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.

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.

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.

Predicting Dark Energy Survey Results within the Haug-Tatum Cosmology Model

Given the pending completion and publication of the final Dark Energy Survey (DESI) results, this letter presents the corresponding predictions of the Haug-Tatum cosmology (HTC) model. In particular, we show in tabular and graphic form the “dark energy decay” curve which the HTC model predicts for cosmological redshifts covering the range of 0 - 2.0 z. Furthermore, we present the HTC model distance-vs-redshift curve in comparison to the three very different curves (for luminosity distance, angular diameter distance, and co-moving distance) calculated within the Lambda-CDM model. Whether the expansion of our universe is actually undergoing slight acceleration or the finely-tuned cosmic coasting at constant velocity of Rh = ct models, including HTC, will hopefully soon be answered by the many pending observational studies.

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.

Gravitational Wave Detection Technology Development and Its Contribution to Cosmology

Gravitational wave detection has ushered in a new era of observing the universe, providing humanity with a novel window for cosmic cognition. This theoretical study systematically traces the developmental trajectory of gravitational wave detection technology and delves into its profound impact on cosmological research. From Einstein’s prediction in general relativity to LIGO’s groundbreaking discovery, the article meticulously delineates the key theoretical and technological milestones in gravitational wave detection, with particular emphasis on elucidating the principles and evolution of core detection technologies such as laser interferometers. The research thoroughly explores the theoretical application value of gravitational waves in verifying general relativity, studying the physics of compact celestial bodies like black holes and neutron stars, and precisely measuring cosmological parameters. The article postulates that gravitational wave observations may offer new research perspectives for addressing cosmological conundrums such as dark matter, dark energy, and early universe evolution. The study also discusses the scientific prospects of combining gravitational wave observations with electromagnetic waves, neutrinos, and other multi-messenger observations, analyzing the potential value of this multi-messenger astronomy in deepening cosmic cognition. Looking ahead, the article examines cutting-edge concepts such as space-based gravitational wave detectors and predicts potential developmental directions for gravitational wave astronomy. This research not only elucidates the theoretical foundations of gravitational wave detection technology but also provides a comprehensive theoretical framework for understanding the far-reaching impact of gravitational waves on modern cosmology.

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.

Time Dilation Cosmology 3: Mathematical Proof of the 3 Temporal and 2 Spatial Acceleration Factors

This is the fifth paper in a series on Time Dilation Cosmology, TDC. TDC is an eternal holographic model of the universe based on time dilation that ties astrophysics to quantum physics and resolves all the conundrums in astrophysics and serves as a model for the unified field. In the author’s previous four TDC papers, it was demonstrated that all gravitationally induced velocities are compensation for the apparent difference in the rates of time, “dRt”, due to mass/energy densities, and, vice-versa, in all force-induced velocities the dRt is compensation for the velocity, so the uniform evolution of the continuum at c is maintained at the invariant 1 s/s rate of time of the universe as a whole. These compensations make it impossible for an event to lag behind or get ahead of the evolving continuum. When the author did the first velocity formula derivations in “General Relativity: Effects in Time as Causation” [1], the author felt the explanations for the appearance of the 2spatial and the 3temporal acceleration factors in the formulas were correct, but poorly explained and incomplete. This paper is a proof of the temporal and spatial acceleration factors used in the time dilation-based velocity formula derivations in the Time Dilation Cosmology model.

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.

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.

Friedmann Cosmology with a Generalized Equation of State and Bulk Viscosity

The universe content is considered as a non-perfect fluid with bulk viscosity and is described by a more general equation of state （endowed some deviation from the conventionally assumed cosmic perfect fluid model）. We assume the bulk viscosityis a linear combination of two terms： one is constant, and the other is proportional to the scalar expansion 0 = 3a/a. The equation of state is described as p = （γ - 1）p ＋ po, where po is a parameter. In this framework we demonstrate that this model can be used to explain the dark energy dominated universe, and different proper choices of the parameters may lead to three kinds of fates of the cosmological evolution： no future singularity, big rip, or Type-Ⅲ singularity as presented in IS. Nojiri, S.D. Odintsov, and S. Tsujikawa, Phys. Rev. D 71 （2005） 063004].

A critique of supernova data analysis in cosmology

Observational astronomy has shown significant growth over the last decade and has made important contributions to cosmology. A major paradigm shift in cosmology was brought about by observations of Type Ia supernovae. The notion that the universe is accelerating has led to several theoretical challenges. Unfortunately, although high-quality supernovae data-sets are being produced, their statistical anal- ysis leaves much to be desired. Instead of using the data to directly test the model, several studies seem to concentrate on assuming the model to be correct and limiting themselves to estimating model parameters and internal errors. As shown here, the important purpose of testing a cosmological theory is thereby vitiated.

Calculation of Quantum Probability in O（2,2） String Cosmology with a Dilaton Potential

The quantum properties of O（2,2） string cosmology with a dilaton potential are studied in this paper. The cosmological solutions are obtained on three-dlmensional space-time. Moreover, the quantum probability of transition between two duality universe is calculated through a Wheeler-De Witt approach.

Space Drive Propulsion Principle from the Aspect of Cosmology

This paper describes the propulsion principle using the concept of space drive and the pressure of the field induced by local rapid expansion of space based on the latest cosmology. Assuming that space vacuum is an infinite continuum, the propulsion principle utilizes the pressure field derived from the geometrical structure of space, by applying both continuum mechanics and general relativity to space. The propulsive force is a pressure thrust that arises from the interaction of space-time around the spaceship external environment and the spaceship itself; the spaceship is propelled by the pressure used against the space-time structure. As is well known in cosmology, the expansion rule of the universe is governed by the Friedman＇s equations and the Robertson-Walker metric. In this time, the propulsion principle of space drive is introduced from another angle （cosmology）, that is, the pressure of the field induced by local expansion of space is completely considered in the propulsion principle.

The Ring Produced by an Extra-Galactic Superbubble in Flat Cosmology

A superbubble which advances in a symmetric Navarro-Frenk-White density profile or in an auto-gravitating density profile generates a thick shell with a radius that can reach 10 kpc. The application of the symmetric and asymmetric image theory to this thick 3D shell produces a ring in the 2D map of intensity and a characteristic “U” shape in the case of 1D cut of the intensity. A comparison of such a ring originating from a superbubble is made with the Einstein’s ring. A Taylor approximation of order 10 for the angular diameter distance is derived in order to deal with high values of the redshift.

Friedmann Cosmology with Bulk Viscosity:A Concrete Model for Dark Energy

The universe content is considered as a non-perfect fluid with bulk viscosity and can be described by a general equation of state （endowed some deviation from the conventionally assumed cosmic perfect fluid model）. An explicitly bulk viscosity dark energy model is proposed to confront consistently with the current observational data sets by statistical analysis and is shown consistent with （not deviated away much from） the concordant A Cold Dark Matter （CDM） model by comparing the decelerating parameter. Also we compare our relatively simple viscosity dark energy model with a more complicated one by contrast with the concordant ACDM model and find our model improves for the viscosity dark energy model building. Finally we discuss the perspectives of dark energy probes for the coming years with observations.

A new interpretation of zero Lyapunov exponents in BKL time for Mixmaster cosmology

A global relationship between cosmological time and Belinskii-Khalatnikov -Lifshitz （BKL） time during the entire evolution of the Mixmaster Bianchi IX universe is used to explain why all the Lyapunov exponents are zero at the BKL time. The actual reason is that the domain of the cosmological time is finite as the BKL time runs from minus infinity to infinity.