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Birth of De Sitter Universe from a Time Crystal Universe
PHYSICAL REVIEW D 100, 123531 (2019) Birth of de Sitter universe from a time crystal universe † Daisuke Yoshida * and Jiro Soda Department of Physics, Kobe University, Kobe 657-8501, Japan (Received 30 September 2019; published 18 December 2019) We show that a simple subclass of Horndeski theory can describe a time crystal universe. The time crystal universe can be regarded as a baby universe nucleated from a flat space, which is mediated by an extension of Giddings-Strominger instanton in a 2-form theory dual to the Horndeski theory. Remarkably, when a cosmological constant is included, de Sitter universe can be created by tunneling from the time crystal universe. It gives rise to a past completion of an inflationary universe. DOI: 10.1103/PhysRevD.100.123531 I. INTRODUCTION Euler-Lagrange equations of motion contain up to second order derivatives. Actually, bouncing cosmology in the Inflation has succeeded in explaining current observa- Horndeski theory has been intensively investigated so far tions of the large scale structure of the Universe [1,2]. [23–29]. These analyses show the presence of gradient However, inflation has a past boundary [3], which could be instability [30,31] and finally no-go theorem for stable a true initial singularity or just a coordinate singularity bouncing cosmology in Horndeski theory was found for the depending on how much the Universe deviates from the spatially flat universe [32]. However, it was shown that the exact de Sitter [4], or depending on the topology of the no-go theorem does not hold when the spatial curvature is Universe [5]. -
Expanding Space, Quasars and St. Augustine's Fireworks
Universe 2015, 1, 307-356; doi:10.3390/universe1030307 OPEN ACCESS universe ISSN 2218-1997 www.mdpi.com/journal/universe Article Expanding Space, Quasars and St. Augustine’s Fireworks Olga I. Chashchina 1;2 and Zurab K. Silagadze 2;3;* 1 École Polytechnique, 91128 Palaiseau, France; E-Mail: [email protected] 2 Department of physics, Novosibirsk State University, Novosibirsk 630 090, Russia 3 Budker Institute of Nuclear Physics SB RAS and Novosibirsk State University, Novosibirsk 630 090, Russia * Author to whom correspondence should be addressed; E-Mail: [email protected]. Academic Editors: Lorenzo Iorio and Elias C. Vagenas Received: 5 May 2015 / Accepted: 14 September 2015 / Published: 1 October 2015 Abstract: An attempt is made to explain time non-dilation allegedly observed in quasar light curves. The explanation is based on the assumption that quasar black holes are, in some sense, foreign for our Friedmann-Robertson-Walker universe and do not participate in the Hubble flow. Although at first sight such a weird explanation requires unreasonably fine-tuned Big Bang initial conditions, we find a natural justification for it using the Milne cosmological model as an inspiration. Keywords: quasar light curves; expanding space; Milne cosmological model; Hubble flow; St. Augustine’s objects PACS classifications: 98.80.-k, 98.54.-h You’d think capricious Hebe, feeding the eagle of Zeus, had raised a thunder-foaming goblet, unable to restrain her mirth, and tipped it on the earth. F.I.Tyutchev. A Spring Storm, 1828. Translated by F.Jude [1]. 1. Introduction “Quasar light curves do not show the effects of time dilation”—this result of the paper [2] seems incredible. -
3 the Friedmann-Robertson-Walker Metric
3 The Friedmann-Robertson-Walker metric 3.1 Three dimensions The most general isotropic and homogeneous metric in three dimensions is similar to the two dimensional result of eq. (43): dr2 ds2 = a2 + r2dΩ2 ; dΩ2 = dθ2 + sin2 θdφ2 ; k = 0; 1 : (46) 1 kr2 − The angles φ and θ are the usual azimuthal and polar angles of spherical coordinates, with θ [0; π], φ [0; 2π). As before, the parameter k can take on three different values: for k = 0, 2 2 the above line element describes ordinary flat space in spherical coordinates; k = 1 yields the metric for S , with constant positive curvature, while k = 1 is AdS and has constant 3 − 3 negative curvature. As in the two dimensional case, the change of variables r = sin χ (k = 1) or r = sinh χ (k = 1) makes the global nature of these manifolds more apparent. For example, − for the k = 1 case, after defining r = sin χ, the line element becomes ds2 = a2 dχ2 + sin2 χdθ2 + sin2 χ sin2 θdφ2 : (47) This is equivalent to writing ds2 = dX2 + dY 2 + dZ2 + dW 2 ; (48) where X = a sin χ sin θ cos φ ; Y = a sin χ sin θ sin φ ; Z = a sin χ cos θ ; W = a cos χ ; (49) which satisfy X2 + Y 2 + Z2 + W 2 = a2. So we see that the k = 1 metric corresponds to a 3-sphere of radius a embedded in 4-dimensional Euclidean space. One also sees a problem with the r = sin χ coordinate: it does not cover the whole sphere. -
Cosmological Distances and Fractal Statistics of Galaxy Distribution
Astronomy & Astrophysics manuscript no. 1469 June 13, 2018 (DOI: will be inserted by hand later) Cosmological distances and fractal statistics of galaxy distribution Marcelo B. Ribeiro Physics Institute, University of Brazil–UFRJ, CxP 68532, CEP 21945-970, Rio de Janeiro, Brazil; E-mail: [email protected] Received 15 June 2004 / Accepted August 2004 Abstract. This paper studies the effect of the distance choice in radial (non-average) statistical tools used for fractal characterization of galaxy distribution. After reviewing the basics of measuring distances of cosmological sources, various distance definitions are used to calculate the differential density γ and the integral differential density γ∗ of the dust distribution in the Einstein-de Sitter cosmology. The main results are as follows: (1) the choice of distance plays a crucial role in determining the scale where relativistic corrections must be taken ∗ into account, as both γ and γ are strongly affected by such a choice; (2) inappropriate distance choices may lead to failure to find evidence of a galaxy fractal structure when one calculates those quantities, even if such a structure does occur in the galaxy distribution; (3) the comoving distance and the distance given by Mattig’s ∗ formula are unsuitable to probe for a possible fractal pattern as they render γ and γ constant for all redshifts; (4) a possible galaxy fractal system at scales larger than 100Mpc (z ≈ 0.03) may only be found if those statistics ∗ are calculated with the luminosity or redshift distances, as they are the ones where γ and γ decrease at higher redshifts; (5) C´el´erier and Thieberger’s (2001) critique of Ribeiro’s (1995) earlier study are rendered impaired as their objections were based on misconceptions regarding relativistic distance definitions. -
An Analysis of Gravitational Redshift from Rotating Body
An analysis of gravitational redshift from rotating body Anuj Kumar Dubey∗ and A K Sen† Department of Physics, Assam University, Silchar-788011, Assam, India. (Dated: July 29, 2021) Gravitational redshift is generally calculated without considering the rotation of a body. Neglect- ing the rotation, the geometry of space time can be described by using the spherically symmetric Schwarzschild geometry. Rotation has great effect on general relativity, which gives new challenges on gravitational redshift. When rotation is taken into consideration spherical symmetry is lost and off diagonal terms appear in the metric. The geometry of space time can be then described by using the solutions of Kerr family. In the present paper we discuss the gravitational redshift for rotating body by using Kerr metric. The numerical calculations has been done under Newtonian approximation of angular momentum. It has been found that the value of gravitational redshift is influenced by the direction of spin of central body and also on the position (latitude) on the central body at which the photon is emitted. The variation of gravitational redshift from equatorial to non - equatorial region has been calculated and its implications are discussed in detail. I. INTRODUCTION from principle of equivalence. Snider in 1972 has mea- sured the redshift of the solar potassium absorption line General relativity is not only relativistic theory of grav- at 7699 A˚ by using an atomic - beam resonance - scat- itation proposed by Einstein, but it is the simplest theory tering technique [5]. Krisher et al. in 1993 had measured that is consistent with experimental data. Predictions of the gravitational redshift of Sun [6]. -
On Asymptotically De Sitter Space: Entropy & Moduli Dynamics
On Asymptotically de Sitter Space: Entropy & Moduli Dynamics To Appear... [1206.nnnn] Mahdi Torabian International Centre for Theoretical Physics, Trieste String Phenomenology Workshop 2012 Isaac Newton Institute , CAMBRIDGE 1 Tuesday, June 26, 12 WMAP 7-year Cosmological Interpretation 3 TABLE 1 The state of Summarythe ofart the cosmological of Observational parameters of ΛCDM modela Cosmology b c Class Parameter WMAP 7-year ML WMAP+BAO+H0 ML WMAP 7-year Mean WMAP+BAO+H0 Mean 2 +0.056 Primary 100Ωbh 2.227 2.253 2.249−0.057 2.255 ± 0.054 2 Ωch 0.1116 0.1122 0.1120 ± 0.0056 0.1126 ± 0.0036 +0.030 ΩΛ 0.729 0.728 0.727−0.029 0.725 ± 0.016 ns 0.966 0.967 0.967 ± 0.014 0.968 ± 0.012 τ 0.085 0.085 0.088 ± 0.015 0.088 ± 0.014 2 d −9 −9 −9 −9 ∆R(k0) 2.42 × 10 2.42 × 10 (2.43 ± 0.11) × 10 (2.430 ± 0.091) × 10 +0.030 Derived σ8 0.809 0.810 0.811−0.031 0.816 ± 0.024 H0 70.3km/s/Mpc 70.4km/s/Mpc 70.4 ± 2.5km/s/Mpc 70.2 ± 1.4km/s/Mpc Ωb 0.0451 0.0455 0.0455 ± 0.0028 0.0458 ± 0.0016 Ωc 0.226 0.226 0.228 ± 0.027 0.229 ± 0.015 2 +0.0056 Ωmh 0.1338 0.1347 0.1345−0.0055 0.1352 ± 0.0036 e zreion 10.4 10.3 10.6 ± 1.210.6 ± 1.2 f t0 13.79 Gyr 13.76 Gyr 13.77 ± 0.13 Gyr 13.76 ± 0.11 Gyr a The parameters listed here are derived using the RECFAST 1.5 and version 4.1 of the WMAP[WMAP-7likelihood 1001.4538] code. -
Gravitational Redshift/Blueshift of Light Emitted by Geodesic
Eur. Phys. J. C (2021) 81:147 https://doi.org/10.1140/epjc/s10052-021-08911-5 Regular Article - Theoretical Physics Gravitational redshift/blueshift of light emitted by geodesic test particles, frame-dragging and pericentre-shift effects, in the Kerr–Newman–de Sitter and Kerr–Newman black hole geometries G. V. Kraniotisa Section of Theoretical Physics, Physics Department, University of Ioannina, 451 10 Ioannina, Greece Received: 22 January 2020 / Accepted: 22 January 2021 / Published online: 11 February 2021 © The Author(s) 2021 Abstract We investigate the redshift and blueshift of light 1 Introduction emitted by timelike geodesic particles in orbits around a Kerr–Newman–(anti) de Sitter (KN(a)dS) black hole. Specif- General relativity (GR) [1] has triumphed all experimental ically we compute the redshift and blueshift of photons that tests so far which cover a wide range of field strengths and are emitted by geodesic massive particles and travel along physical scales that include: those in large scale cosmology null geodesics towards a distant observer-located at a finite [2–4], the prediction of solar system effects like the perihe- distance from the KN(a)dS black hole. For this purpose lion precession of Mercury with a very high precision [1,5], we use the killing-vector formalism and the associated first the recent discovery of gravitational waves in Nature [6–10], integrals-constants of motion. We consider in detail stable as well as the observation of the shadow of the M87 black timelike equatorial circular orbits of stars and express their hole [11], see also [12]. corresponding redshift/blueshift in terms of the metric physi- The orbits of short period stars in the central arcsecond cal black hole parameters (angular momentum per unit mass, (S-stars) of the Milky Way Galaxy provide the best current mass, electric charge and the cosmological constant) and the evidence for the existence of supermassive black holes, in orbital radii of both the emitter star and the distant observer. -
A Hypothesis About the Predominantly Gravitational Nature of Redshift in the Electromagnetic Spectra of Space Objects Stepan G
A Hypothesis about the Predominantly Gravitational Nature of Redshift in the Electromagnetic Spectra of Space Objects Stepan G. Tiguntsev Irkutsk National Research Technical University 83 Lermontov St., Irkutsk, 664074, Russia [email protected] Abstract. The study theoretically substantiates the relationship between the redshift in the electromagnetic spectrum of space objects and their gravity and demonstrates it with computational experiments. Redshift, in this case, is a consequence of a decrease in the speed of the photons emitted from the surface of objects, which is caused by the gravity of these objects. The decline in the speed of photons due to the gravity of space gravitating object (GO) is defined as ΔC = C-C ', where: C' is the photon speed changed by the time the receiver records it. Then, at a change in the photon speed between a stationary source and a receiver, the redshift factor is determined as Z = (C-C ')/C'. Computational experiments determined the gravitational redshift of the Earth, the Sun, a neutron star, and a quasar. Graph of the relationship between the redshift and the ratio of sizes to the mass of any space GOs was obtained. The findings indicate that the distance to space objects does not depend on the redshift of these objects. Keywords: redshift, computational experiment, space gravitating object, photon, radiation source, and receiver. 1. Introduction In the electromagnetic spectrum of space objects, redshift is assigned a significant role in creating a physical picture of the Universe. Redshift is observed in almost all space objects (stars, galaxies, quasars, and others). As a consequence of the Doppler effect, redshift indicates the movement of almost all space objects from an observer on the Earth [1]. -
Galaxy Formation Within the Classical Big Bang Cosmology
Galaxy formation within the classical Big Bang Cosmology Bernd Vollmer CDS, Observatoire astronomique de Strasbourg Outline • some basics of astronomy small structure • galaxies, AGNs, and quasars • from galaxies to the large scale structure of the universe large • the theory of cosmology structure • measuring cosmological parameters • structure formation • galaxy formation in the cosmological framework • open questions small structure The architecture of the universe • Earth (~10-9 ly) • solar system (~6 10-4 ly) • nearby stars (> 5 ly) • Milky Way (~6 104 ly) • Galaxies (>2 106 ly) • large scale structure (> 50 106 ly) How can we investigate the universe Astronomical objects emit elctromagnetic waves which we can use to study them. BUT The earth’s atmosphere blocks a part of the electromagnetic spectrum. need for satellites Back body radiation • Opaque isolated body at a constant temperature Wien’s law: sun/star (5500 K): 0.5 µm visible human being (310 K): 9 µm infrared molecular cloud (15 K): 200 µm radio The structure of an atom Components: nucleus (protons, neutrons) + electrons Bohr’s model: the electrons orbit around the nucleus, the orbits are discrete Bohr’s model is too simplistic quantum mechanical description The emission of an astronomical object has 2 components: (i) continuum emission + (ii) line emission Stellar spectra Observing in colors Usage of filters (Johnson): U (UV), B (blue), V (visible), R (red), I (infrared) The Doppler effect • Is the apparent change in frequency and wavelength of a wave which is emitted by -
The High Redshift Universe: Galaxies and the Intergalactic Medium
The High Redshift Universe: Galaxies and the Intergalactic Medium Koki Kakiichi M¨unchen2016 The High Redshift Universe: Galaxies and the Intergalactic Medium Koki Kakiichi Dissertation an der Fakult¨atf¨urPhysik der Ludwig{Maximilians{Universit¨at M¨unchen vorgelegt von Koki Kakiichi aus Komono, Mie, Japan M¨unchen, den 15 Juni 2016 Erstgutachter: Prof. Dr. Simon White Zweitgutachter: Prof. Dr. Jochen Weller Tag der m¨undlichen Pr¨ufung:Juli 2016 Contents Summary xiii 1 Extragalactic Astrophysics and Cosmology 1 1.1 Prologue . 1 1.2 Briefly Story about Reionization . 3 1.3 Foundation of Observational Cosmology . 3 1.4 Hierarchical Structure Formation . 5 1.5 Cosmological probes . 8 1.5.1 H0 measurement and the extragalactic distance scale . 8 1.5.2 Cosmic Microwave Background (CMB) . 10 1.5.3 Large-Scale Structure: galaxy surveys and Lyα forests . 11 1.6 Astrophysics of Galaxies and the IGM . 13 1.6.1 Physical processes in galaxies . 14 1.6.2 Physical processes in the IGM . 17 1.6.3 Radiation Hydrodynamics of Galaxies and the IGM . 20 1.7 Bridging theory and observations . 23 1.8 Observations of the High-Redshift Universe . 23 1.8.1 General demographics of galaxies . 23 1.8.2 Lyman-break galaxies, Lyα emitters, Lyα emitting galaxies . 26 1.8.3 Luminosity functions of LBGs and LAEs . 26 1.8.4 Lyα emission and absorption in LBGs: the physical state of high-z star forming galaxies . 27 1.8.5 Clustering properties of LBGs and LAEs: host dark matter haloes and galaxy environment . 30 1.8.6 Circum-/intergalactic gas environment of LBGs and LAEs . -
“De Sitter Effect” in the Rise of Modern Relativistic Cosmology
The role played by the “de Sitter effect” in the rise of modern relativistic cosmology ● Matteo Realdi ● Department of Astronomy, Padova ● Sait 2009. Pisa, 7-5-2009 Table of contents ● Introduction ● 1917: Einstein, de Sitter and the universes of General Relativity ● 1920's: the debates on the “de Sitter effect”. The connection between theory and observation and the rise of scientific cosmology ● 1930: the expanding universe and the decline of the interest in the de Sitter effect ● Conclusion 1 - Introduction ● Modern cosmology: study of the origin, structure and evolution of the universe as a whole, based on the interpretation of astronomical observations at different wave- lengths through the laws of physics ● The early years: 1917-1930. Extremely relevant period, characterized by new ideas, discoveries, controversies, in the light of the first comparison of theoretical world-models with observations at the turning point of relativity revolution ● Particular attention on the interest in the so-called “de Sitter effect”, a theoretical redshift-distance relation which is predicted through the line element of the empty universe of de Sitter ● The de Sitter effect: fundamental influence in contributions that scientists as de Sitter, Eddington, Weyl, Lanczos, Lemaître, Robertson, Tolman, Silberstein, Wirtz, Lundmark, Stromberg, Hubble offered during the 1920's both in theoretical and in observational cosmology (emergence of the modern approach of cosmologists) ➔ Predictions and confirmations of an appropriate redshift- distance relation marked the tortuous process towards the change of viewpoint from the 1917 paradigm of a static universe to the 1930 picture of an expanding universe evolving both in space and in time 2 - 1917: the Universes of General Relativity ● General relativity: a suitable theory in order to describe the whole of space, time and gravitation? ● Two different metrics, i.e. -
Observation of Exciton Redshift-Blueshift Crossover in Monolayer WS2
Observation of exciton redshift-blueshift crossover in monolayer WS2 E. J. Sie,1 A. Steinhoff,2 C. Gies,2 C. H. Lui,3 Q. Ma,1 M. Rösner,2,4 G. Schönhoff,2,4 F. Jahnke,2 T. O. Wehling,2,4 Y.-H. Lee,5 J. Kong,6 P. Jarillo-Herrero,1 and N. Gedik*1 1Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States 2Institut für Theoretische Physik, Universität Bremen, P.O. Box 330 440, 28334 Bremen, Germany 3Department of Physics and Astronomy, University of California, Riverside, California 92521, United States 4Bremen Center for Computational Materials Science, Universität Bremen, 28334 Bremen, Germany 5Materials Science and Engineering, National Tsing-Hua University, Hsinchu 30013, Taiwan 6Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States *Corresponding Author: [email protected] Abstract: We report a rare atom-like interaction between excitons in monolayer WS2, measured using ultrafast absorption spectroscopy. At increasing excitation density, the exciton resonance energy exhibits a pronounced redshift followed by an anomalous blueshift. Using both material-realistic computation and phenomenological modeling, we attribute this observation to plasma effects and an attraction-repulsion crossover of the exciton-exciton interaction that mimics the Lennard- Jones potential between atoms. Our experiment demonstrates a strong analogy between excitons and atoms with respect to inter-particle interaction, which holds promise to pursue the predicted liquid and crystalline phases of excitons in two-dimensional materials. Keywords: Monolayer WS2, exciton, plasma, Lennard-Jones potential, ultrafast optics, many- body theory Table of Contents Graphic Page 1 of 13 Main Text: Excitons in semiconductors are often perceived as the solid-state analogs to hydrogen atoms.