Classical Cosmology II. The Einstein Ring

The Einstein ring is usually explained in the framework of the gravitational lens. Conversely here we apply the framework of the expansion of a superbubble (SB) in order to explain the spherical appearance of the ring. Two classical equations of motion for SBs are derived in the presence of a linear and a trigonometric decrease for density. A relativistic equation of motion with an inverse square dependence for the density is derived. The angular distance, adopting the minimax approximation, is derived for three relativistic cosmologies: the standard, the flat and the wCDM. We derive the relation between redshift and Euclidean distance, which allows fixing the radius of the Einstein ring. The details of the ring are explained by a simple version of the theory of images.

Legendre-Jacobi’s Elliptic Integrals Shed Light on the Luminosity Distance in Cosmology

This article concerns the integral related to the transverse comoving distance and, in turn, to the luminosity distance both in the standard non-flat and flat cosmology. The purpose is to determine a straightforward mathematical formulation for the luminosity distance as function of the transverse comoving distance for all cosmology cases with a non-zero cosmological constant by adopting a different mindset. The applied method deals with incomplete elliptical integrals of the first kind associated with the polynomial roots admitted in the comoving distance integral according to the scientific literature. The outcome shows that the luminosity distance can be obtained by the combination of an analytical solution followed by a numerical integration in order to account for the redshift. This solution is solely compared to the current Gaussian quadrature method used as basic recognized algorithm in standard cosmology.

Classical Cosmology I. Anomalous Redshift for Galaxies in NED-D

Three mechanisms for an alternative to the Doppler effect as an explanation for the redshift are reviewed. A fourth mechanism is the attenuation of the light as given by the Beer-Lambert law. The average value of the Hubble constant is therefore derived by processing the galaxies of the NED-D catalog in which the distances are independent of the redshift. The observed anisotropy of the Hubble constant is reproduced by adopting a rim model, a chord model, and both 2D and 3D Voronoi diagrams.

Classical Cosmology III. Modified Tired Light and Distance Modulus for Supernovae

We analyze a simple model for tired light in a cosmological environment, a generalized model, and a spectroscopic model. The three models are tested on different compilations for the distance modulus of supernovae. The tests are negative for the simple tired light and the spectroscopic models, but positive for the generalized tired light model. The percentage error of the distance modulus for the generalized tired light model compared with the distance modulus of standard cosmology is less than one percent over the considered ranges in redshift.

Upsilon Constants and Their Usefulness in Planck Scale Quantum Cosmology

This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.

How the Flat Space Cosmology Model Correlates the Recombination CMB Temperature of 3000 K with a Redshift of 1100

This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the Tatum and Seshavatharam Hubble temperature formulae can be derived using the Stephan-Boltzmann dispersion law. Thus, as explained herein, the era of high precision Planck scale quantum cosmology has arrived.

The Tension Cosmology, Largest Cosmic Structures and Explosions of Supernovae from SST

Here, using the Scale-Symmetric Theory (SST) we explain the cosmological tension and the origin of the largest cosmic structures. We show that a change in value of strong coupling constant for cold baryonic matter leads to the disagreement in the galaxy clustering amplitude, quantified by the parameter S8. Within the same model we described the Hubble tension. We described also the mechanism that transforms the gravitational collapse into an explosion—it concerns the dynamics of virtual fields that lead to dark energy. Our calculations concern the Type Ia supernovae and the core-collapse supernovae. We calculated the quantized masses of the progenitors of supernovae, emitted total energy during explosion, and we calculated how much of the released energy was transferred to neutrinos. Value of the speed of sound in the strongly interacting matter measured at the LHC confirms that presented here model is correct. Our calculations show that the Universe is cyclic.

Cosmology without the Cosmological Principle and without Violating the Copernican Principle: Taub-NUT Universe

We develop a theory of cosmology, which is not based on the cosmological principle. We achieve this without violating the Copernican principle. It is well known that the gravitational redshift associated with the Schwarzschild solution applied to the distant supernova does not lead to the observed redsift-distance relationship. We show, however, that generalizations of the Schwarzschild metric, the Taub-NUT metrics, do indeed lead to the observed redshift-distance relationship and to the observed time dilation. These universes are not expanding rather the observed cosmological redshift is due to the gravitational redshift associated with these solutions. Time dilation in these stationary universes has the same dependency on redshift that generally has been seen as proof that space is expanding. Our theory resolves the Hubble tension.

Time Dilation Cosmology 2

This paper is a further elaboration of the author’s Time Dilation Cosmology (TDC) holographic model that ties gravitation and celestial mechanics and kinematics directly to time dilation, resolving all the major conundrums in astrophysics, and ties astrophysics directly to quantum physics. It begins with a brief summary of the TDC model and contains the new derivation for the time dilation version of the formula for summing relativistic velocities, Einstein’s gravitational constant and the time dilation versions for the Lorentz factor and the Euclidean norm of the 3d velocity vector, the two of which can then be used in the Four-velocity formula. It is demonstrated how orbital curvature is manifested as the resultant of two time dilation-manifested velocities. It also explains why an interferometer cannot distinguish free fall from zero gravity and further elaborates on the author’s previous explanations of how spiral galaxies are formed, and contains mathematical proof that Black Holes are actually Magnetospheric Eternally Collapsing Objects (MECOs) that are massless spacetime vortices.

On Some Mathematical Connections between the Cyclic Universe, Inflationary Universe, p-Adic Inflation, p-Adic Cosmology and Various Sectors of Number Theory

This paper is a review, a thesis, of some interesting results that have been obtained in various research concerning the “brane collisions in string and M-theory” (Cyclic Universe), p-adic inflation and p-adic cosmology. In Section 2, we have described some equations concerning cosmic evolution in a Cyclic Universe. In Section 3, we have described some equations concerning the cosmological perturbations in a Big Crunch/Big Bang space-time, the M-theory model of a Big Crunch/Big Bang transition and some equations concerning the solution of a braneworld Big Crunch/Big Bang Cosmology. In Section 4, we have described some equations concerning the generating ekpyrotic curvature perturbations before the Big Bang, some equations concerning the effective five-dimensional theory of the strongly coupled heterotic string as a gauged version of N=1five-dimensional supergravity with four-dimensional boundaries, and some equations concerning the colliding branes and the origin of the Hot Big Bang. In Section 5, we have described some equations regarding the “null energy condition” violation concerning the inflationary models and some equations concerning the evolution to a smooth universe in an ekpyrotic contracting phase with w>1. In Section 6, we have described some equations concerning the approximate inflationary solutions rolling away from the unstable maximum of p-adic string theory. In Section 7, we have described various equations concerning the p-adic minisuperspace model, zeta strings, zeta nonlocal scalar fields and p-adic and adelic quantum cosmology. In Section 8, we have shown various and interesting mathematical connections between some equations concerning the p-adic inflation, the p-adic quantum cosmology, the zeta strings and the brane collisions in string and M-theory. Furthermore, in each section, we have shown the mathematical connections with various sectors of Number Theory, principally the Ramanujan’s modular equations, the Aurea Ratio and the Fibonacci’s numbers.

类Chen-Qi混沌系统的固定时间自适应同步控制

类Chen-Qi四维混沌系统的渐近稳定控制的同步误差不能在有限时间内收敛到零,有限时间控制的同步误差收敛到零的状况与初值有关.因此,本文应用固定时间控制技术,设计了自适应控制器和参数估计律,试图使得驱动系统与同类型的参数未知的响应系统在固定时间内达到同步,完成了理论证明.应用数值仿真考察同步误差收敛到零的状况.选取不同参数值,不同状态初值,考察状态时程图、同步误差曲线等.结果表明:混沌运动时,固定时间内同步误差收敛到零的效果较好,与状态初值无关,收敛时间符合理论计算值;周期运动时,固定时间内前三个状态的同步误差收敛到零的效果较好,收敛时间符合理论计算值,但第四个状态的同步误差的收敛时间不符合理论计算值,其原因是系统存在的三次非线性项的不平衡、不匹配.

Cosmology of a Chaplygin Gas Model Under f(T)Gravity and Evolution of Primordial Perturbations

This paper reports a detailed study of generalized Chaplygin gas(GCG)with power law form of scale factor and truncated form of the scale factor using binomial expansion in both interacting and non-interacting scenarios along with its cosmological consequences,studied in terms of equation of state(EoS)parameter.In the non-interacting scenario,the EoS parameter behaves as quintessence in both forms of the scale factor.In the interacting scenario,the EoS parameter behaves as phantom and for the truncated form of the scale factor,it violates the constraints of the positive parameterα.The cosmological implementation of GCG interacting with pressureless dark matter is investigated in the framework of f(T)modified gravity,where T is the torsion scalar in teleparallelism.The interaction term is directly proportional to the GCG density with positive coupling constant.In f(T)gravity,the EoS is behaving like phantom.The stability of the reconstructed model is investigated and it is found to be stable against small gravitational perturbations,i.e.,the squared speed of sound is non-negative and an increasing function of cosmic time t.We have observed that our reconstructed f(T)model satisfies one of the sufficient conditions of a realistic reconstructed model and it is consistent with the CMB constraints and primordial nucleosynthesis.Cosmology of primordial perturbations has also been analyzed and the self-interacting potential has been found to be an increasing function of cosmic time t.

Trials to Resolve Black Holes Instabilities in Brane World Cosmology Models

In this letter, we report on our trials to remove the instability of black holes in brane world cosmological models consisting of two branes and a bulk. In order to resolve this problem, general types of interaction potentials were employed. Careful analyses have shown that although the black holes instabilities were removed, a sort of arbitrariness adherent to the motion of the two branes towards each other has taken place leading to an unstable system. Thus, the models seem to us rather paradoxical.

Time Dilation Cosmology

This model ties gravitation and celestial mechanics and kinematics directly to time dilation. It is a new theory of cosmology and the evolution of galaxies. Space and time are not two separate things, but two aspects of a single thing, “spacetime”. Whatever affects space, affects time, and vice-versa. If time speeds up, space must contract to maintain the speed of light, c, and when space thickens into a mass, it is harder to evolve forward, and time appears to slow. If spatial events are spinning as time passes, then the forward direction of time is spinning. This is Einstein’s curvature in the forward direction of time. Herein, the basis is outlined for time dilation cosmology in a spacetime/quantum continuum, including the time dilation-based derivation of the mass of the Cosmic Microwave Background Radiation (CMBR), and time dilation formulas are derived for stellar system orbital, and galactic rotation, velocities, the force in time in Newtons, the Hamiltonian, the Hubble shift, the empirical gravitational constant, G, and other formulas, showing their direct relationship to the difference in the rate of time between the far distant observer’s invariant 1 s/s rate of time and the slower rate of time at the coordinate point, proving the universe is not composed of separate bodies moving through space, but is an evolving 3-dimensional holographic continuum containing varying densities evolving forward in the forward direction of time, the 4th dimension, at apparently different rates of time, the velocities merely being compensation for those slower rates of time in a continuum evolving forward overall at c, which is why light propagates at c, even from a moving source. As per General Relativity, if there is no rate of time difference between coordinate points, there is no gravitational attraction between those points, and no gravitationally induced velocity. This model resolves all the major conundrums in astrophysics, eliminating Dark Energy and Dark Matter, and ties astrophysics directly to quantum physics.

Cosmological Constraints on Neutrino Masses in Light of JWST Red and Massive Candidate Galaxies

The overabundance of the red and massive candidate galaxies observed by the James Webb Space Telescope(JWST)implies efficient structure formation or large star formation efficiency at high redshift z~10.In the scenario of a low or moderate star formation efficiency,because massive neutrinos tend to suppress the growth of structure of the universe,the JWST observation tightens the upper bound of the neutrino masses.Assuming A cold dark matter cosmology and a star formation efficiency∈[0.05,0.3](flat prior),we perform joint analyses of Planck+JWST and Planck+BAO+JWST,and obtain improved constraints∑m_(ν)<0.196 eV and ∑m_(ν)+<0.111 eV at 95% confidence level,respectively.Based on the above assumptions,the inverted mass ordering,which implies ∑m_(ν)≥0.1 eV,is excluded by Planck+BAO+JWST at 92.7% confidence level.

Decisive Role of Gravitational Parameter G in Cosmology

In 1937, P. Dirac proposed the Large Number Hypothesis and the Hypothesis of the variable gravitational “constant”, and later added the notion of continuous creation of Matter in the World. The Hypersphere World-Universe Model (WUM) follows these ideas, albeit introducing a different mechanism of Matter creation. In this paper, we show that Gravitational parameter G that can be measured directly makes measurable all Cosmological parameters, which cannot be measured directly.

Quantifying the Tension between Cosmological Models and JWST Red Candidate Massive Galaxies

We develop a Python tool to estimate the tail distribution of the number of dark matter halos beyond a mass threshold and in a given volume in a light-cone.The code is based on the extended Press-Schechter model and is computationally efficient,typically taking a few seconds on a personal laptop for a given set of cosmological parameters.The high efficiency of the code allows a quick estimation of the tension between cosmological models and the red candidate massive galaxies released by the James Webb Space Telescope,as well as scanning the theory space with the Markov Chain Monte Carlo method.As an example application,we use the tool to study the cosmological implication of the candidate galaxies presented in Labbéet al.The standard Λcold dark matter(ΛCDM)model is well consistent with the data if the star formation efficiency can reach~0.3 at high redshift.For a low star formation efficiency ε~0.1,theΛCDM model is disfavored at~2σ-3σconfidence level.

Prospects of the Multi-channel Photometric Survey Telescope in the Cosmological Application of Type Ia Supernovae

The Multi-channel Photometric Survey Telescope(Mephisto)is a real-time,three-color photometric system designed to capture the color evolution of stars and transients accurately.This telescope system can be crucial in cosmological distance measurements of low-redshift(low-z,z■0.1)Type Ia supernovae(SNe Ia).To optimize the capabilities of this instrument,we perform a comprehensive simulation study before its official operation is scheduled to start.By considering the impact of atmospheric extinction,weather conditions,and the lunar phase at the observing site involving the instrumental features,we simulate light curves of SNe Ia obtained by Mephisto.The best strategy in the case of SN Ia cosmology is to take the image at an exposure time of 130 s with a cadence of 3 days.In this condition,Mephisto can obtain hundreds of high-quality SNe Ia to achieve a distance measurement better than 4.5%.Given the on-time spectral classification and monitoring of the Lijiang 2.4 m Telescope at the same observatory,Mephisto,in the whole operation,can significantly enrich the well-calibrated sample of supernovae at low-z and improve the calibration accuracy of high-z SNe Ia.

Cosmological Redshift Caused by Head-On Collisions with CMB Photons, Not by Expansion of Space

The Big Bang model was first proposed in 1931 by Georges Lemaitre. Lemaitre and Hubble discovered a linear correlation between distances to galaxies and their redshifts. The correlation between redshifts and distances arises in all expanding models of universe as the cosmological redshift is commonly attributed to stretching of wavelengths of photons propagating through the expanding space. Fritz Zwicky suggested that the cosmological redshift could be caused by the interaction of propagating light photons with certain inherent features of the cosmos to lose a fraction of their energy. However, Zwicky did not provide any physical mechanism to support his tired light hypothesis. In this paper, we have developed the mechanism of producing cosmological redshift through head-on collision between light and CMB photons. The process of repeated energy loss of visual photons through n head-on collisions with CMB photons, constitutes a primary mechanism for producing the Cosmological redshift z. While this process results in steady reduction in the energy of visual photons, it also results in continuous increase in the number of photons in the CMB. After a head-on collision with a CMB photon, the incoming light photon, with reduced energy, keeps moving on its original path without any deflection or scattering in any way. After propagation through very large distances in the intergalactic space, all light photons will tend to lose bulk of their energy and fall into the invisible region of the spectrum. Thus, this mechanism of producing cosmological redshift through gradual energy depletion, also explains the Olbers’s paradox.

On a Cosmological Model with Variable Time Flow

The Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of the Einstein field equations and it describes a homogeneous, isotropic and expanding universe. The FLRW metric and the Friedmann equations form the basis of the ΛCDM model. In this article, a metric which is based on the FLRW metric and that includes a space scale factor and a newly introduced time scale factor T(t)is elaborated. The assumption is that the expansion or contraction of the dimensions of space and time in a homogeneous and isotropic universe depend on the energy density. The Christoffel symbols, Ricci tensor and Ricci scalar are derived. By evaluating the results using Einstein’s field equations and the energy momentum tensor, a hypothetical modified cosmological model is obtained. This theoretical model provides for a cosmic inflation, the accelerated expansion of spacetime as well avoids the flatness and fine-tuning problems.