Observational Cosmology

The Big Bang theory remains the dominant paradigm in modern cosmology, yet it is founded upon several internal inconsistencies that challenge its logical coherence. This section analyzes the principal contradictions embedded in the standard narrative-ranging from the undefined nature of the primordial singularity to the unjustified causality of inflation and expansion. Using the NMSI-New Subquantum Information Mechanics framework, the present study reveals that many of these contradictions arise from an inappropriate treatment of time and matter as geometric constants rather than oscillatory logical constructs. A reevaluation is proposed based on infobitic subquantum dynamics.

In this article, we show that our expanding cosmos probably is inside a supergiant spherical shell. In fact, here we show that probably the reason for the accelerated expansion of the universe, the origin of CMB radiation and the origin of a part of the anisotropies of this radiation is the existence of a huge rigid spherical shell that surrounds entire of the universe. In the last part of the article, we show that between the theory of the cosmos’s shell and the theory of the last scattering surface, it is more logical to consider the cosmic shell as the cause of the existence of CMB.

Exotic matter, a term often associated with theoretical physics, particularly in the contexts of general relativity and quantum mechanics, refers to materials or forms of energy that possess unusual properties, such as negative mass, negative energy density, or negative pressure. This paper aims to provide a comprehensive review of the concept of exotic matter, tracing its origins from the early days of theoretical physics to its current speculative role in advanced concepts such as wormholes, warp drives, and other areas of modern cosmology.

We measure the large-scale real-space power spectrum P (k) using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loève eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to redshift-space distortions, with narrow and well-behaved window functions in the range 0.01 h/Mpc < k < 0.2 h/Mpc. Results from the LRG and main galaxy samples are consistent, with the former providing higher signal-to-noise. Our results are robust to omitting angular and radial density fluctuations and are consistent between different parts of the sky. They provide a striking confirmation of the predicted large-scale ΛCDM power spectrum. Combining only SDSS LRG and WMAP data places robust constraints on many cosmological parameters that complement prior analyses of multiple data sets. The LRGs provide independent cross-checks on Ωm and the baryon fraction in good agreement with WMAP. Within the context of flat ΛCDM models, our LRG measurements complement WMAP by sharpening the constraints on the matter density, the neutrino density and the tensor amplitude by about a factor of two, giving Ωm = 0.24±0.02 (1σ), mν ∼ < 0.9 eV (95%) and r < 0.3 (95%). Baryon oscillations are clearly detected and provide a robust measurement of the comoving distance to the median survey redshift z = 0.35 independent of curvature and dark energy properties. Within the ΛCDM framework, our power spectrum measurement improves the evidence for spatial flatness, sharpening the curvature constraint Ωtot = 1.05±0.05 from WMAP alone to Ωtot = 1.003 ± 0.010. Assuming Ωtot = 1, the equation of state parameter is constrained to w = -0.94 ± 0.09, indicating the potential for more ambitious future LRG measurements to provide precision tests of the nature of dark energy. All these constraints are essentially independent of scales k > 0.1h/Mpc and associated nonlinear complications, yet agree well with more aggressive published analyses where nonlinear modeling is crucial.

In this review we present a thoroughly comprehensive survey of recent work on modified theories of gravity and their cosmological consequences. Amongst other things, we cover General Relativity, Scalar-Tensor, Einstein-Aether, and Bimetric theories, as well as TeVeS, f (R), general higher-order theories, Hořava-Lifschitz gravity, Galileons, Ghost Condensates, and models of extra dimensions including Kaluza-Klein, Randall-Sundrum, DGP, and higher co-dimension braneworlds. We also review attempts to construct a Parameterised Post-Friedmannian formalism, that can be used to constrain deviations from General Relativity in cosmology, and that is suitable for comparison with data on the largest scales. These subjects have been intensively studied over the past decade, largely motivated by rapid progress in the field of observational cosmology that now allows, for the first time, precision tests of fundamental physics on the scale of the observable Universe. The purpose of this review is to provide a reference tool for researchers and students in cosmology and gravitational physics, as well as a self-contained, comprehensive and up-to-date introduction to the subject as a whole.

In the complete absence of ordinary matter, the Friedmann-Lemaître-Robertson-Walker (FLRW) metric in the dark energy-dominated era of late cosmological evolution features a constant curvature scalar (the Ricci scalar R) that is proportional to the cosmological constant Λ. Indeed, in the distant future the universe is expected to approach a pure de Sitter spacetime, in which stray high-entropy photons make up the bulk of the universe's energy. However, similar conditions may have also existed immediately following the Big Bang, when radiation from highly-relativistic neutrinos and photons comprised the majority of the energy in the expanding universe. If true, then it is plausible that the curvature scalar R was also constant in the radiation-dominated era of the early universe. This motivates the possibility of a metric that involves a constant R in the intervening matter-dominated era, which existed between some 50,000 years after the Big Bang and roughly four billion years ago, when dark energy began to overcome the dominance of gravitating matter. To investigate the consequence of a constant universal curvature scalar, the FLRW metric is derived from Einstein's field equations featuring both Λ and a constant R in the presence of non-interacting matter having a proper density ρ(t) and pressure P(ρ). The results indicate that the formalism is valid only for a relativistic fluid with the dimensionless equation of state parameters ω = -1 and ω = 1/3, corresponding to the very early and very late universe, respectively.

We present a new suite of over 1,500 cosmological N-body simulations with varied Warm Dark Matter (WDM) models ranging from 2.5 to 30 keV. We use these simulations to train Convolutional Neural Networks (CNNs) to infer WDM particle masses from images of DM field data. Our fiducial setup can make accurate predictions of the WDM particle mass up to 7.5 keV at a 95% confidence level from small maps that cover an area of (25 ℎ -1 Mpc) 2 . We vary the image resolution, simulation resolution, redshift, and cosmology of our fiducial setup to better understand how our model is making predictions. Using these variations, we find that our models are most dependent on simulation resolution, minimally dependent on image resolution, not systematically dependent on redshift, and robust to varied cosmologies. We also find that an important feature to distinguish between WDM models is present with a linear size between 100 and 200 h -1 kpc. We compare our fiducial model to one trained on the power spectrum alone and find that our field-level model can make 2× more precise predictions and can make accurate predictions to 2× as massive WDM particle masses when used on the same data. Overall, we find that the field-level data can be used to accurately differentiate between WDM models and contain more information than is captured by the power spectrum. This technique can be extended to more complex DM models and opens up new opportunities to explore alternative DM models in a cosmological environment.

This paper mainly studies the Gravitational Time Dilation Effect inside "black holes", and the inevitability of the existence of "Black galaxy" (the galaxy itself is a black hole) and "Black galaxy cluster" (the galaxy cluster itself is a black hole). As is well known, light and matter from outside can pass through the "event horizon" into the "black hole", indicating that the inside of the "black hole" is not completely dark, but rather has light. This study demonstrates that time within a "black hole" is not stationary. Based on the theory of the Big Bang and the current known mass of ordinary matter in the universe, approximately 1.6x10 53 kg, within the timeframe from before the Big Bang to 7.42 billion years post-Big Bang (a rough estimate), the universe itself is an extremely large "black hole" with a Schwarzschild radius exceeding 25 billion light-years. Therefore, the existence of "Black galaxies", "Black galaxy clusters", and even larger-scale "black holes" in the universe is not surprising. Therefore, the possibility that the Milky Way itself is a galaxy located inside an extremely large "black hole" cannot be ruled out. In theory, the Schwarzschild radius formula supports the existence of "black galaxies" and "black galaxy clusters" with huge radii in the universe. This study breaks down the boundaries between "black holes", "Black galaxies", and "cosmic voids". Keywords: Black hole, Black galaxy (the galaxy itself is a black hole) , Black galaxy cluster (the galaxy cluster itself is a black hole), cosmic voids, CMB Cold Spot, Gravitational Time Dilation

We present cosmological solutions for (1 + 3 + n)-dimensional steady state universe in dilaton gravity with an arbitrary dilaton coupling constant w and exponential dilaton self-interaction potentials in the string frame. We focus particularly on the class in which the 3-space expands with a time varying deceleration parameter. We discuss the number of the internal dimensions and the value of the dilaton coupling constant to determine the cases that are consistent with the observed universe and the primordial nucleosynthesis. The 3-space starts with a decelerated expansion rate and evolves into accelerated expansion phase subject to the values of w and n, but ends with a Big Rip in all cases. We discuss the cosmological evolution in further detail for the cases w = 1 and w = 1 2 that permit exact solutions. We also comment on how the universe would be conceived by an observer in four dimensions who is unaware of the internal dimensions and thinks that the conventional general relativity is valid at cosmological scales.

We use Type Ia supernovae studied by the High-Z Supernova Search Team to constrain the properties of an energy component which may have contributed to accelerating the cosmic expansion. We find that for a flat geometry the equation of state parameter for the unknown component, α x = P x /ρ x , must be less than -0.55 (95% confidence) for any value of Ω m and is further limited to α x < -0.60 (95%) if Ω m is assumed to be greater than 0.1 . These values are inconsistent with the unknown component being topological defects such as domain walls, strings, or textures. The supernova data are consistent with a cosmological constant (α x = -1) or a scalar field which has had, on average, an equation of state parameter similar to the cosmological constant value of -1 over the redshift range of z ≈ 1 to the present. Supernova and cosmic microwave background

First, it is shown that Einstein's attempt to establish the relativity of simultaneity is simply incorrect, as he tries to arbitrarily redefine simultaneity, while either ignoring or not recognizing its frame-independence. Next, it is shown that Einstein's attempt to render space and time relative by applying Lorentz transformations is incompatible with the relativity principle and, consequently, with some axiomatic propositions of Newton's first law of motion. Then, the theory of relativity is shown to lead to such absurdities, such as observer-dependent multiple realities, which, of course, should be considered foreign to science. Thus, it is concluded that science must refuse the idea of relative space and time; i.e. to consider them motion-dependent as Einstein's theory of relativity suggests.

This paper presents a comprehensive framework for understanding physical reality through a revitalized Aether concept, demonstrating its capacity to unify quantum phenomena, gravitational interactions, and conscious observation. We formulate the Aether as a turbulent, fractal medium described by quaternionic flow fields (Φ = 𝐸 + 𝑖𝐵), where electromagnetic components emerge as orthogonal projections and gravity arises from radial pressure gradients (𝐺 =-∇ ⋅ Φ). Key innovations include: (1) A deterministic resolution to quantum "weirdness" via Aethermediated measurement interactions, (2) Derivation of mass as an

A new time-dependent, scale-independent parameter, ̟, is employed in a phenomenological model of the deviation from General Relativity in which the Newtonian and longitudinal gravitational potentials slip apart on cosmological scales as dark energy, assumed to be arising from a new theory of gravitation, appears to dominate the universe. A comparison is presented between ̟ and other parameterized post-Friedmannian models in the literature. The effect of ̟ on the cosmic microwave background anisotropy spectrum, the growth of large scale structure, the galaxy weak-lensing correlation function, and cross-correlations of cosmic microwave background anisotropy with galaxy clustering are illustrated. Cosmological models with conventional maximum likelihood parameters are shown to find agreement with a narrow range of gravitational slip.

The persistent discrepancy in Hubble constant measurements between early-universe probes (H 0 = 67.4 ± 0.5 km/s/Mpc from Planck CMB) and late-time observations (73.0 ± 1.0 km/s/Mpc from SH0ES) presents a fundamental challenge to ΛCDM cosmology. We demonstrate that Quantum-Weber Theory (QWT) naturally resolves this tension by predicting H 0 = 70.2 ± 1.8 km/s/Mpc through three key mechanisms: (1) A dynamic scalar field λ replacing cold dark matter while modifying the sound horizon r s , (2) A graviton mass m g = (3.1 ± 0.2) × 10-32 eV/c 2 emerging directly from CMB thermodynamics, and (3) A modified expansion history from the λ 8 potential. The theory reproduces all major CMB features while making testable predictions for BAO and ISW measurements.

Radar and lidar are the most powerful and straightforward tools for demonstrating the features of relativity. To measure the velocity of an object, these tools introduce the velocity of light into the equation. According to the special theory of relativity, if a velocity is added to the velocity of light , the result will still be the velocity . On the other hand, according to Galilean relativity, if a velocity is added to the velocity , then a relative velocity ( ) is obtained, which generally differs from two the ingredients ( and ). The result of measuring the velocity using radar and lidar clearly shows which theory the experiment supports.

Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Many researchers have studied this theory and developed several models to solve decision-making and medical diagnostic problems, but most of these models deal only one set of parameters. This causes problems for users, especially with those who use questionnaires in their work and studies. Also Alkhazaleh and Salleh, also introduced the concept of soft-expert sets. This structure can be considered as a generalization of soft-sets in which experts and their opinions have been added to make decision analysis easier to handle. In our model, is more generalization of soft-set and soft-expert set, the collection of more specific information about object sets using mappings. This concept is more powerful for information tables, since collection of the information is very particular to define by mapping and also this model is approaches to rough set theory and information system.

An exact solution for the bulk 5-dimensional geometry is derived for F(R) gravity with non-flat de-Sitter 3-branes located at the M4 × Z2 orbifold boundaries. The corresponding form of F(R) that leads to such an exact solution of the bulk metric is derived which turns out to have all positive integer powers of R. In such a scenario the stability issue of the modulus (radion field) is analyzed critically for different curvature epochs in both Einstein and Jordan frames. The radion in the effective 4-d theory exhibits a phantom epoch making this model viable for a non-singular bounce. Simultaneous resolution of the gauge hierarchy problem is exhibited through the resulting stable vaue of the radion field in the effective 3 + 1 dimensional theory.

Recent cosmic microwave background (CMB) measurements combined with recent supernovae limits and other observational data have ambushed Ω Λ and Ω m . These cosmological culprits are trapped in a small pocket of parameter space: Ω Λ = 0.62 ± 0.16 and Ω m = 0.24 ± 0.10. If this is correct then an unknown 2/3 of the Universe has been identified.

This work is devoted to a formulation and an investigation of a boundary value problem with Gellerstedt conditions on different characteristics for the loaded parabolic-hyperbolic type equation of the second kind.By using the extremum principle and the method of energy integrals, there are proved the uniqueness of solution of the formulated problem, and the existence of a solution to the problem -by the method integral equations.

This article extends the five-dimensional (5D) model of wave-particle duality presented in [1] by integrating gravitational effects through a curved 5D metric and a generalized Lorentz factor that accommodates frame-dependent light speed. The original framework interpreted quantum phenomena, such as wave-particle duality, as projections from a higher-dimensional spacetime with a variable speed of light. Here, we enhance this model by introducing gravity and modifying the Lorentz factor, providing a novel linkage between quantum mechanics, relativity, and gravitational physics. This approach suggests a potential pathway toward unifying these domains.

Within the framework of Einstein-Cartan gravity we consider an action, containing up to quadratic terms of the Ricci scalar and the Holst invariant, coupled non-minimal to a scalar field, including couplings of its derivatives to curvature. We derive the equivalent metric theory, featuring an extra dynamical pseudoscalar degree of freedom associated with the presence of the Holst term in the action. We study the evolution of the resulting two-field system in a FRW background and show that it evolves rapidly into an effective single-field inflationary model. We find that the model is consistent with the latest observational data for a wide range of its parameters, determining the necessary upper limits on derivative coupling parameters.

We determine cosmological and evolutionary parameters from the 3CR K-band Hubble diagram and K-band number counts, assuming that the galaxies in question undergo pure luminosity evolution. Separately the two data sets are highly degenerate with respect to choice of cosmological and evolutionary parameters, but in combination the degeneracy is resolved. Of models that either are flat or have V L ¼ 0, the preferred ones are close to the canonical case V cold matter ¼ 1, V L ¼ 0, with luminosity evolution amounting to 1 mag brighter at z ¼ 1.

Recent observations suggest that Hubble's constant is large, and hence that the Universe appears to be younger than some of its constituents. The traditional escape route, which assumes that the expansion is accelerating, appears to be blocked by observations of Type Ia supernovae, which suggest that the Universe is decelerating. These observations are reconciled in a model in which the Universe has experienced an inflationary phase in the recent past, driven by an ultralight inflaton, the Compton wavelength of which is of the same order as the Hubble radius.

In homogeneous isotropic cosmological models the angular size e of a standard measuring rod changes with redshift z in a manner that depends upon the parameters of the model. It has been argued that as a population ultracompact (milliarcsecond) radio sources measured by very long-baseline interferometry (VLBI) do not evolve with cosmic epoch, and thus comprise a set of standard objects, at least in a statistical sense. Here we examine the angular-size/redshift relation for 256 ultracompact sources with z in the range 0.5 to 3.8 for cosmological models with two degrees of freedom (no and Ao). The canonical inflationary cold dark matter model (00 = 1, Ao = 0) appears to be ruled out by the observed relationship, whereas low-density models with a cosmological constant of either sign are favoured.

Universes with two degrees of freedom (Q o and Ao) are examined in the light of Kellerman's compilation of angular-size/redshift data for ultracompact radio sources. We find that low-density (Q o -0.2) models which are violently decelerating and have a large negative cosmological constant (qo --Ao -3) fit the data very well, as well as the canonical cold dark matter (CDM) universe, and very much better than the spatially flat accelerating case; if Q o ::;;O.2, then 95 per cent confidence limits are -3.8 ::;;Ao::;; -1.1, the lower limit being fixed by Holo ~ 0.56. The significant qualitative feature of the ()-z curve in this context is asymptotic flatness (in the limit Q o ...... 0, Ao # 0), rather than a pronounced minimum angular size. We give a mathematically rigorous argument, based upon the focusing of congruences of null geodesics, which shows that this feature is a singular property of vacuum-dominated universes.

In homogeneous isotropic cosmological models the angular size e of a standard measuring rod changes with redshift z in a manner that depends upon the parameters of the model. It has been argued that as a population ultracompact (milliarcsecond) radio sources measured by very long-baseline interferometry (VLBI) do not evolve with cosmic epoch, and thus comprise a set of standard objects, at least in a statistical sense. Here we examine the angular-size/redshift relation for 256 ultracompact sources with z in the range 0.5 to 3.8 for cosmological models with two degrees of freedom (no and Ao). The canonical inflationary cold dark matter model (00 = 1, Ao = 0) appears to be ruled out by the observed relationship, whereas low-density models with a cosmological constant of either sign are favoured.

Universes with two degrees of freedom (Q o and Ao) are examined in the light of Kellerman's compilation of angular-size/redshift data for ultracompact radio sources. We find that low-density (Q o -0.2) models which are violently decelerating and have a large negative cosmological constant (qo --Ao -3) fit the data very well, as well as the canonical cold dark matter (CDM) universe, and very much better than the spatially flat accelerating case; if Q o ::;;O.2, then 95 per cent confidence limits are -3.8 ::;;Ao::;; -1.1, the lower limit being fixed by Holo ~ 0.56. The significant qualitative feature of the ()-z curve in this context is asymptotic flatness (in the limit Q o ...... 0, Ao # 0), rather than a pronounced minimum angular size. We give a mathematically rigorous argument, based upon the focusing of congruences of null geodesics, which shows that this feature is a singular property of vacuum-dominated universes.

We determine cosmological and evolutionary parameters from the 3CR K-band Hubble diagram and K-band number counts, assuming that the galaxies in question undergo pure luminosity evolution. Separately the two data sets are highly degenerate with respect to choice of cosmological and evolutionary parameters, but in combination the degeneracy is resolved. Of models that either are flat or have V L ¼ 0, the preferred ones are close to the canonical case V cold matter ¼ 1, V L ¼ 0, with luminosity evolution amounting to 1 mag brighter at z ¼ 1.

Recent observations suggest that Hubble's constant is large, and hence that the Universe appears to be younger than some of its constituents. The traditional escape route, which assumes that the expansion is accelerating, appears to be blocked by observations of Type Ia supernovae, which suggest that the Universe is decelerating. These observations are reconciled in a model in which the Universe has experienced an inflationary phase in the recent past, driven by an ultralight inflaton, the Compton wavelength of which is of the same order as the Hubble radius.

"Some intellectuals are of the opinion that matter is bottled-up energy," explains Dharma guru Prabhat Ranjan Sarkar. "No, matter is not bottled-up energy." "It is the known "I" in the Cosmic arena in different planes of inferences, and these planes of inferences have nothing to do with one another." "Regarding the strength or influence of energy and microvita(1), this much can be said-energy is stronger in the physical planes of inferences than in the physico-psycho-spiritual planes of the unit and collective propensities. And microvita are stronger in the physico-psycho-spiritual realm of the unit mind." "The "doing" entity in the physical level is microvita and the "done" portion is the world of physicality." "It is the duty of the intellectuals of the world to continue doing research work regarding the movements of energy and of microvita when passing through the "done" world of the cosmic and individual propensities." "I would like intellectuals in the future to do this research in their external physical laboratories and also in their internal psychospiritual laboratories." Prabhat Ranjan Sarkar (1921-1990) was a spiritual guru in the tradition of Shiva and Krishna, and founded the international socio-spiritual organization Ananda Marga ("the Path of Bliss") and Renaissance Universal, a movement for an intellectual and spiritual renaissance.

Each generation of physicists, or natural philosophers, has sought to place universal gravitation in the context of its own worldview. Often this has entailed an effort to reduce gravitation to something more fundamental. But what is deemed fundamental has, of course, changed with time. Each generation attacked the problem of universal gravitation with the tools of its day and brought

We measure the large-scale real-space power spectrum Pk using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loe `ve eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to

We measure the large-scale real-space power spectrum Pk using luminous red galaxies (LRGs) in the Sloan Digital Sky Survey (SDSS) and use this measurement to sharpen constraints on cosmological parameters from the Wilkinson Microwave Anisotropy Probe (WMAP). We employ a matrix-based power spectrum estimation method using Pseudo-Karhunen-Loe `ve eigenmodes, producing uncorrelated minimum-variance measurements in 20 k-bands of both the clustering power and its anisotropy due to

The apparent discrepancy between abundances of light nuclides predicted by the standard Big-Bang and observational data is explained, by assuming the presence of metastable H dibaryons at the nucleosynthesis era. These dibaryons could be formed out of a small fraction of strange quarks at the moment of the confinement transition. For a primordial deuterium abundance of the order of 3 × 10 -5 , the measured differences in the 4 He abundances requires a relative abundance of H dibaryons of the order of n H /n B ∼ 0.07, decaying in a timescale of the order of 10 5 s.

In this paper, we propose a revised energy-momentum relation that allows for superluminal velocities without leading to singularities or violations of causality. The standard relativistic energy equation predicts infinite energy requirements for objects approaching the speed of light. We introduce an alternative formulation:


E = \frac{mc^2}{\sqrt{|1 - \frac{v^2}{c^2}|}}


which ensures that energy remains finite and real even for  v > c . This framework treats superluminal motion as a phase transition rather than an absolute barrier, offering a natural explanation for the early universe’s conditions.

We discuss the implications of this model in cosmology, particularly regarding the Big Bang and inflation. Our approach suggests that the Big Bang was not a singularity, but rather a transition from a superluminal to a subluminal state. This removes the need for an ad hoc inflationary model and provides a consistent mechanism for explaining the observed isotropy of the cosmic microwave background (CMB).

Additionally, we propose experimental and observational tests, including potential signatures in high-energy particle physics (e.g., LHC collisions), anomalies in the CMB, and unexplained astrophysical phenomena such as ultra-high-energy cosmic rays.

This work presents a fundamental revision of relativistic physics, suggesting that superluminal motion may play a critical role in our understanding of time, energy, and the structure of the universe.

This article investigates the signatures of various models of dark energy on weak gravitational lensing, including the complementarity of the linear and nonlinear regimes. It investigates quintessence models and their extension to scalar-tensor gravity. The various effects induced by this simplest extension of general relativity are discussed. It is shown that, given the constraints in the Solar System, models such as a quadratic nonminimal coupling do not leave any signatures that can be detected while other models, such as a runaway dilaton, which include attraction toward general relativity, can let an imprint of about 10%.

We present an activity to illustrate the Hubble-Lemaître law and the cosmological principle. Using an elastic band to represent the expanding universe and dots on the band to represent galaxies, we use Tracker software to measure recession velocities as a function of distance and analyse their relationship in different reference frames. Unlike previous work, which has focused on changes in position, this approach allows direct and quick measurement of velocities for different reference frames and different expansion rates. The activity is simple and can be incorporated into different learning cycles or used as homework.

This article represents the culmination of a decade-long effort to develop the World-Universe Cosmology (WUC), building upon a series of published works. These include the first one, "5D World-Universe Model. Space-Time-Energy" [1] and the last one, "JWST Discoveries and the Hypersphere World-Universe Model. Transformative New Cosmology" [2], both featured in the Journal of High Energy Physics, Gravitation and Cosmology. WUC is a unified model of the World built around the concept of the Cosmic Medium, composed of particles (protons, electrons, photons, neutrinos, and universe-created particles). WUC provides a mathematical framework that enables precise calculation of Medium-bound physical parameters: Gravitational parameter, Hubble's parameter, Absolute age of the World, Intergalactic plasma parameters, Temperature of microwave background radiation and the Minimum energy of photons. This paper aligns WUC with the theoretical framework developed by P. Wesson and J. Overduin [3], [4], albeit assigning a new physical meaning to the fourth spatial coordinate associated with the total energy of the observable World.

We have previously shown that spherically symmetric, inhomogeneous universe models can explain both the supernova data and the location of the first peak in the CMB spectrum without resorting to dark energy. In this work, we investigate whether it is possible to get an even better fit to the supernova data by allowing the observer to be positioned away from the origin in the spherically symmetric coordinate system. In such a scenario, the observer sees an anisotropic relation between redshifts and the luminosity distances of supernovae. The level of anisotropy allowed by the data will then constrain how far away from the origin the observer can be located, and possibly even allow for a better fit. Our analysis shows that the fit is indeed improved, but not by a significant amount. Furthermore, it shows that the supernova data do not place a rigorous constraint on how far off-center the observer can be located.

We investigate f (R) theories of gravity within the Palatini approach and show how one can determine the expansion history, H(a), for an arbitrary choice of f (R). As an example, we consider cosmological constraints on such theories arising from the supernova type Ia, large-scale structure formation, and cosmic microwave background observations. We find that the best fit to the data is a nonnull leading order correction to the Einstein gravity. However, the current data exhibits no significant trend toward such corrections compared to the concordance ΛCDM model. Our results show that the oft-considered 1/R models are not compatible with the data. The results demonstrate that background expansion alone can act as a good discriminator between modified gravity models when multiple data sets are used.

The current authors have previously shown that inhomogeneous, but spherically symmetric universe models containing only matter can yield a very good fit to the SNIa data and the position of the first CMB peak. In this work we examine how far away from the center of inhomogeneity the observer can be located in these models and still fit the data well. Furthermore, we investigate whether such an off-center location can explain the observed alignment of the lowest multipoles of the CMB map. We find that the observer has to be located within a radius of ∼ 15 Mpc from the center for the induced dipole to be less than that observed by the COBE satellite. But for such small displacements from the center, the induced quadru-and octopoles turn out to be insufficiently large to explain the alignment.

We have previously shown that spherically symmetric, inhomogeneous universe models can explain both the supernova data and the location of the first peak in the CMB spectrum without resorting to dark energy. In this work, we investigate whether it is possible to get an even better fit to the supernova data by allowing the observer to be positioned away from the origin in the spherically symmetric coordinate system. In such a scenario, the observer sees an anisotropic relation between redshifts and the luminosity distances of supernovae. The level of anisotropy allowed by the data will then constrain how far away from the origin the observer can be located, and possibly even allow for a better fit. Our analysis shows that the fit is indeed improved, but not by a significant amount. Furthermore, it shows that the supernova data do not place a rigorous constraint on how far off-center the observer can be located.

We investigate f (R) theories of gravity within the Palatini approach and show how one can determine the expansion history, H(a), for an arbitrary choice of f (R). As an example, we consider cosmological constraints on such theories arising from the supernova type Ia, large-scale structure formation, and cosmic microwave background observations. We find that the best fit to the data is a nonnull leading order correction to the Einstein gravity. However, the current data exhibits no significant trend toward such corrections compared to the concordance ΛCDM model. Our results show that the oft-considered 1/R models are not compatible with the data. The results demonstrate that background expansion alone can act as a good discriminator between modified gravity models when multiple data sets are used.