 'pivot' moment at which the expansion of the universe stopped slowing down due to gravity and started to accelerate instead, due to a mysterious force dubbed "dark energy." The nature of this "dark energy" is one of the big mysteries in cosmology today, and scientists need precise measurements of the expansion history of the universe to unravel this mystery -- BOSS provides this kind of data.
    [Show full text]
  • Quintom Potential from Quantum Anisotropic Cosmological Models
    Provisional chapter Chapter 9 Quintom Potential from Quantum Anisotropic CosmologicalQuintom Potential Models from Quantum Anisotropic Cosmological Models J. Socorro, Paulo A. Rodríguez , O. Núñez-Soltero, J.Rafael Socorro, Hernández Paulo and A. AbrahamRodríguez, Espinoza-García O. Núñez-Soltero, Rafael Hernández and Abraham Espinoza-García Additional information is available at the end of the chapter Additional information is available at the end of the chapter http://dx.doi.org/10.5772/52054 1. Introduction At the present time, there are some paradigms to explain the observations for the accelerated expansion of the universe. Most of these paradigms are based on the dynamics of a scalar (quintessence) or multiscalar field (quintom) cosmological models of dark energy, (see the ′ review [1–3]). The main discussion yields over the evolution of these models in the ω-ω plane (ω is the equation of state parameter of the dark energy) [4–12, 14–19, 21–25]). In the present study we desire to perform our investigation in the case of quintom cosmology, constructed using both quintessence (σ) and phantom (φ) fields, mantaining a nonspecific potential form V(φ, σ). There are many works in the literature that deals with this type of problems, but in a general way, and not with a particular ansatz, one that considers dynamical systems [12, 13, 20]. One special class of potentials used to study this behaviour corresponds to the case of the exponential potentials [4, 6, 9, 26, 28] for each field, where the corresponding energy density of a scalar field has the range of scaling behaviors [29, 30], i.e, −m it scales exactly as a power of the scale factor like, ρφ ∝ a , when the dominant component has an energy density which scales in a similar way.
    [Show full text]
  • Exploring Bouncing Cosmologies with Cosmological Surveys
    Exploring Bouncing Cosmologies with Cosmological Surveys Yi-Fu Cai1, ∗ 1Department of Physics, McGill University, Montr´eal,QC, H3A 2T8, Canada In light of the recent observational data coming from the sky we have two significant directions in the field of theoretical cosmology recently. First, we are now able to make use of present observations, such as the Planck and BICEP2 data, to examine theoretical predictions from the standard inflationary ΛCDM which were made decades of years ago. Second, we can search for new cosmological signatures as a way to explore physics beyond the standard cosmic paradigm. In particular, a subset of early universe models admit a nonsingular bouncing solution that attempts to address the issue of the big bang singularity. These models have achieved a series of considerable developments in recent years, in particular in their perturbative frameworks, which made brand-new predictions of cosmological signatures that could be visible in current and forthcoming observations. In this article we present two representative paradigms of very early universe physics. The first is the so-called new matter (or matter-ekpyrotic) bounce scenario in which the universe starts with a matter-dominated contraction phase and transitions into an ekpyrotic phase. In the setting of this paradigm, we propose some possible mechanisms of generating a red tilt for primordial curvature perturbations and confront its general predictions with recent cosmological observations. The second is the matter-bounce inflation scenario which can be viewed as an extension of inflationary cosmology with a matter contraction before inflation. We present a class of possible model constructions and review its implications on the current CMB experiments.
    [Show full text]
  • On Perturbations of a Quintom Bounce J JCAP03(2008)013 ] 2 1 6 2 4 ]
    ournal of Cosmology and Astroparticle Physics JAn IOP and SISSA journal On perturbations of a quintom bounce Yi-Fu Cai1,TaotaoQiu1, Robert Brandenberger2,3, Yun-Song Piao4 and Xinmin Zhang1,5 JCAP03(2008)013 1 Institute of High Energy Physics, Chinese Academy of Sciences, PO Box 918-4, Beijing 100049, People’s Republic of China 2 Department of Physics, McGill University, Montreal, QC, H3A 2T8, Canada 3 Kavli Institute for Theoretical Physics, Zhong Guan Cun East Street 55, Beijing 100080, People’s Republic of China 4 College of Physical Sciences, Graduate School of Chinese Academy of Sciences, Beijing 100049, People’s Republic of China 5 Theoretical Physics Center for Science Facilities (TPCSF), CAS, People’s Republic of China E-mail: [email protected], [email protected], [email protected], [email protected] and [email protected] Received 20 November 2007 Accepted 27 February 2008 Published 17 March 2008 Online at stacks.iop.org/JCAP/2008/i=03/a=013 doi:10.1088/1475-7516/2008/03/013 Abstract. A quintom universe with an equation of state crossing the cosmological constant boundary can provide a bouncing solution dubbed the quintom bounce and thus resolve the big bang singularity. In this paper, we investigate the cosmological perturbations of the quintom bounce both analytically and numerically. We find that the fluctuations in the dominant mode in the post-bounce expanding phase couple to the growing mode of the perturbations in the pre-bounce contracting phase. Keywords: cosmological perturbation theory, cosmology of theories beyond the SM, physics of the early universe ArXiv ePrint: 0711.2187 c 2008 IOP Publishing Ltd and SISSA 1475-7516/08/03013+24$30.00 On perturbations of a quintom bounce Contents 1.
    [Show full text]
  • Emergent Universe Scenario Via Quintom Matter
    Physics Letters B 718 (2012) 248–254 Contents lists available at SciVerse ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Emergent universe scenario via Quintom matter ∗ Yi-Fu Cai a,b, , Mingzhe Li c,d, Xinmin Zhang e a Department of Physics, McGill University, Montréal, QC, H3A 2T8, Canada b Department of Physics, Arizona State University, Tempe, AZ 85287, USA c Department of Physics, Nanjing University, Nanjing 210093, China d Joint Center for Particle, Nuclear Physics and Cosmology, Nanjing University, Purple Mountain Observatory, Nanjing 210093, China e Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China article info abstract Article history: The emergent universe scenario provides a possible alternative to bouncing cosmology to avoid the Big Received 3 October 2012 Bang singularity problem. In this Letter we study the realization of the emergent universe scenario by Received in revised form 23 October 2012 making use of Quintom matter with an equation of state across the cosmological constant boundary. We Accepted 23 October 2012 will show explicitly the analytic and numerical solutions of emergent universe in two Quintom models, Available online 26 October 2012 which are a phenomenological fluid and a nonconventional spinor field, respectively. Editor: M. Trodden © 2012 Elsevier B.V. All rights reserved. 1. Introduction universe has to cross over the cosmological constant boundary w =−1 twice. This type of bounce model was extensively studied Inflation is considered as the most successful model of describ- in the literature in recent years (for example see [15–18] and ref- ing physics of very early universe, which has explained concep- erences therein, and see [19] for a review on Quintom cosmology).
    [Show full text]
  • 28 Jul 2008 Oscillating Universe with Quintom Matter
    Oscillating universe with quintom matter Hua-Hui Xiong1, Yi-Fu Cai1, Taotao Qiu1, Yun-Song Piao2, Xinmin Zhang1,3 1 Institute of High Energy Physics, Chinese Academy of Sciences, P.O. Box 918-4, Beijing 100049, P. R. China 2 College of Physical Sciences, Graduate School of Chinese Academy of Sciences, YuQuan Road 19A, Beijing 100049, P. R. China 3 Theoretical Physics Center for Science Facilities (TPCSF), CAS, P. R. China Abstract In this paper, we study the possibility of building a model of the oscillating universe with quintom matter in the framework of 4-dimensional Friedmann- Robertson-Walker background. Taking the two-scalar-field quintom model as an example, we find in the model parameter space there are five different types of solutions which correspond to: (I) a cyclic universe with the minimal and maximal values of the scale factor remaining the same in every cycle, (II) an oscillating universe with its minimal and maximal values of the scale factor arXiv:0805.0413v2 [astro-ph] 28 Jul 2008 increasing cycle by cycle, (III) an oscillating universe with its scale factor always increasing, (IV) an oscillating universe with its minimal and maximal values of the scale factor decreasing cycle by cycle, and (V) an oscillating universe with its scale factor always decreasing. 1 1 Introduction The quintom scenario of dark energy firstly proposed in Ref. [1] for the purpose of understanding the dynamical feature with the equation-of-state (EoS) crossing over the cosmological constant boundary w = 1 differs from the quintessence or phantom − or other scenario of dark energy in the determination of the evolution of the Universe.
    [Show full text]
  • Planar Yang-Mills 101 Nicholas R. Wright Natchitoches
    Planar Yang-Mills 101 Nicholas R. Wright Natchitoches, Louisiana, USA [email protected] Abstract The point is to define the limiting continuum field theory. In principle, this might even be done without taking limits. The Hamiltonian, the operator on the quantum Hilbert space which generates time translations, has a square root called the supercharge. Here we use the Moon model and Parfait logic. Furthermore, although one has changed the problem, one still has a fairly close relation to the original problem using the ideology of the renormalization group. We can start with a supersymmetric theory, and add supersymmetry breaking terms to the action which only become important at long distances as many lattice spacings, to obtain a theory with the better renormalization properties of the supersymmetric theory at short distances, but which reduces to conventional Yang-Mills theory at longer distances. Thus, a solution to the problem in a sufficiently general class of supersymmetric theories, would in fact imply the solution of the original problem. We propose a Cacace tetraoxygen universe relative to a Poincaré Dodecahedral Space. This is called an oxozone. Keywords: Yang-Mills, mass gap, Moon model, Parfait, Poincaré Dodecahedral Space, core- cusp problem, dwarf galaxy problem Introduction Given a simple Lie Group G (such as SU (2) or SU (3)). Show that: A. There exists a fully renormalized quantum version of Yang-Mills theory on R4 based on this group, and B. There is a number Δ > 0 such that every state in the theory (except the vacuum) has energy at least Δ. In other words, there are no massless particles in the theory.
    [Show full text]
  • Research Article Dynamics of Mixed Dark Energy Domination in Teleparallel Gravity and Phase-Space Analysis
    Hindawi Publishing Corporation Advances in High Energy Physics Volume 2015, Article ID 608252, 20 pages http://dx.doi.org/10.1155/2015/608252 Research Article Dynamics of Mixed Dark Energy Domination in Teleparallel Gravity and Phase-Space Analysis Emre Dil1 and Erdinç Kolay2 1 Department of Physics, Sinop University, Korucuk, 57000 Sinop, Turkey 2Department of Statistics, Sinop University, Korucuk, 57000 Sinop, Turkey Correspondence should be addressed to Emre Dil; [email protected] Received 16 October 2015; Revised 26 November 2015; Accepted 29 November 2015 Academic Editor: Frank Filthaut Copyright © 2015 E. Dil and E. Kolay. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3. We consider a novel dark energy model to investigate whether it will provide an expanding universe phase. Here we propose a mixed dark energy domination which is constituted by tachyon, quintessence, and phantom scalar fields nonminimally coupled to gravity, in the absence of background dark matter and baryonic matter, in the framework of teleparallel gravity. We perform the phase-space analysis of the model by numerical methods and find the late-time accelerated attractor solutions implying the acceleration phase of universe. 1. Introduction quantity of dark energy; its equation of state parameter DE = DE/DE,whereDE and DE are the pressure and energy The universe is known to be experiencing an accelerating density of the dark energy, respectively. For cosmological expansion by astrophysical observations such as Supernova constant boundary DE =−1,butforquintessencethe Ia [1, 2], large scale structure [3, 4], the baryon acoustic parameter DE ≥−1,forphantomDE ≤−1,andfor oscillations [5], and cosmic microwave background radiation nonminimally coupled tachyon with gravity both DE ≤−1 [6–9].
    [Show full text]
  • Coframes, Spinors and Torsion
    Coframes, spinors and torsion James Burnett A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy of University College London. Department of Mathematics University College London November 2011 I, James Burnett confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Abstract This thesis is based on five articles, four of which have been published in the Journal of Math- ematical Physics, Physical Review D, Modern Physics Letters A and Journal of High Energy Physics. The fifth has been submitted to Mathematika. In these works we study several distinct problems within the broad subject area of Mathematical Physics. The common feature is that all these works deal with rotations of one form or another. In particular, we show an equivalence between the massless and massive Dirac equations and models based on the concept of rotating material points. We also solve an open problem in Einstein-Cartan theory, namely, we find a natural matter source for a non-trivial spin angular momentum tensor. Finally, we construct a complete class of non-standard (non-local) spinor field theories and examine their possible applications in Cosmology. Acknowledgements I would like to express profound gratitude to my main supervisor Dmitri Vassiliev, with whom I have had numerous political discussions, and my pseudo second supervisor Christian Boehmer. They have both been tremendously helpful, understanding, and above all, entertaining! I also thank my second supervisor Ofer Lahav, an inspirational academic. I have been fortunate to have a good network of friends also completing their PhDs, whose helpful discussions spurred me on when needed: Finn Gubay, Dara McCutcheon, David West- ern, Doug Lazenby, Louise Jottrand, and, of course, Hannah Fry.
    [Show full text]