Static Universe Research Articles

Cosmological dynamics of dark energy in teleparallel gravity

In this paper, we study a cosmological model governed by a generalized scalar field nonminimally coupled to scalar torsion in the framework of teleparallel gravity. By applying the Noether symmetry approach, we attempt to explore the explicit forms of the coupling function and the scalar field potential in the Friedmann–Lemaitre–Robertson–Walker (FLRW) flat spacetime. The existence of such symmetry permits the equations of motion to take a simpler form and provides an exponential form cosmological solution for both the scale factor and scalar field. It is shown that the tachyon field behaves as the origin of inflation and contributes significantly to the accelerating expansion of the universe in the early times. While, in the late times, gravitational sources are a pressureless matter field together with the tachyon field, which plays the essential role of dark energy and is the origin of deceleration-acceleration phase transition. Later on, it is also shown that the present model contains a cosmological degeneracy in the sense that different coupling parameters and tachyonic potentials can contribute to the same cosmological behaviors such as the cosmic acceleration, age, equation of state and mean Hubble of FLRW universe.

ON THE 100TH ANNIVERSARY OF MATHEMATICAL COSMOLOGY

Mathematical cosmology is that branch of theoretical physics where some of the most intricate, complex, and deeply unresolved issues lie. Beginning with the Einstein static universe in 1917, in this brief paper we freely float above all major developments that shaped the field until today. We discuss highlights that are further documented in the authors’ recent survey ‘100 years of mathematical cosmology’ scheduled to appear in the Theme Issue ‘The Future of Mathematical Cosmology’. This Theme Issue is to be published in two parts by the Philosophical Transactions of the Royal Society A, and contain a number of important contributions by key researchers in the field.

High efficient pH-universal photo-Fenton degradation of antibiotics by amorphous FeSiB microspheres decorated TiO2 nanowire hybrid film

Immobilized reactors with catalyst films fixed in are widely used for photodegradation of water pollutants, in which the photocatalyst film is critical for the reactors’ performance. In this work, trace amount of amorphous FeSiB microspheres decorated TiO2 nanowires hybrid films were fabricated by the simple painting method, and they exhibit excellent photodegradability for antibiotic contaminants. The heterogenous photocatalytic films were characterized by microscopic, spectroscopic and photoelectrochemical techniques, and were demonstrated with great tetracycline degradation at universal pH conditions between 2 and 12. By optimizing the FeSiB content in the composite film, it was found that the film containing 1 wt% FeSiB exhibited the best performance with the tetracycline degradation efficiencies of 98.2% (pH = 2) and 85.5% (pH = 12) within 4 h. Furthermore, the FeSiB/TiO2 hybrid films exhibited a high degradation efficiency of > 80% after 3 recycling, and the enhanced reusability was attributed to the corrosion resistance of FeSiB microspheres wound by the TiO2 nanowires. This study combines the merits of FeSiB metallic glass and TiO2 nanowires to improve their degradation performance of antibiotics through building the Z-Scheme FeSiB-TiO2 heterojunction, which accelerated the separation of photogenerated electrons/holes on the photocatalyst films and the conversion between Fe2+ and Fe3+ in the photo-Fenton reactions.

The Impact of Observing Strategy on Cosmological Constraints with LSST

Abstract The generation-defining Vera C. Rubin Observatory will make state-of-the-art measurements of both the static and transient universe through its Legacy Survey for Space and Time (LSST). With such capabilities, it is immensely challenging to optimize the LSST observing strategy across the survey’s wide range of science drivers. Many aspects of the LSST observing strategy relevant to the LSST Dark Energy Science Collaboration, such as survey footprint definition, single-visit exposure time, and the cadence of repeat visits in different filters, are yet to be finalized. Here, we present metrics used to assess the impact of observing strategy on the cosmological probes considered most sensitive to survey design; these are large-scale structure, weak lensing, type Ia supernovae, kilonovae, and strong lens systems (as well as photometric redshifts, which enable many of these probes). We evaluate these metrics for over 100 different simulated potential survey designs. Our results show that multiple observing strategy decisions can profoundly impact cosmological constraints with LSST; these include adjusting the survey footprint, ensuring repeat nightly visits are taken in different filters, and enforcing regular cadence. We provide public code for our metrics, which makes them readily available for evaluating further modifications to the survey design. We conclude with a set of recommendations and highlight observing strategy factors that require further research.

On Universal D-Semifaithful Coding for Memoryless Sources With Infinite Alphabets

The problem of variable length and fixed-distortion universal source coding (or D-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets ($\infty$-alphabets) is addressed in this paper. The main results of this work offer a set of sufficient conditions (from weaker to stronger) to obtain weak minimax universality, strong minimax universality, and corresponding achievable rates of convergences for the worse-case redundancy for the family of stationary memoryless sources whose densities are dominated by an envelope function (or the envelope family) on $\infty$-alphabets. An important implication of these results is that universal D-semifaithful source coding is not feasible for the complete family of stationary and memoryless sources on $\infty$-alphabets. To demonstrate this infeasibility, a sufficient condition for the impossibility is presented for the envelope family. Interestingly, it matches the well-known impossibility condition in the context of lossless (variable-length) universal source coding. More generally, this work offers a simple description of what is needed to achieve universal D-semifaithful coding for a family of distributions $\Lambda$. This reduces to finding a collection of quantizations of the product space at different block-lengths -- reflecting the fixed distortion restriction -- that satisfy two asymptotic requirements: the first is a universal quantization condition with respect to $\Lambda$, and the second is a vanishing information radius (I-radius) condition for $\Lambda$ reminiscent of the condition known for lossless universal source coding.

The Nonlinear Field Equation of the Three-point Correlation Function of Galaxies: to the Second Order of Density Perturbation

Based on the field theory of density fluctuation under Newtonian gravity, we obtain analytically the nonlinear equation of 3-pt correlation function ζ of galaxies in a homogeneous, isotropic, static universe. The density fluctuation has been kept up to second order. By the Fry–Peebles ansatz and the Groth-Peebles ansatz, the equation of ζ becomes closed and differs from the Gaussian approximate equation. Using the boundary condition inferred from the data of SDSS, we obtain the solution ζ(r, u, θ) at fixed u = 2, which exhibits a shallow U-shape along the angle θ and, nevertheless, decreases monotonously along the radial r. We show its difference with the Gaussian solution. As a direct criterion of non-Gaussianity, the reduced Q(r, u, θ) deviates from the Gaussianity plane Q = 1, exhibits a deeper U-shape along θ and varies weakly along r, agreeing with the observed data.

Reconstruction of modified Gauss–Bonnet gravity for emergent universe

We present a flat emergent universe model in modified Gauss–Bonnet gravity in four dimensions. The emergent universe model is free from a big-bang singularity and also describes the observed universe fairly well. It is assumed that the present universe emerged from a static Einstein universe phase that exists in the infinite past. To obtain the flat emergent universe model, we reconstruct mimetic modified [Formula: see text]-gravity ([Formula: see text] representing Gauss–Bonnet terms). The functional form of [Formula: see text]-gravity is determined with or without matter, and can accommodate the early inflation and late accelerating phases satisfactorily. In contrast, in Einstein’s general theory of relativity, a flat emergent universe was obtained within the modified matter sector.

100 years of mathematical cosmology: Models, theories, and problems, Part A.

An elementary survey of mathematical cosmology is presented. We cover certain key ideas and developments in a qualitative way, from the time of the Einstein static universe in 1917 until today. We divide our presentation into four main periods, the first one containing important cosmologies discovered until 1960. The second period (1960–80) contains discussions of geometric extensions of the standard cosmology, singularities, chaotic behaviour and the initial input of particle physics ideas into cosmology. Our survey for the third period (1980–2000) continues with brief descriptions of the main ideas of inflation, the multiverse, quantum, Kaluza-Klein and string cosmologies, wormholes and baby universes, cosmological stability and modified gravity. The last period that ends today includes various more advanced topics such as M-theoretic cosmology, braneworlds, the landscape, topological issues, the measure problem, genericity, dynamical singularities and dark energy. We emphasize certain threads that run throughout the whole period of development of theoretical cosmology and underline their importance in the overall structure of the field. This is Part A of our survey covering the first two periods of development of the subject. The second part will include the third and fourth periods. We end this outline with an inclusion of the abstracts of all papers contributed to the Philosophical Transactions of the Royal Society A theme issue, ‘The Future of Mathematical Cosmology’.This article is part of the theme issue ‘The future of mathematical cosmology, Volume 1’.

Optical properties of Mo and amorphous MoOx, and application to antireflection coatings for metals

To form antireflection (AR) coatings to hide metal architecture in display technologies, we deposited thin films of metal Mo and oxide MoOx by sputtering targets of various compositions using pure Ar sputter gas. The optical constants [n,k] of these samples were measured by the direct numerical solution of reflectance and transmittance at each wavelength point measured. We find that 50 nm films are uniform in the growth direction, but for thicker 100 nm samples, evidence exists for nonuniform growth, where the top 20 nm appears to be metal rich. From these [n,k], negative Tauc bandgap energies show these oxides are semi-metals. We then identified the specific composition (x) that optimizes the AR response for a host of metals (Al, Cu, Ag, Au). Finally, two methods were used to understand why these MoOx materials function well as AR media, including (i) using phasor rays and (ii) developing a universal expression for the AR condition that applies to both dielectric and metal substrates. In (i), we find two characteristics for AR of metals: (a) its optical thickness should be roughly π3, not the π2 for dielectrics, since for MoOx, their [r^ij,t^ij] Fresnel phases differ from the usual [180°, 0°] of dielectrics; and (b) the medium incorporates a k-dominant strategy whose function is to absorb the energy that is reflected at the AR/metal interface. In (ii), the universal AR condition is found to be r^01+r^12z^=0. For dielectrics, this reduces to the well-known nAR=nairnsub condition. However, for metals, a concise analytic expression is lacking since this expression is highly nonlinear but is easily solved by numerical methods.

Rentals for Housing: A Property Fixed-Effects Estimator of Inflation from Administrative Data

Abstract Official rentals for housing (rent) price inflation statistics are of considerable public interest. Matched-sample estimators, such as that used for nearly two-decades in New Zealand (2000–2019), require an unrealistic assumption of a static universe of rental properties. This article investigates (1) a property fixed-effects estimator that better reflects the dynamic universe of rental properties by implicitly imputing for price change associated with new and disappearing rental properties; (2) length-alignment simulations and property life-cycle metrics to inform the choice of data window length (eight years) and preferred splice methodology (mean-splice); and (3) stock-imputation to convert administrative data from a ‘flow’ (new tenancy price) to ‘stock’ (currently paid rent) concept. The derived window-length sensitivity findings have important implications for inflation measurement. It was found that the longer the data window used to fit the model, the greater the estimated rate of inflation. Using administrative data, a range of estimates from 55% (window length: three-quarters) to 127% (window of 90-quarters) were found for total inflation, over the 25-years to 2017 Q4.

Bubble universes and traversable wormholes

Bubble universes and traversable wormholes in general relativity can be realized as two sides of the same concept. To exemplify, we find, display, and study in a unified manner a Minkowski-Minkowski closed universe and a Minkowski-Minkowski traversable wormhole. By joining two 3-dimensional flat balls along a thin shell two-sphere of matter, i.e., a spherical domain wall, into a single spacetime one gets a Minkowski-Minkowski static closed universe, i.e., a bubble universe. By joining two 3-dimensional complements of flat balls along a thin shell two-sphere of matter, i.e., a spherical throat, into a single spacetime one gets a Minkowski-Minkowski static open universe which is a traversable wormhole. Thus, Minkowski-Minkowski bubble universes and wormholes can be seen as complementary. It is also striking that these two spacetimes have resemblances with two well-known static universes. The Minkowski-Minkowski static closed universe resembles the Einstein universe, a static closed spherical universe homogeneously filled with dust matter and with a cosmological constant. The Minkowski-Minkowski static open universe resembles the Friedmann static universe, a static open hyperbolic universe homogeneously filled with negative energy density dust and with a negative cosmological, a universe with two disjoint branes that can be considered a failed wormhole. In this light, the Einstein and Friedmann universes are also two sides of the same concept. A linear stability analysis for all these spacetimes is performed. The complementarity between bubble universes and traversable wormholes, that exists for these static spacetimes, can be can carried out for dynamical spacetimes, indicating that such a complementarity is general. The study suggests that bubble universes and traversable wormholes can be seen as coming out of the same concept, and thus, if ones exist the others should also exist.

Phase-matching condition in rotatory nonlinear optics

Polarization rotation of light beams, such as optical activity and Faraday rotation, is a natural effect that generates the rotation of the polarized direction of light and some undiscovered characteristics in nonlinear optics. In our previous study, we theoretically investigated the second-harmonic generation process in rotatory nonlinear optics and found an unprecedented phase-matching condition. Here, the optical phase-matching condition in the second-harmonic generation with rotatory polarization is theoretically analyzed and associated with the angular rotation-induced phases of mixing waves, which goes beyond the previous theoretical analysis. Moreover, the Pancharatnam-Berry topological phase was found to be periodically generated and could be employed to compensate for the mismatched phase during nonlinear optical interaction. Possible experimental schemes were proposed and discussed. This work provides not only a universal and flexible (quasi-) phase-matching condition for the rotatory nonlinear optics existing in most nonlinear optical media but may also inspire the development of modern photonics.

Training Future Primary School Teachers to Organize Game-Based Music Activities

The article analyzes the current role of a game as a universal cognitive method based on relevant literary sources to justify the need to reform the system of professional training for primary school teachers. The article aims to develop, theoretically justify and experimentally verify the newly modelled pedagogical conditions for training future primary school teachers to organize game-based music activities of primary school pupils, as well as methods of implementing these conditions in teacher education. Importantly, the article demonstrates how the author’s methodology for implementing these pedagogical conditions has been developed, implemented and quasiexperimentally verified. As part of preliminary, technological-practical, and creative-organizational stages of such professional training, the new model involves the consistent use of the author’s techniques and algorithms to organize students’ activities in the framework of professional-oriented courses, research projects, as well as an optional course “Practice of Organizing Game-Based Music Activities for Primary School Pupils”. The international relevance of the article lies in developing and implementing universal educational conditions to train future primary school teachers to organize game-based music activities under today’s conditions of globalization and informatization. The obtained data indicate some positive changes in quasi-experimental groups due to the implemented pedagogical conditions at the final stage of the research.

Inhomogeneous generalization of Einstein’s static universe with Sasakian space

Abstract We construct exact static inhomogeneous solutions to Einstein’s equations with counter flow of particle fluid and a positive cosmological constant by using the Sasaki metrics on three-dimensional spaces. The solutions, which admit an arbitrary function that denotes the inhomogeneous number density of particles, are a generalization of Einstein’s static universe. For some examples of explicit solutions, we discuss non-linear density contrast and deviation of the metric functions.

General Conditions for Universality of Quantum Hamiltonians

Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on explicit constructions, tailored to each specific family of universal Hamiltonians. In this work we go beyond this approach, and completely classify the simulation ability of quantum Hamiltonians by their complexity classes. We do this by deriving necessary and sufficient complexity theoretic conditions characterising universal quantum Hamiltonians. Although the result concerns the theory of analogue Hamiltonian simulation - a promising application of near-term quantum technology - the proof relies on abstract complexity theoretic concepts and the theory of quantum computation. As well as providing simplified proofs of previous Hamiltonian universality results, and offering a route to new universal constructions, the results in this paper give insight into the origins of universality. For example, finally explaining the previously noted coincidences between families of universal Hamiltonian and classes of Hamiltonians appearing in complexity theory.

A quantum state for the late Universe

We consider the quantum description of a toy model universe in which the Schwarzschild-de Sitter geometry emerges from the coherent state of a massless scalar field. Although highly idealised, this simple model allows us to find clear hints supporting the conclusion that the reaction of the de Sitter background to the presence of matter sources induces i) a modified Newtonian dynamics at galactic scales and ii) different values measured for the present Hubble parameter. Both effects stem from the conditions required to have a normalisable quantum state.

Generalized tachyonic dark energy

In this paper, a generalized tachyonic dark energy scenario is presented in the framework of a homogeneous and isotropic Friedmann–Lemaître–Robertson–Walker (FLRW) flat universe, in which a noncanonical scalar field is coupled to gravity nonminimally. By utilizing the Noether symmetry method, we found the explicit form of both potential density and coupling function, as a function of the scalar field. It is found that the tachyon field acts as the source of inflation and accelerates the evolution of the universe in the early times considerably. While, in the late times, gravitational sources are a pressureless matter field together with the tachyon field, which is the nature of dark energy and plays an essential role in the deceleration-acceleration phase transition of the universe. Further, the role of the coefficient function of tachyon potential, alongside the potential, is considered in the evolution of the universe. It is shown that this model involves a cosmological degeneracy in the sense that different coupling parameters and tachyonic potentials may be equivalent to the same cosmological standards such as the cosmic acceleration, age, equation of state and mean Hubble of the FLRW universe. The physical characteristics of the main cosmological observables are studied in detail, which suggests that the generalized tachyon field is a remarkable dark energy candidate.

Feature Selection and Detection Method of Weak Arc Faults in Photovoltaic Systems With Strong Noises Based on Stochastic Resonance

Due to strong noises from system components and measurement devices, arc faults would become weak to bring about detection challenges. Therefore, new measurements should be taken to acquire obvious arc fault features under complex operation disturbances in photovoltaic application scenes. In this paper, weak arc fault signals are acquired from the designed experimental and simulation platform with different system structures and signal acquisition devices firstly. Arc fault features would become weak in initial transient arc fault stages and higher frequency bands above 15.6 kHz, which could not be directly acquired by applying designed digital filters with existing wavelets. Next, the ant colony algorithm based stochastic resonance (ACA-SR) method is proposed to enhance arc fault features, which is verified to be effective under various inverter and resistor conditions. Then the feature enhancement ability of stochastic resonance method is evaluated to select the optimal arc fault feature, which is proved to have the average feature enhancement ability of 3.23 times. The selected wavelet is proved to have the superiority of symmetry and shorter support width. Finally, the proposed method is conducted with universal conditions containing weak arc faults via numerical and hardware tests, which is proved to improve the detection accuracy of arc faults by 24.57% on average respectively compared with existing methods.

Rapid and specific detection of Trichophyton rubrum and Trichophyton mentagrophytes using a loop-mediated isothermal amplification assay

Trichophyton rubrum and Trichophyton mentagrophytes are the main causative pathogens of onychomycosis. However, the sensitivity and specificity of conventional microscopic tests are insufficient for reliable diagnoses of onychomycosis. In this study, we developed loop-mediated isothermal amplification (LAMP) assays for the rapid and specific identification of the two major Trichophytons spp. We designed LAMP primers targeting the internal transcribed spacer 1 region of the T. rubrum and T. mentagrophytes. Through rigorous optimization of the reaction conditions, we defined a universal reaction condition for both LAMP assays.

An all-inclusive approach: A universal protocol for the successful amplification of four genetic loci of all Onscidea

Accounting more than 3,700 described species, Oniscidea is the largest and at the same time the only terrestrial isopod suborder inhabiting almost all terrestrial biomes. Despite the great effort dedicated on describing taxonomic diversity of Oniscidea, mainly employing morphology, there is still a considerable number of species/genera of uncertain generic/familiar assignment. Based on different morphological characters, alternative evolutionary relationships have been proposed to describe the diversity of Oniscidea at different phylogenetic levels. Accumulating morphological and genetic data are repeatedly challenging the monophyly of established taxa, undermining the validity of several morphological characters traditionally used in terrestrial isopod taxonomy, leading to often revisions of the current taxonomy of the Oniscidea . The use of genetic data facilitates the efforts to reconstruct the complex evolutionary history of the focal group by providing important data for the identification, delimitation, and description of species. The proposed protocol with universal PCR conditions and primers was used to successfully amplify COI, 16S, 28S and NAK loci in diverse Oniscidea taxa. The application of this protocol is anticipated to facilitate the generation of new genetic data and hence promote scientific research in Isopoda taxonomy, evolution, ecology, and other related fields.