Universe

912 KiB

Open AccessArticle

by Máté Csanád

Universe 2017, 3(4), 85; https://doi.org/10.3390/universe3040085 - 18 Dec 2017

Cited by 7 | Viewed by 2956

In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in

\sqrt{s_{N N}} = 200

GeV Au + Au collisions in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a [...] Read more.

In this paper we present the measurement of charged pion two-particle femtoscopic correlation functions in

\sqrt{s_{N N}} = 200

GeV Au + Au collisions in 31 average transverse mass bins, separately for positive and negative pion pairs. Lévy-shaped source distributions yield a statistically acceptable description of the measured correlation functions, with three physical parameters: correlation strength parameter

λ

, Lévy index

α

and Lévy scale parameter R. The transverse mass dependence of these Lévy parameters is then investigated. Their physical interpretation is also discussed, and the appearance of a new scaling variable is observed. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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1481 KiB

Open AccessArticle

Perturbative Accelerating Solutions of Relativistic Hydrodynamics

by Bálint Kurgyis and Máté Csanád

Universe 2017, 3(4), 84; https://doi.org/10.3390/universe3040084 - 14 Dec 2017

Cited by 4 | Viewed by 2948

Abstract

In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter [...] Read more.

In ultra-relativistic collisions of heavy ions, the strongly interacting Quark Gluon Plasma (sQGP) is created. The fluid nature of the sQGP was one of the important discoveries of high energy heavy ion physics in the last decades. Henceforth the explosion of this matter may be described by hydrodynamical models. Besides numerical simulations, it is important to study the analytic solutions of the equations of hydrodynamics, as these enable us to understand the connection of the final and initial states better. In this paper we present a perturbative, accelerating solution of relativistic hydrodynamics, on top of a known class of solutions describing Hubble-expansion. We describe the properties of this class of perturbative solutions, and investigate a few selected solutions in detail. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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2223 KiB

Open AccessArticle

On Maximal Homogeneous 3-Geometries and Their Visualization

by Emil Molnár, István Prok and Jeno Szirmai

Universe 2017, 3(4), 83; https://doi.org/10.3390/universe3040083 - 4 Dec 2017

Cited by 2 | Viewed by 3603

Abstract

The motivation for this talk and paper is related to the classification of the homogeneous simply connected maximal 3-geometries (the so-called Thurston geometries:

E^{3}

,

S^{3}

,

H^{3}

,

S^{2} \times R

,

H^{2} \times R

, [...] Read more.

The motivation for this talk and paper is related to the classification of the homogeneous simply connected maximal 3-geometries (the so-called Thurston geometries:

E^{3}

,

S^{3}

,

H^{3}

,

S^{2} \times R

,

H^{2} \times R

,

\tilde{S L_{2} R}

,

Nil

, and

Sol

) and their applications in crystallography. The first author found in (Molnár 1997) (see also the more popular (Molnár et al. 2010; 2015) with co-author colleagues, together with more details) a unified projective interpretation for them in the sense of Felix Klein’s Erlangen Program: namely, each S of the above space geometries and its isometry group

Isom (S)

can be considered as a subspace of the projective 3-sphere:

S \subset P S^{3}

, where a special maximal group

G = Isom (S) \subseteq Coll (P S^{3})

of collineations acts, leaving the above subspace S invariant. Vice-versa, we can start with the projective geometry, namely with the classification of

Coll (P S^{3})

through linear transforms of dual pairs of real 4-vector spaces

(V^{4}, V_{4}, R, \sim)

=

P S^{3}

(up to positive real multiplicative equivalence ∼) via Jordan normal forms. Then, we look for projective groups with 3 parameters, and with appropriate properties for convenient geometries described above and in this paper. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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330 KiB

Open AccessArticle

Enhancement of Elliptic Flow of π⁻ under Intense Magnetic Field in √ ^sNN = 200 GeV Au+Au Collisions: A (2 + 1)-Dimensional Reduced-MHD Model Study

by Victor Roy

Universe 2017, 3(4), 82; https://doi.org/10.3390/universe3040082 - 30 Nov 2017

Cited by 2 | Viewed by 2352

Abstract

We investigate the effect of intense magnetic fields on the

(2 + 1)

-dimensional reduced- magnetohydrodynamical (MHD) expansion of hot and dense quark–gluon plasma (QGP) produced in

\sqrt{s_{NN}}

= 200 GeV Au+Au collisions. For the sake of simplicity, we consider [...] Read more.

We investigate the effect of intense magnetic fields on the

(2 + 1)

-dimensional reduced- magnetohydrodynamical (MHD) expansion of hot and dense quark–gluon plasma (QGP) produced in

\sqrt{s_{NN}}

= 200 GeV Au+Au collisions. For the sake of simplicity, we consider the case in which the magnetic field points in the direction perpendicular to the reaction plane. We also consider this field to be external, with energy density parametrized as a two-dimensional Gaussian. The width of the Gaussian along the directions orthogonal to the beam axis varies with the centrality of the collision. The dependence of the magnetic field on proper time (

τ

) is parametrized for the case of zero and finite electrical conductivity of the QGP. We solve the equations of motion of ideal hydrodynamics for such an external magnetic field. For collisions with a non-zero impact parameter we observe a considerable increase in the elliptic-flow coefficient

v_{2}

of

π^{-}

in the presence of an external magnetic field, and the increment in

v_{2}

is found to depend on the evolution and the initial magnitude of the magnetic field. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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6443 KiB

Open AccessReview

Weak Lensing Data and Condensed Neutrino Objects

by Peter Morley and Douglas Buettner

Universe 2017, 3(4), 81; https://doi.org/10.3390/universe3040081 - 23 Nov 2017

Cited by 6 | Viewed by 4741

Abstract

Condensed Neutrino Objects (CNO) are a candidate for the Dark Matter which everyone has been looking for. In this article, from Albert Einstein’s original 1911 and 1917 papers, we begin the journey from weak lensing data to neutrino signatures. New research results include [...] Read more.

Condensed Neutrino Objects (CNO) are a candidate for the Dark Matter which everyone has been looking for. In this article, from Albert Einstein’s original 1911 and 1917 papers, we begin the journey from weak lensing data to neutrino signatures. New research results include an Einasto density profile that fits to a range of candidate degenerate neutrino masses, goodness-of-fit test results for our functional CNO mass/radius relationship which fits to available weak lensing data, and new results based on revised constraints for the CNO that our Local Group of galaxies is embedded in. Full article

(This article belongs to the Special Issue Progress in Cosmology in the Centenary of the 1917 Einstein Paper)

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253 KiB

Open AccessArticle

Gauge Non-Invariant Higher-Spin Currents in AdS₄

by Pavel Smirnov and Mikhail Vasiliev

Universe 2017, 3(4), 78; https://doi.org/10.3390/universe3040078 - 16 Nov 2017

Cited by 6 | Viewed by 2712

Abstract

Conserved currents of any spin

t > 0

built from bosonic symmetric massless gauge fields of arbitrary integer spins

s_{1} + s_{2} > t

in

A d S_{4}

are found. Analogous to the case of

4 d

Minkowski space, currents [...] Read more.

Conserved currents of any spin

t > 0

built from bosonic symmetric massless gauge fields of arbitrary integer spins

s_{1} + s_{2} > t

in

A d S_{4}

are found. Analogous to the case of

4 d

Minkowski space, currents considered in this paper are not gauge invariant, but generate gauge-invariant conserved charges. Full article

(This article belongs to the Special Issue Higher Spin Gauge Theories)

1176 KiB

Open AccessArticle

Effective Interactions and Prospects for Resolution of the Fundamental Cosmological Problems in Quantum Gravity

by Boris A. Arbuzov

Universe 2017, 3(4), 80; https://doi.org/10.3390/universe3040080 - 15 Nov 2017

Viewed by 3751

Abstract

Wouldbe consequences of the existence of effective interactions in quantum gravitation theory are considered. In the framework of the approach, the example of a running gravitational coupling is presented, corresponding to an adequate description of effects, which nowadays are usually prescribed to dark [...] Read more.

Wouldbe consequences of the existence of effective interactions in quantum gravitation theory are considered. In the framework of the approach, the example of a running gravitational coupling is presented, corresponding to an adequate description of effects, which nowadays are usually prescribed to dark matter and dark energy. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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287 KiB

Open AccessConference Report

Directed Flow in Heavy-Ion Collisions and Its Implications for Astrophysics

by Yuri B. Ivanov

Universe 2017, 3(4), 79; https://doi.org/10.3390/universe3040079 - 14 Nov 2017

Cited by 3 | Viewed by 3137

Abstract

Analysis of directed flow (

v_{1}

) of protons, antiprotons and pions in heavy-ion collisions is performed in the range of collision energies

\sqrt{s_{N N}}

= 2.7–39 GeV. Simulations have been done within a three-fluid model employing a purely hadronic equation [...] Read more.

Analysis of directed flow (

v_{1}

) of protons, antiprotons and pions in heavy-ion collisions is performed in the range of collision energies

\sqrt{s_{N N}}

= 2.7–39 GeV. Simulations have been done within a three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS with deconfinement transitions: a first-order phase transition and a smooth crossover transition. The crossover EoS is unambiguously preferable for the description of experimental data at lower collision energies

\sqrt{s_{N N}} ≲

20 Gev. However, at higher collision energies

\sqrt{s_{N N}} ≳

20 Gev. the purely hadronic EoS again becomes advantageous. This indicates that the deconfinement EoS in the quark-gluon sector should be stiffer at high baryon densities than those used in the calculation. The latter finding is in agreement with that discussed in astrophysics in connection with existence of hybrid stars with masses up to about two solar masses. Full article

(This article belongs to the Special Issue Compact Stars in the QCD Phase Diagram)

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656 KiB

Open AccessArticle

Exploring Free Matrix CFT Holographies at One-Loop

by Jin-Beom Bae, Euihun Joung and Shailesh Lal

Universe 2017, 3(4), 77; https://doi.org/10.3390/universe3040077 - 9 Nov 2017

Cited by 7 | Viewed by 3569

Abstract

We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the

S U (N)

adjoint representation to other matrix models, namely the free

S O (N)

and [...] Read more.

We extend our recent study on the duality between stringy higher spin theories and free conformal field theories (CFTs) in the

S U (N)

adjoint representation to other matrix models, namely the free

S O (N)

and

S p (N)

adjoint models as well as the free

U (N) \times U (M)

bi-fundamental and

O (N) \times O (M)

bi-vector models. After determining the spectrum of the theories in the planar limit by Polya counting, we compute the one loop vacuum energy and Casimir energy for their respective bulk duals by means of the Character Integral Representation of the Zeta Function (CIRZ) method, which we recently introduced. We also elaborate on possible ambiguities in the application of this method. Full article

(This article belongs to the Special Issue Higher Spin Gauge Theories)

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2115 KiB

Open AccessFeature PaperArticle

Femtoscopy with Identified Hadrons in pp, pPb, and PbPb Collisions in CMS

by Ferenc Siklér

Universe 2017, 3(4), 76; https://doi.org/10.3390/universe3040076 - 8 Nov 2017

Cited by 3 | Viewed by 3084

Abstract

Short-range correlations of identified charged hadrons in pp (

\sqrt{s} =

0.9, 2.76, and 7 TeV), pPb (

\sqrt{s_{_{NN}}} =

5.02 TeV), and peripheral PbPb collisions (

\sqrt{s_{_{NN}}} =

2.76 TeV) are studied with the CMS detector at the LHC. Charged [...] Read more.

Short-range correlations of identified charged hadrons in pp (

\sqrt{s} =

0.9, 2.76, and 7 TeV), pPb (

\sqrt{s_{_{NN}}} =

5.02 TeV), and peripheral PbPb collisions (

\sqrt{s_{_{NN}}} =

2.76 TeV) are studied with the CMS detector at the LHC. Charged pions, kaons, and protons at low momentum and in laboratory pseudorapidity

| η | < 1

are identified via their energy loss in the silicon tracker. The two-particle correlation functions show effects of quantum statistics, Coulomb interaction, and also indicate the role of multi-body resonance decays and mini-jets. The characteristics of the one-, two-, and three-dimensional correlation functions are studied as a function of transverse pair momentum,

k_{T}

, and the charged-particle multiplicity of the event. The extracted radii are in the range 1–5 fm, reaching highest values for very high multiplicity pPb, also for similar multiplicity PbPb collisions, and decrease with increasing

k_{T}

. The dependence of radii on multiplicity and

k_{T}

largely factorizes and appears to be insensitive to the type of the colliding system and center-of-mass energy. Full article

(This article belongs to the Special Issue BGL2017: 10th Bolyai-Gauss-Lobachevsky Conference on Non-Euclidean Geometry and Its Applications)

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3176 KiB

Open AccessArticle

The Sounds of the Little and Big Bangs

by Edward Shuryak

Universe 2017, 3(4), 75; https://doi.org/10.3390/universe3040075 - 1 Nov 2017

Cited by 5 | Viewed by 3670

Abstract

Studies on heavy ion collisions have discovered that tiny fireballs of a new phase of matter—quark gluon plasma (QGP)—undergo an explosion, called the Little Bang. In spite of its small size, not only is it well described by hydrodynamics, but even small perturbations [...] Read more.

Studies on heavy ion collisions have discovered that tiny fireballs of a new phase of matter—quark gluon plasma (QGP)—undergo an explosion, called the Little Bang. In spite of its small size, not only is it well described by hydrodynamics, but even small perturbations on top of the explosion turned out to be well described by hydrodynamical sound modes. The cosmological Big Bang also went through phase transitions, related with Quantum Chromodynamics (QCD) and electroweak/Higgs symmetry breaking, which are also expected to produce sounds. We discuss their subsequent evolution and hypothetical inverse acoustic cascade, amplifying the amplitude. Ultimately, the collision of two sound waves leads to the formation of one gravity waves. We briefly discuss how these gravity waves can be detected. Full article

(This article belongs to the Special Issue Quark-Gluon Plasma in the Early Universe and in Ultra-Relativistic Heavy-Ion Collisions)

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449 KiB

Open AccessArticle

Higher Spin Matrix Models

by Mauricio Valenzuela

Universe 2017, 3(4), 74; https://doi.org/10.3390/universe3040074 - 30 Oct 2017

Cited by 2 | Viewed by 2909

Abstract

We propose a hybrid class of theories for higher spin gravity and matrix models, i.e., which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev’s higher spin gravity, but part of the equations of motion are provided [...] Read more.

We propose a hybrid class of theories for higher spin gravity and matrix models, i.e., which handle simultaneously higher spin gravity fields and matrix models. The construction is similar to Vasiliev’s higher spin gravity, but part of the equations of motion are provided by the action principle of a matrix model. In particular, we construct a higher spin (gravity) matrix model related to type IIB matrix models/string theory that have a well defined classical limit, and which is compatible with higher spin gravity in

A d S

space. As it has been suggested that higher spin gravity should be related to string theory in a high energy (tensionless) regime, and, therefore to M-Theory, we expect that our construction will be useful to explore concrete connections. Full article

(This article belongs to the Special Issue Higher Spin Gauge Theories)

408 KiB

Open AccessArticle

Inflationary f (R) Cosmologies

by Heba Sami, Joseph Ntahompagaze and Amare Abebe

Universe 2017, 3(4), 73; https://doi.org/10.3390/universe3040073 - 24 Oct 2017

Cited by 10 | Viewed by 3281

Abstract

This paper discusses a simple procedure to reconstruct

f (R)

-gravity models from exact cosmological solutions of the Einstein field equations with a non-interacting classical scalar field-and-radiation background. From the type of inflationary scenario we are interested in, we show how [...] Read more.

This paper discusses a simple procedure to reconstruct

f (R)

-gravity models from exact cosmological solutions of the Einstein field equations with a non-interacting classical scalar field-and-radiation background. From the type of inflationary scenario we are interested in, we show how the potential functions can be obtained. We then show how an

f (R)

gravitational Lagrangian density that mimics the same cosmological expansion as the scalar field-driven inflation of general relativity (GR) can be reconstructed. As a demonstration, we calculate the slow-roll parameters (the spectral index

n_{s}

and the tensor-to-scalar ratio r) and compare these to the Planck data. Full article

(This article belongs to the Special Issue F(R) Gravity)

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424 KiB

Open AccessArticle

Dark Energy and Inflation from Gravitational Waves

by Leonid Marochnik

Universe 2017, 3(4), 72; https://doi.org/10.3390/universe3040072 - 18 Oct 2017

Cited by 5 | Viewed by 4525

Abstract

In this seven-part paper, we show that gravitational waves (classical and quantum) produce the accelerated de Sitter expansion at the start and at the end of the cosmological evolution of the Universe. In these periods, the Universe contains no matter fields but contains [...] Read more.

In this seven-part paper, we show that gravitational waves (classical and quantum) produce the accelerated de Sitter expansion at the start and at the end of the cosmological evolution of the Universe. In these periods, the Universe contains no matter fields but contains classical and quantum metric fluctuations, i.e., it is filled with classical and quantum gravitational waves. In such evolution of the Universe, dominated by gravitational waves, the de Sitter state is the exact solution to the self-consistent equations for classical and quantum gravitational waves and background geometry for the empty space-time with FLRW metric. In both classical and quantum cases, this solution is of the instanton origin since it is obtained in the Euclidean space of imaginary time with the subsequent analytic continuation to real time. The cosmological acceleration from gravitational waves provides a transparent physical explanation to the coincidence, threshold and “old cosmological constant” paradoxes of dark energy avoiding recourse to the anthropic principle. The cosmological acceleration from virtual gravitons at the start of the Universe evolution produces inflation, which is consistent with the observational data on CMB anisotropy. Section 1 is devoted to cosmological acceleration from classical gravitational waves. Section 2 is devoted to the theory of virtual gravitons in the Universe. Section 3 is devoted to cosmological acceleration from virtual gravitons. Section 4 discusses the consistency of the theory with observational data on dark energy and inflation. The discussion of mechanism of acceleration and cosmological scenario are contained in Sections 5 and 6. Appendix contains the theory of stochastic nonlinear gravitational waves of arbitrary wavelength and amplitude in an isotropic Universe. Full article

(This article belongs to the Special Issue Progress in Cosmology in the Centenary of the 1917 Einstein Paper)

483 KiB

Open AccessArticle

Quantum Cramer–Rao Bound for a Massless Scalar Field in de Sitter Space

by Marcello Rotondo and Yasusada Nambu

Universe 2017, 3(4), 71; https://doi.org/10.3390/universe3040071 - 13 Oct 2017

Cited by 5 | Viewed by 3179

Abstract

How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory, the variance of an unbiased parameter estimator is bounded from below by the inverse of measurement-dependent Fisher information and ultimately by quantum [...] Read more.

How precisely can we estimate cosmological parameters by performing a quantum measurement on a cosmological quantum state? In quantum estimation theory, the variance of an unbiased parameter estimator is bounded from below by the inverse of measurement-dependent Fisher information and ultimately by quantum Fisher information, which is the maximization of the former over all positive operator-valued measurements. Such bound is known as the quantum Cramer –Rao bound. We consider the evolution of a massless scalar field with Bunch–Davies vacuum in a spatially flat FLRW spacetime, which results in a two-mode squeezed vacuum out-state for each field wave number mode. We obtain the expressions of the quantum Fisher information as well as the Fisher informations associated to occupation number measurement and power spectrum measurement, and show the specific results of their evolution for pure de Sitter expansion and de Sitter expansion followed by a radiation-dominated phase as examples. We will discuss these results from the point of view of the quantum-to-classical transition of cosmological perturbations and show quantitatively how this transition and the residual quantum correlations affect the bound on the precision. Full article

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338 KiB

Open AccessArticle

Three Point Functions in Higher Spin AdS₃ Holography with 1/N Corrections

by Yasuaki Hikida and Takahiro Uetoko

Universe 2017, 3(4), 70; https://doi.org/10.3390/universe3040070 - 9 Oct 2017

Cited by 9 | Viewed by 3127

Abstract

We examine three point functions with two scalar operators and a higher spin current in 2d W

_{N}

minimal model to the next non-trivial order in

1 / N

expansion. The minimal model was proposed to be dual to a 3d higher spin [...] Read more.

We examine three point functions with two scalar operators and a higher spin current in 2d W

_{N}

minimal model to the next non-trivial order in

1 / N

expansion. The minimal model was proposed to be dual to a 3d higher spin gauge theory, and

1 / N

corrections should be interpreted as quantum effects in the dual gravity theory. We develop a simple and systematic method to obtain three point functions by decomposing four point functions of scalar operators with Virasoro conformal blocks. Applying the method, we reproduce known results at the leading order in

1 / N

and obtain new ones at the next leading order. As confirmation, we check that our results satisfy relations among three point functions conjectured before. Full article

(This article belongs to the Special Issue Higher Spin Gauge Theories)

357 KiB

Open AccessArticle

Gravitational Waves in Locally Rotationally Symmetric (LRS) Class II Cosmologies

by Michael Bradley, Mats Forsberg and Zoltán Keresztes

Universe 2017, 3(4), 69; https://doi.org/10.3390/universe3040069 - 2 Oct 2017

Cited by 12 | Viewed by 3180

Abstract

In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS), using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that [...] Read more.

In this work we consider perturbations of homogeneous and hypersurface orthogonal cosmological backgrounds with local rotational symmetry (LRS), using a method based on the 1 + 1 + 2 covariant split of spacetime. The backgrounds, of LRS class II, are characterised by that the vorticity, the twist of the 2-sheets, and the magnetic part of the Weyl tensor all vanish. They include the flat Friedmann universe as a special case. The matter contents of the perturbed spacetimes are given by vorticity-free perfect fluids, but otherwise the perturbations are arbitrary and describe gravitational, shear, and density waves. All the perturbation variables can be given in terms of the time evolution of a set of six harmonic coefficients. This set decouples into one set of four coefficients with the density perturbations acting as source terms, and another set of two coefficients describing damped source-free gravitational waves with odd parity. We also consider the flat Friedmann universe, which has been considered by several others using the 1 + 3 covariant split, as a check of the isotropic limit. In agreement with earlier results we find a second-order wavelike equation for the magnetic part of the Weyl tensor which decouples from the density gradient for the flat Friedmann universes. Assuming vanishing vector perturbations, including the density gradient, we find a similar equation for the electric part of the Weyl tensor, which was previously unnoticed. Full article

(This article belongs to the Special Issue Gravitational Waves: Prospects after the First Direct Detections)

524 KiB

Open AccessArticle

Dark Energy, QCD Axion, and Trans-Planckian-Inflaton Decay Constant

by Jihn E. Kim

Universe 2017, 3(4), 68; https://doi.org/10.3390/universe3040068 - 26 Sep 2017

Cited by 1 | Viewed by 4117

Abstract

Pseudoscalars appear frequently in particle spectra. They can be light if they appear as pseudo-Goldstone bosons from some spontaneously broken global symmetries with the decay constant f. Since any global symmetry is broken at least by quantum gravitational effects, all pseudoscalars are [...] Read more.

Pseudoscalars appear frequently in particle spectra. They can be light if they appear as pseudo-Goldstone bosons from some spontaneously broken global symmetries with the decay constant f. Since any global symmetry is broken at least by quantum gravitational effects, all pseudoscalars are massive. The mass scale of a pseudoscalar is determined by the spontaneous symmetry breaking scale f of the corresponding global symmetry and the explicit breaking terms in the effective potential. The explicit breaking terms can arise from anomaly terms with some non-Abelian gauge groups among which the best-known example is the potential of the QCD axion. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms in the potential in which case the leading term suppressed by f determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a quintessential axion. In the other extreme that the breaking scales are large, still the pseudo-Goldstone boson mass scales are in general smaller than the decay constants. In such a case, still the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model. We review these ideas in the bosonic collective motion framework. Full article

(This article belongs to the Special Issue Progress in Cosmology in the Centenary of the 1917 Einstein Paper)

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559 KiB

Open AccessArticle

A Unique Mathematical Derivation of the Fundamental Laws of Nature Based on a New Algebraic-Axiomatic (Matrix) Approach^‡

by Ramin Zahedi

Universe 2017, 3(4), 67; https://doi.org/10.3390/universe3040067 - 22 Sep 2017

Cited by 7 | Viewed by 3570

Abstract

In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Section 2), “it is shown that certain mathematical forms of [...] Read more.

In this article, as a new mathematical approach to origin of the laws of nature, using a new basic algebraic axiomatic (matrix) formalism based on the ring theory and Clifford algebras (presented in Section 2), “it is shown that certain mathematical forms of fundamental laws of nature, including laws governing the fundamental forces of nature (represented by a set of two definite classes of general covariant massive field equations, with new matrix formalisms), are derived uniquely from only a very few axioms.” In agreement with the rational Lorentz group, it is also basically assumed that the components of relativistic energy-momentum can only take rational values. In essence, the main scheme of this new mathematical axiomatic approach to the fundamental laws of nature is as follows: First, based on the assumption of the rationality of D-momentum and by linearization (along with a parameterization procedure) of the Lorentz invariant energy-momentum quadratic relation, a unique set of Lorentz invariant systems of homogeneous linear equations (with matrix formalisms compatible with certain Clifford and symmetric algebras) is derived. Then by an initial quantization (followed by a basic procedure of minimal coupling to space-time geometry) of these determined systems of linear equations, a set of two classes of general covariant massive (tensor) field equations (with matrix formalisms compatible with certain Clifford, and Weyl algebras) is derived uniquely as well. Full article

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