Observable Universe Research Articles

Propagation and fluxes of ultra-high energy cosmic rays in f(R)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{f(R)}$$\\end{document} gravity theory

In this work, we study the effect of diffusion of ultra-high energy cosmic ray (UHECR) protons in the presence of turbulent magnetic fields (TMFs) in the light of the f(R) theory of gravity. The f(R) theory of gravity is a successful modified theory of gravity in explaining the various aspects of the observable Universe including its current state of expansion. For this work, we consider two most studied f(R) gravity models, viz., the power-law model and the Starobinsky model. With these two models, we study the diffusive character of the propagation of UHECR protons in terms of their density enhancement. The density enhancement is a measure of how the density of CRs changes due to their diffusion in the intergalactic medium and interaction with the cosmic microwave background (CMB) radiation. Ankle, instep and Greisen–Zatsepin–Kuzmin (GZK) cutoff are all spectrum characteristics that extragalactic UHECRs acquire when they propagate through the CMB. We analyse all these characteristics through the diffusive flux as well as its modification factor. Model dependence of the modification factor is minimal compared to the diffusive flux. We compare the UHECR proton spectra calculated for the considered f(R) gravity models with the available data of the Telescope Array (TA) and Pierre Auger Observatory (PAO). We see that both models of f(R) gravity predict energy spectra of UHECRs with all experimentally observed features, which lay well within the range of combined data of both experiments throughout the energy range of concern. It is to be noted that our present work is only to investigate the possible effects of f(R) gravity theory on the UHECRs propagation, using pure proton composition as a simplified case study since protons are least affected by magnetic fields. Hence, at this stage, our results cannot be used to favor or disfavor f(R) cosmology over Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM cosmology as more work is needed in this regard.

ЖИТТЯ ГАЛАКТИК У СПОСТЕРЕЖУВАНОМУ ВСЕСВІТІ. ЧАСТИНА 2

The exchange of hydrogen between galaxies and the galactic structures that ensure this process are considered. This exchange between the main objects of the Universe was given in the first part of the article, but it was not considered there as another and important process of the galactic cycle. However, the largest structures in the observable Universe are associated with the exchange of the lightest gas. This circumstance allows us to rightfully distinguish it as the next process of the galactic cycle. In the second process, determined by the phase of the quasar in the galactic core, stellar waste is disposed of. Weak quasar jets eject the results of recycling either into the halo of their own galaxy or into its immediate vicinity. From these emissions, stars are formed directly in the galaxy, or near it. As a rule, these are stars from the galaxy's own matter. High-speed jets contain particles at their bases that move at speeds faster than the speed of light. This allows jets to eject matter far beyond the boundaries of the parent galaxy. The matter of such a jet leaves the galaxy forever. Quasars turn on periodically and relatively rarely change the direction of their emissions. Therefore, they often send streams of matter in one direction. Observable intergalactic filaments are formed from energetic flows. Given that clusters contain many galaxies and each of them goes through quasar stages, several filaments may emerge from the cluster. Therefore, filaments begin and end on galaxies, or their clusters. Outgoing filaments, if they are located nearby and equally directed, can unite with each other, forming large filaments. The question of the forces contributing to the unification of almost parallel jets remains open. The filaments contain hot hydrogen, some dust, “metals,” stars and galaxies. Hydrogen in filaments is expected with a minimal percentage of “metals”. In the filaments, stars and galaxies can form from the available gas. This often happens where the threads intersect with each other. Filaments from other sources fall into the gravitational field of a galaxy, or cluster of galaxies. By delivering the necessary building material, filaments introduce new stellar life into the basic elements of the Universe. Therefore, filaments are channels that provide life to galaxies. This process of hydrogen exchange between galaxies is the fourth galactic process. He refines the model of galaxy life in the observable Universe, which is presented in the first part of the article

Evolution And Its Misinterpretation By The Scientific Community

Allah has created the heavens and the earth in stages as he declares in the Holy Quran. It is Allah Who creates, develops and sustains life, and ensures harmony and diversity in all things, living and non-living. The verses from the Quran make it obvious that the conditions required for God’s ultimate creation to exist and survive are only possible if the universe contains matter, energy, water, and other entities as they are. The total measure of these entities cannot be altered, which means the total energy and matter in the universe is constant. These values are actually the result of the fine-tuned universe, where any deviation from it will lead to its instability and hence its extinction. This balance is maintained by the eternal and extremely intelligent being through His commands, and these commands, by observers, are conceived as laws of nature or scientific laws. This universe is solely meant for the trial of the ultimate creation, hence puzzling, brain-teasing, and other sorts of entangled phenomena in the observable universe are inevitable. This kind of nature is intentionally imparted to the universe by God to test mankind (God’s ultimate creation). The definition of biological evolution in modern science is actually an illusion and hence a trial for humans, since God calls this universe by the word "Garoor," meaning illusion or unreal. In conclusion, the misinterpretation of evolution by the scientific community can be attributed to the lack of understanding of the true nature of human existence and the purpose of life on Earth. By examining religious scriptures, we can see that humans are sent on Earth for minor and major trials by God, with minor trials such as evolutionary theory and other incomplete sciences being part of this category. It is evident that God initially formed the shape of a human from stagnant dark mud and then preserved it in a dry state. He did not breathe life into the mould until all the necessary conditions for human existence on Earth were ensured. After God infused life or spirit into the mould of Adam (AW), He taught Adam (AW) the names of things. Thus, it can be inferred that life on Earth was created by God in stages, and these stages are designed in a way that life and the species on Earth may appear to disbelievers as a result of natural selection or random evolution. However, as Muslims, it is important to remember that everything we observe in the universe is intended to test us by God, so it is best to avoid engaging in vague discussions on this matter. Know well that the life of this world is but an amusement and diversion, and adornment and boasting to one another, and competition in increase of wealth and children. This worldly life is no more than play and amusement. But the Hereafter is indeed the real life, if only they knew.(The Quran 29:64)

Stability of a realistic astrophysical pulsar and its mass–radius relation in higher-order curvature gravity

The objective of this research is to explore compact celestial objects while considering the framework of an extended gravitational theory known as R+f(G) gravity. The notations R and G denote the Ricci scalar and the Gauss–Bonnet invariant, respectively. Radio pulsars, which are neutron stars with masses greater than 1.8 times that of the Sun (M⊙), provide exceptional opportunities for delving into fundamental physics in extraordinary environments unparalleled in the observable universe and surpassing the capabilities of experiments conducted on Earth. Through the utilization of both the linear and quadratic expressions of the function f(G)=α1G2, where α1 (with dimensional units of [length6]) are incorporated, we have achieved an accurate analytical solution for anisotropic perfect-fluid spheres in a state of hydrostatic equilibrium. By integrating the dimensional parameters α1 and the compactness factor, defined as C=2GMRc2, we showcase our capacity to encompass and depict all physical characteristics within the stellar structure. We illustrate that the model is capable of producing a stable arrangement for the pulsar PSR J0740+6620, encompassing its geometric and physical properties. We illustrate that by utilizing the quadratic form of G in the R+f(G) framework, the Krori-Barua ansatz establishes semi-analytical relationships between radial pressure (pr), tangential pressure (pt), and density (ρ). Remarkably, in the context of the positive/negative α1 quadratic R+f(G) gravity framework, the maximum compactness is inherently restricted to values fail below the Buchdahl limit when the surface density exceeds 4×1014 g/cm3. This differs from General Relativity (GR) in which the compactness is unlikely to approach the black hole limit. The model predicts a core density that is multiple times greater than the saturation nuclear density, represented as ρnuc=4×1014 g/cm3, and a surface density ρs that surpasses the nuclear saturation density. We offer the mass–radius diagram associated with the boundary density we have determined, and this diagram has been shown to be consistent with other observational discoveries.

Measuring the Lense–Thirring Orbital Precession and the Neutron Star Moment of Inertia with Pulsars

Neutron stars (NSs) are compact objects that host the densest forms of matter in the observable universe, providing unique opportunities to study the behaviour of matter at extreme densities. While precision measurements of NS masses through pulsar timing have imposed effective constraints on the equation of state (EoS) of dense matter, accurately determining the radius or moment of inertia (MoI) of an NS remains a major challenge. This article presents a detailed review on measuring the Lense–Thirring (LT) precession effect in the orbit of binary pulsars, which would give access to the MoI of NSs and offer further constraints on the EoS. We discuss the suitability of certain classes of binary pulsars for measuring the LT precession from the perspective of binary star evolution and highlight five pulsars that exhibit properties promising to realise these goals in the near future. Finally, discoveries of compact binaries with shorter orbital periods hold the potential to greatly enhance measurements of the MoI of NSs. The MoI measurements of binary pulsars are pivotal to advancing our understanding of matter at supranuclear densities, as well as improving the precision of gravity tests, such as the orbital decay due to gravitational wave emission, and of tests of alternative gravity theories.

Dark Matter and Mirror World.

Overwhelming astronomical evidence for dark matter and absence of any laboratory evidence for it despite many dedicated searches have fueled speculation that dark matter may reside in a parallel universe interacting with the familiar universe only via gravitational interactions as well as possibly via some ultra-weak forces. In this scenario, we postulate that the visible universe co-exists with a mirror world consisting of an identical duplicate of forces and matter of our world, obeying a mirror symmetry. This picture, motivated by particle physics considerations, not only provides a natural candidate for dark matter but also has the potential to explain the matter dark matter coincidence problem, i.e., why the dark matter content of the universe is only a few times the visible matter content. One requirement for mirror models is that the mirror world must be colder than our world to maintain the success of big bang nucleosynthesis. After a review of the basic features of the model, we present several new results: first is that the consistency between the coldness of the mirror world and the explanation of the matter dark matter coincidence implies an upper bound on the inflation reheat temperature of the universe to be around 106.5 GeV. We also argue that the coldness implies the mirror world consists mainly of mirror Helium and very little mirror hydrogen, which is the exact opposite of what we see in the visible world.

An approximate application of quantum gravity to the rotation problem

Arbitrary initial conditions allow solutions of Einstein’s field equations for General Relativity to have arbitrarily large relative rotation of matter and inertial frames. The ‘Rotation Problem’ is to explain why the measured relative rotation rate is so small. As it turns out, nearly any reasonable theory of quantum gravity can solve the rotation problem by phase interference. Even as early as about a quarter of a second after the initial simgularity, quantum cosmology would limit the cosmologies that contribute significantly to a path integral calculation to have relative rms rotation rates less than about 10−51 radians per year. Those calculations are based on using 50 e-foldings during inflation. For 55 or 60 e-foldings, the cosmologies contributing significantly to the path integral would have even smaller relative rotation rates. In addition, although inflation dominates the calculation, even if there had been no inflation, the cosmologies contributing significantly to the path integral would have relative rotation rates less than about 10−32 radians per year at about a quarter of a second after the initial singularity. These calculations are insensitive to the details of the theory of quantum gravity because the main factor depends only on the size of the visible Universe, the Planck time, the free-space speed of light, the Hubble parameter, and the number of e-foldings during inflation. These calculations use the Einstein–Hilbert action in quantum gravity, including large-scale relative rotation of inertial frames and the matter distribution, in which each ‘path’ is a cosmology with a different rms relative rotation rate. The calculations include inflation for 50, 55, and 60 e-foldings, and for values of the dependence of relative rotation rate on cosmological scale factor a as a −m for various values of m. The calculation shows that the action is an extremum at zero rms relative rotation rate.

Investigation of scalar and fermion dark matter in mono-photon production at high-energy colliders

Many theories about dark matter have emerged due to its strong theoretical appeal in explaining astrophysical phenomena. However, experimental and theoretical particle physics have yet not provided evidence that dark matter is part of the observable Universe. Our work aims to investigate the interaction between Standard Model (SM) fermions and different species of dark matter (DM) particles in high-energy collisions through interaction of a new massive vector mediator, Z′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Z^{\\prime }$$\\end{document}. The production of scalar and fermion DM pairs via fermion annihilation into the new vector boson is investigated near a resonance (mχ∼MZ′/2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(m_{\\chi }\\sim M_{Z^{\\prime }}/2)$$\\end{document}, where a SM signal from hard photon emission is considered as initial state radiation, namely a mono-photon production. Values of coupling constants between the DM and the SM particles are mapped in contrast to the Planck satellite data for thermal relic density DM computed in the correct framework for the relic density near a resonance, where a weaker suppression of the relic density is expected. We show for the CLIC and LHC kinematic regimes that certain mass ranges and coupling constants of these DM particles are in agreement with the expected relic density near a resonance and are not excluded by collider and astrophysical limits.

A Classical Interpretation of the Quantum Universe Extrapolated from the Fine Structure Constant

The Fine Structure Constant (FSC) model of the universe is a conceptual perspective based on a classical method for analyzing the Fine Structure Constant (α). A Python algorithm calculates prime number property sets where the sum of the elements equals the whole number values for αequal to 137 and 139. A hybrid coupling of these property sets produces a U{137/139}twin prime metaverse where α=137.036, an almost exact match to the observed value. The FSC Model projects that the Fractional Coupling Constant (α137= 0.036)is a more accurate measure of its relative electromagnetic (EM) strength. This same calculation is used to determine the Fractional Coupling Constants (αm) for the twin prime metaverses (U{2/3}, U{3/5}, U{5/7}through U{197/199}) to estimate their respective electromagnetic forces. The results suggest that this model mirrors our observable universe and offers an abstract landscape into the quantum nature of electromagnetic forces, including Baryonic Matter, Dark Matter, Dark Energy, and a possible variable speed of light.

Shining light on the hosts of the nano-Hertz gravitational wave sources: a theoretical perspective

ABSTRACT The formation of supermassive black holes (SMBHs) in the Universe and its role in the properties of the galaxies is one of the open questions in astrophysics and cosmology. Though, traditionally, electromagnetic waves have been instrumental in direct measurements of SMBHs, significantly influencing our comprehension of galaxy formation, gravitational waves (GW) bring an independent avenue to detect numerous binary SMBHs in the observable Universe in the nano-Hertz range using the pulsar timing array observation. This brings a new way to understand the connection between the formation of binary SMBHs and galaxy formation if we can connect theoretical models with multimessenger observations namely GW data and galaxy surveys. Along these lines, we present here the first paper on this series based on romulus25 cosmological simulation on the properties of the host galaxies of SMBHs and propose on how this can be used to connect with observations of nano-Hertz GW signal and galaxy surveys. We show that the most dominant contribution to the background will arise from sources with high chirp masses which are likely to reside in low-redshift early-type galaxies with high stellar mass, largely old stellar population, and low star formation rate, and that reside at centres of galaxy groups and manifest evidence of recent mergers. The masses of the sources show a correlation with the halo mass and stellar mass of the host galaxies. This theoretical study will help in understanding the host properties of the GW sources and can help in establishing a connection with observations.

Inflation alternative via the gravitational field of a singularity

We explore the scenario that the observable Universe emerged from the vicinity of a negative mass ring singularity, and all content of the Universe travels at the same group velocity close to the speed of light on a geodesic trajectory along the axis of rotation of the singularity. In appropriate coordinate parametrization and evaluated on the trajectory, we find that the metric tensor in the vicinity of the trajectory exhibits a conformal scale factor a(η) with contraction and subsequent expansion properties that solve the horizon problem. We then introduce a static flow of gravitating radiation along the trajectory (perturbatively with respect to the mass scale of the singularity) to model a homogeneous radiation dominated Universe. Solving the Einstein field equations with a physically motivated ansatz of metric perturbation then reveals that the effective conformal scale factor indeed grows asymptotically with the same power law as expected in a conventional radiation dominated Universe.

Generative β-hairpin design using a residue-based physicochemical property landscape

De novo peptide design is a new frontier that has broad application potential in the biological and biomedical fields. Most existing models for de novo peptide design are largely based on sequence homology that can be restricted based on evolutionarily derived protein sequences and lack the physicochemical context essential in protein folding. Generative machine learning for de novo peptide design is a promising way to synthesize theoretical data that are based on, but unique from, the observable universe. In this study, we created and tested a custom peptide generative adversarial network intended to design peptide sequences that can fold into the β-hairpin secondary structure. This deep neural network model is designed to establish a preliminary foundation of the generative approach based on physicochemical and conformational properties of 20 canonical amino acids, for example, hydrophobicity and residue volume, using extant structure-specific sequence data from the PDB. The beta generative adversarial network model robustly distinguishes secondary structures of β hairpin from α helix and intrinsically disordered peptides with an accuracy of up to 96% and generates artificial β-hairpin peptide sequences with minimum sequence identities around 31% and 50% when compared against the current NCBI PDB and nonredundant databases, respectively. These results highlight the potential of generative models specifically anchored by physicochemical and conformational property features of amino acids to expand the sequence-to-structure landscape of proteins beyond evolutionary limits.

What can we learn from a master plot of energy rate versus mass for a very wide variety of (complex) systems?

Mass and energy rate (ER) data have been collected for a wide variety of (complex) systems from the biological, cultural, and cosmological realms. They range from the cytochrome oxidase protein (10-22 kg and 6x10-19 W) to the observable universe (1.5x1053 kg and 1048 W) and, thus, span 75 mass and 66 ER orders of magnitude. Many of these systems are relevant for the big history (BH) narrative, i.e., the development of complexity over “big time” from the Big Bang up to the human society on Earth of today. The purpose of this paper is not per se to describe their history though, but to explore a master plot of ER vs. mass. Notably, the development of systems over big time has followed a rather tortuous path criss-crossing over this ER vs. mass master plot. The true mass of the system as a whole is used (for example trees including the non-living wood, living organisms including their intrinsic water, and social systems including the built constructs), because these inactive parts are essential for the performance of the system and facilitate its ER. A double logarithmic master plot of all ER vs. mass data shows clusters of data points. To some extent, this provides quantitative support for the distinction between the (sub-)realms, which is based on a qualitative description of their material structure and energy processing. In the master plot, small systems with low mass and ER converge into larger systems with larger mass and ER, which is typically accompanied by a decrease of the energy rate density (ERD = ER/mass). Correlation of ER with mass for various groups of systems demonstrates both sub- and supra-linear scaling with the power law β constant varying between 0.5 and 4.0, showing that the mechanisms of self-organisation are quite different for the corresponding system groups. The combination of convergence and scaling with β always larger than zero explains why the ER & mass data points fall in a diagonal band with a width of 17 orders of magnitude.
 ER and mass have changed over wide ranges during the evolution of groups of systems, suggesting that evolution can be viewed as a process of systems exploring a larger ER vs. mass area until they run into ER and/or mass limitations. Indeed, there is a diagonal ER vs. mass limit for stable systems in all realms, corresponding to an ERD value of around 105 W/kg. Systems with ER & mass combinations above this limit, such as bombs, super-novae and cosmological transients, are unstable and “explosive”. This raises the interesting question of whether such an ERD maximum puts a limit on the development of complexity over big time. It seems that the low, right side of the master plot is empty. However, it is argued here that it is full of systems with low ER, such as dormant, living organisms, technological systems with their power adjusted or even switched off, as well as cooling, cosmological objects. Such systems are typically considered of less interest in a BH context, but they are viewed here as simple, complex systems which are out of equilibrium with matter, energy and information stored in their structure. While ERD appears to increase with the ‘advancement’ of systems over big time [5,51,52], there are quite some confounding factors regarding the efficacy of ERD as a metric for complexity in BH. For example, ERD decreases during the lifetime of a human and the human society (the mass of human-made constructs has grown faster than the global energy consumption), as well as during the evolution of living organisms and stars, whereas complexity is considered to increase. High ERD values of system parts may be illustrative for the complexity of the larger system, but are not representative for ERD of the system itself. Machines with an increased efficiency of energy conversion have a lower ERD, but could be considered more complex. The smallest and largest ERD values observed for the various realms appear to correlate with activity level and reciprocally with size, which do not per se reflect complexity. It is hoped that the raw data collected and the major trends observed in this paper will offer new insights into various aspects of the evolution of the universe over big time, and serve as an important resource for other related studies.

Irreversible behaviour of a gas owing to Unruh radiation

When gas molecules collide, they accelerate, and therefore encounter the Fulling-Davies-Unruh and Moore-DeWitt effects. The size of these effects is sufficient to randomize the motion of the gas molecules after about 1 nanosecond at standard temperature and pressure. Such observations show that quantum field theory modifies what is required to isolate a physical system sufficiently for its behaviour to be unitary. In practice the requirements are never satisfied exactly. Therefore the evolution of the observable universe is non-unitary and thermodynamically irreversible.

Low-Temperature Plasma Techniques in Biomedical Applications and Therapeutics: An Overview.

Plasma, the fourth fundamental state of matter, comprises charged species and electrons, and it is a fascinating medium that is spread over the entire visible universe. In addition to that, plasma can be generated artificially under appropriate laboratory techniques. Artificially generated thermal or hot plasma has applications in heavy and electronic industries; however, the non-thermal (cold atmospheric or low temperature) plasma finds its applications mainly in biomedicals and therapeutics. One of the important characteristics of LTP is that the constituent particles in the plasma stream can often maintain an overall temperature of nearly room temperature, even though the thermal parameters of the free electrons go up to 1 to 10 keV. The presence of reactive chemical species at ambient temperature and atmospheric pressure makes LTP a bio-tolerant tool in biomedical applications with many advantages over conventional techniques. This review presents some of the important biomedical applications of cold-atmospheric plasma (CAP) or low-temperature plasma (LTP) in modern medicine, showcasing its effect in antimicrobial therapy, cancer treatment, drug/gene delivery, tissue engineering, implant modifications, interaction with biomolecules, etc., and overviews some present challenges in the field of plasma medicine.

Informational Nature of Dark Matter and Dark Energy and the Cosmological Constant

In this article, realistic quantitative estimation of dark matter and dark energy considered as informational phenomena have been computed, thereby explaining certain anomalies and effects within the universe. Moreover, by the same conceptual approach, the cosmological constant problem has been reduced by almost 120 orders of magnitude in the prediction of the vacuum energy from a quantum point of view. We argue that dark matter is an informational field with finite and quantifiable negative mass, distinct from the conventional fields of matter of quantum field theory and associated with the number of bits of information in the observable universe, while dark energy is negative energy, calculated as the energy associated with dark matter. Since dark energy is vacuum energy, it emerges from dark matter as a collective potential of all particles with their individual zero-point energy via Landauer's principle.

COSMOLOGICAL SCALE FACTOR IN THE RELATIONAL APPROACH

In recent years, within the framework of the relational approach to the description of space-time and physical interactions, a number of studies have been carried out to substantiate the observed cosmological effects. In particular, it has been shown that the cosmological redshift described by the linear part of the Hubble law and the cosmic microwave background can be the result of contributions from emitted but not absorbed electromagnetic radiation. To describe the nonlinear part of the Hubble law, a logarithmic coordinate transformation was used, associated with the existence of a limiting observed distance, expressed by the gravitational radius of the observable Universe. The use of such a transformation must be justified by showing how it can be obtained in the derivation of space-time concepts for a system of a large number of emitters and absorbers. The article provides this rationale: it is shown that when deriving classical distances in the relational approach, there are two possibilities for determining the distance scale, they correspond to the scales of comoving and proper distances in cosmology, while the scale factor is expressed through the partition function of the configurations of emitters and absorbers.

A Historical Review of Research on the Density-Size Correlation of the Observable Universe

This literature review explores the correlation between the density and size of celestial objects - a key subject in understanding their formation, evolution, and the potential existence of higher-order clusters. It draws attention to the two seminal papers - E. F. Carpenter's density-size correlation study and Gerard De Vaucouleurs's study on matter density in groups and clusters. While acknowledging the limitations and outdated nature of Carpenter's body of work, it underscores the need for a more contemporary, comprehensive examination across various scales from neutron stars to galaxy clusters. The review highlights how such a study can clarify questions surrounding the size and shape of the universe, address Olbers' Paradox, and contribute to theories that describe the universe's origins and dynamics.

Newtonian approximation to estimate the current temperature of the universe

Based on supernovae data, we built a potential for the observable universe. Using classical mechanics, we built a classical Lagrangian and a Hamiltonian to describe the evolution of the universe as a three-dimensional sphere. We then considered the universe as a classical statistical ensemble and determined the partition function of the universe and thus estimated its current temperature. This analysis is classical, quantum approximation was never used.

Return of Harrison–Zeldovich spectrum in light of recent cosmological tensions

ABSTRACT The spectral index ns of scalar perturbation is the significant initial condition set by inflation theory for our observable Universe. According to Planck results, current constraint is ns = 0.965 ± 0.004, while an exact scale-invariant Harrison–Zeldovich spectrum, i.e. ns = 1, has been ruled out at 8.4σ significance level. However, it is well-known that the standard Lambda cold dark matter model is suffering from the Hubble tension, which is at ∼5σ significance level. This inconsistency likely indicates that the comoving sound horizon at last scattering surface is actually lower than expected, which so seems to be calling for the return of ns = 1. Here, in light of recent observations we find strong evidence for a ns = 1 universe. And we show that if so, it would be confirmed conclusively by CMB-S4 experiment.