The Accelerated Expansion of the Universe in the Light of the Maximum Ordinality Principle

The main aim of the paper is to present (and at the same time offer) a differ-ent perspective for the analysis of the accelerated expansion of the Universe. A perspective that can surely be considered as being “in parallel” to the tradition-al ones, such as those based, for example, on the hypotheses of “Dark Matter” and “Dark Energy”, or better as a “com-possible” perspective, because it is not understood as being “exclusive”. In fact, it is an approach that, when con-firmed by experimental results, always keeps its validity from an “operative” point of view. This is because, in analogy to the traditional perspectives, on the basis of Popper’s Falsification Principle the corresponding “Generative” Logic on which it is based has not the property of the perfect induction. The basic difference then only consists in the fact that the Evolution of the Universe is now modeled by considering the Universe as a Self-Organizing System, which is thus analyzed in the light of the Maximum Ordinality Principle.

The Accelerated Expansion of the Universe

We use experimental data from Distant Type 1a Supernovae to calculate the Observed Magnitude (m - M) which is the Apparent Magnitude (m) minus the Absolute Magnitude (M) for different values of the Redshift z which gives us the Distance Modulus. Then, we calculate the average velocity and average acceleration for different z values and plot them as a function of time. The expansion of the space of our 3-D Universe is exponential and it will end with a Big Bang as four 3-D Universes of which we are one will come together to form one 4-D expanding spatial Universe.

Friedmann-Like Cosmological Equations for the Accelerated Expansion of the Universe

In recent papers [1] [2] [3], we framed suitable axioms for Space called Super Space by Wheeler [4]. Using our axioms in Newtonian formalism and considering the density of the universe to be constant in time, we showed in the above references that at t = 0 the radius of the universe need not be zero. And thus, we avoided the problem of singularity. We further showed that the Hubble factor is no longer constant in time and goes on decreasing as confirmed by experiments. We pointed out in the above references that Space is the source of dark energy which is responsible for the accelerated expansion of the universe. With a view to improving the above-mentioned results quantitatively, in this paper, we are discussing the consequences of our axioms using Einstein’s field equations of general theory of relativity. Friedmann-like Cosmological equations with Dark Energy built-in are derived. This derivation is obtained using Robertson-Walker line element and by introducing a suitable expression for Energy-Momentum tensor in terms of matter and Dark energy contents of the universe. The solutions of our cosmological equations obtained here, show that the radius of the universe cannot reach zero but has a minimum value and there is also maximum value for the radius of the universe. The inflationary expansion of the very early universe emerges from our theory.

On a Quantum Gravity Fractal Spacetime Equation: QRG ≃HD + FG and Its Application to Dark Energy—Accelerated Cosmic Expansion

The paper suggests that quantum relativistic gravity (QRG) is basically a higher dimensionality (HD) simulating relativity and non-classical effects plus a fractal Cantorian spacetime geometry (FG) simulating quantum mechanics. This more than just a conceptual equation is illustrated by integer approximation and an exact solution of the dark energy density behind cosmic expansion.

A New Dynamics Expansion Mechanism for Plasma during Pulsed Laser Deposition

The dynamics expansion mechanisms for plasma plume generated by pulsed laser radiation are studied in detail, taking account of plasma ionization effect. Based on the consideration of local conservations of mass, momentum, collected as the assumption that plasma can be viewed as compressible ideal fluid and high temperature-high pressure ideal gas, we develop a new dynamics expansion mechanism for plasma produced by pulsed laser radiation. Using the analytical method, the space number density and pressure evolvement of plasma in cylindrical coordinate are obtained, the dynamics evolvement equations are also derived. The results from the present model indicate that the plasma dynamic expansion behaviour can be evidently influenced by the ionization fraction η. Its effect is similar to a new dynamic source for plasma expansion and increases the expansion acceleration in all directions. The predictions of the expansion of the plasma is affected by the temperature, the average atoms mass and the ionization degree of the plasma are consistent with the experimental results.

Charged Randall-Sundrum Braneworld Type Ⅱ with Higher Order Curvature Corrections from Superstring Arguments and Dominated by Quintessence

We discuss a new class of RSII braneworld cosmology exhibiting accelerated expansion and dominated by quintessence. It is explicitly demonstrated that the universe expansion history （transition from inflation to deceleration epoch to acceleration and effective quintessence era） may naturally occur in such unified theory for some classes of inverse scalar potentials. Besides a decaying effective cosmological constant, the model incorporates an increasing black hole mass, an increasing Maxwellian electrical charge with cosmic time and a time-dependent brahe tension. The cosmological model exhibits several features of cosmological and astrophysical interest for both the early and late universe consistent with recent observations, in particular the ones concerned with the gravitational constants, black holes masses and charges and variation of the gauge coupling parameters with cosmic time. One interesting mark of the constructed model concerns the fact that a black hole mass surrounded by quintessence energy may increase with time even if the horizon disappears.

Oscillating Flat FRW Dark Energy Dominated Cosmology from Periodic Functional Approach

I discuss the modification of Einstein＇s Theory of General Relativity based on a periodic functional approach. In this new approach, a corrected periodic gravitational coupling constant arises and plays the role of periodic damping term acting on the theory. It is found that it is achievable to have an oscillating universe dominated by dark energy and expanding aceeleratedly in time.

Gravity, Density, Acceleration, and the Constants of Nature

The component of light in the 3rd dimension decreases as light enters the 4th dimension created by a Black Hole. Hence particles moving in 3-D space will emit radiation due to the Cherenkov Effect. Gravity and acceleration are the same according to Einstein’s Equivalence Principle. Density also has the same effect as gravity because gravity attracts matter thereby increasing matter density. The laws of Physics and all the constants of nature such as the Speed of light, Planck’s constant, the Gravitational constant, and so on are a function of the dimension of the space they are in since the vacuum energy density of each higher dimension is greater. We analyze the graph of the accelerated expansion of the Universe to calculate the acceleration for small Redshift z and predict what will happen for larger z values.

Standard Model Review and a New 5D Multi-Brane Proposition

Based on a comprehensive review of mainly the non-quantum aspects of the standard model of cosmology, the 5 dimensional models, and the analysis here, we propose a 5 dimensional model with expanding 4D multi-branes. A review of the standard model in the context of many new developments and discoveries in cosmology in the recent times, such as the accelerated expansion of the universe, Plank cosmic microwave measurements, dark energy survey, Hubble tension etc. tends to indicate that the standard model is essentially a patchwork of different theoretical models that have been pieced together in an attempt to explain different aspects of the astrophysical observations, which do not necessarily emanate from a full end-to-end understanding of a physical process. The purpose of each individual theoretical piece such as “inflation” is limited to providing an explanation to the problem area or a gap in our understanding. A number of new theories such as the five-dimensional universe, the bulk and brane, extended theories of gravity, and conformal cyclic cosmology offer alternate ways of addressing the existential aspects of the universe but these models too remain hypothetical with shortcomings and a lack of conclusive evidence. The model proposed by us, presents a way forward in addressing dark matter and dark energy as manifestations of the multiple underlying branes in the aftermath of the big-bang. In the process, we present a theorem of the dimensionality of the expanding universe, which necessitates the need for at least one more dimension in addition to the 4 dimensions of spacetime. While carrying out the review of the standard model, we present new analysis and facts that strengthen the case for the 5th dimension. According to the multi-brane hypothesis presented here, our observed universe could be one of the many branes, and it is more likely than not that in the aftermath of the big-bang that generated our brane, more branes were generated, which further points towards a much more prolonged big-bang event than what has been the perception so far.

Temporal No-Linearity: An Alternative to Dark Energy

Mathematical compatibilities and constraints of a hypothetical 5D space-time with time referenced by two coordinates (3-2) have been revisited in detail in several recent papers. It has been prescribed from the GR the compatibility constraints of the FLRW metric in each temporal brane, to be restricted to Closed Universes, Smooth Initial Singularities, and “Open CTC”. In a first view, this leads to leaving these works considering mathematical games discarded by the Standard Candles data. However, if time would be referred by two coordinates, they would not be linearly related, and it will be mathematically stated that space-time may not be flat in any case because time-like branes geometry will never be. If so, the time scale “lived” over a two-time dimension geodesic necessarily is not constant over its linear projection on one of both coordinates. Consequently, the correlations between Redshift and Distance Modulus—Distance Ladder—may be corrected by a synchronization function (if a no-linear two-time geodesic trajectory over a “warped temporal geometry” is linearly divided into constant segments, then their projections are not linear in any case). We apply an example of time-trajectory over the time slices, matching the Standard Candle data for a Closed Universe dominated by matter (>90%) in a bulk 3-2 configuration, with open temporal branes and smooth singularity. If time can be referred by two coordinates, then there is no need of Darkness to explain astrophysical data and Universe can be closed.

Dark Matter, Dark Energy, and Occam’s Razor

Even though dark matter and dark energy have long been accepted as being of fundamental importance in cosmology, in this paper, we will present arguments to show that neither is necessary. Instead, the phenomena they are thought to be responsible for are consequences of a vacuum whose curvature varies with time. We will focus on three phenomena that are thought to require the existence of dark energy and dark matter. The first is the idea that dark energy is responsible for the observed accelerating expansion of the universe. We will show instead that with time-varying curvature, Einstein’s equations demand such an acceleration without reference to dark or any other form of energy. Turning to dark matter, it is supposedly required to explain the observed constant velocity profile of the stars making up the disks of spiral galaxies and to explain the strong gravitational lensing observed in galaxy clusters. We will show, however, that both phenomena can again be understood in terms of the vacuum and its curvature. In the former case, we will show that galaxies exist within a rotating volume of the vacuum and that this leads directly to the observed constant velocity profiles. In the latter case, gradients of the vacuum curvature serving as a varying index of refraction are responsible. Using numerical results from our new model of nucleosynthesis, we estimate the degree of bending to expect and find that the results are in accord with observation. Our new model very naturally explains the phenomena attributed to dark matter and dark energy and since neither has been observed after several decades of looking, Occam’s razor tells us that neither exists.

Multiverse Model: External Universe(s) as Source of Dark Energy

The Lambda Cold Dark Matter (ΛCDM) model is currently the best model to describe the development of the Universe from the Big Bang to the present time. It is composed of six parameters, two of them, Dark Energy (DE) and CDM, with unknown physical explanations. DE, leading to accelerated expansion of the Universe, is considered a scalar field characterized by exerting its force by repulsive gravity. We examined whether DE can be explained as the warping of spacetime in our Universe by external universes as components of a Multiverse or, in other words, as the gravitational pull exerted by other universes. The acceleration, the resultant kinetic energy, Ekin, and the cosmological constant, Λ, were calculated for one to four external universes. The acceleration is approx. 10-11 m/s2, which is in agreement with observations. Its value is dependent upon the numbers and relative positions of external universes. DE density is approx. 10-29 kg/m3 and Λ is in the range of 10-38 s-2 and 10-55 m-2, respectively. Warping of spacetime by external universes as a physical explanation for DE seems feasible and warrants further considerations.

The Shell Model of the Universe: A Universe Generated from Multiple Big Bangs

The Current Standard Model of the Universe asserts that the universe is generated from a single Big Bang event followed by inflation. There is no center to this universe, hence, no preferential reference frame to describe the motions of celestial objects. We propose a new, Shell Model of the Universe, which contends that the universe is created from multiple, concentric big bangs. Accordingly, that origin presents itself as a unique, preferential reference frame, which furnishes the simplest description of the motions of galaxies in the cosmos. This is similar in manner to how planetary motion is more straightforwardly described via a sun-centered Solar System rather than an earth-centered one. The appeal of the Shell Model of the Universe lies in its simplistic ability to resolve the paradox of quasars, explain the variability in Hubble’s Constant, and solve the problematic accelerated expansion of the universe.

Cantorian-Fractal Kinetic Energy and Potential Energy as the Ordinary and Dark Energy Density of the Cosmos Respectively

In a one-dimension Mauldin-Williams Random Cantor Set Universe, the Sigalotti topological speed of light is where . It follows then that the corresponding topological acceleration must be a golden mean downscaling of c namely . Since the maximal height in the one-dimensional universe must be where is the unit interval length and note that the topological mass (m) and topological dimension (D) where m = D = 5 are that of the largest unit sphere volume, we can conclude that the potential energy of classical mechanics translates to . Remembering that the kinetic energy is , then by the same logic we see that when m = 5 is replaced by for reasons which are explained in the main body of the present work. Adding both expressions together, we find Einstein’s maximal energy . As a general conclusion, we note that within high energy cosmology, the sharp distinction between potential energy and kinetic energy of classical mechanics is blurred on the cosmic scale. Apart of being an original contribution, the article presents an almost complete bibliography on the Cantorian-fractal spacetime theory.

On a Fractal Version of Witten’s M-Theory

Starting from Witten’s eleven dimensional M-theory, the present work develops in an analogous way a corresponding dimensional fractal version where . Subsequently, the new fractal formalism is utilized to determine the measured ordinary energy density of the cosmos which turns out to be intimately linked to the new theory’s fractal dimension via non-integer irrational Lorentzian-like factor: where is Hardy’s probability of quantum entanglement. Consequently, the energy density is found from a limiting classical kinetic energy to be Here, is ‘tHooft’s renormalon of dimensional regularization. The immediate logical, mathematical and physical implication of this result is that the dark energy density of the cosmos must be in astounding agreement with cosmic measurements and observations.

Negative Norms in Quantized Strings as Dark Energy Density of the Cosmos

The present short paper is concerned with accurate explanation as well as quantification of the so called missing dark energy of the cosmos. It was always one of the main objectives of any successful general theory of high energy particle physics and quantum cosmology to keep non-physical negative norms, the so called ghosts completely out of that theory. The present work takes the completely contrary view by admitting these supposedly spurious states as part of the physical Hilbert space. It is further shown that rethinking the ghost free condition with the two critical spacetime dimensions D1 = 26 and D2 = 25 together with the corresponding intercept a1 = 1 and a2 ≤ 1 respectively and in addition imposing, as in Gross et al. heterotic superstrings, an overall 496 dimensional exceptional Lie symmetry group, then one will discover that there are two distinct types of energy. The first is positive norm ordinary energy connected to the zero set quantum particles which is very close to the measured ordinary energy density of the cosmos, namely E(O) = mc2/22. The second is negative norm (i.e. ghost) energy connected to the empty set quantum wave and is equal to the conjectured dark energy density of the cosmos E(D) = mc2 (21/22) presumed to be behind the observed accelerated cosmic expansion. That way we were able to not only explain the physics of dark energy without adding any new concepts or novel additional ingredients but also we were able to compute the dark energy density accurately and in full agreement with measurements and observations.

Quantum Dark Energy from the Hyperbolic Transfinite Cantorian Geometry of the Cosmos

The quintessence of hyperbolic geometry is transferred to a transfinite Cantorian-fractal setting in the present work. Starting from the building block of E-infinity Cantorian spacetime theory, namely a quantum pre-particle zero set as a core and a quantum pre-wave empty set as cobordism or surface of the core, we connect the interaction of two such self similar units to a compact four dimensional manifold and a corresponding holographic boundary akin to the compactified Klein modular curve with SL(2,7) symmetry. Based on this model in conjunction with a 4D compact hy- perbolic manifold M(4) and the associated general theory, the so obtained ordinary and dark en- ergy density of the cosmos is found to be in complete agreement with previous analysis as well as cosmic measurements and observations such as WMAP and Type 1a supernova.

Kähler Dark Matter, Dark Energy Cosmic Density and Their Coupling

We utilize homology and co-homology of a K3-Kähler manifold as a model for spacetime to derive the cosmic energy density of our universe and subdivide it into its three fundamental constituents, namely: 1) ordinary energy;2) pure dark energy and 3) dark matter. In addition, the fundamental coupling of dark matter to pure dark energy is analyzed in detail for the first time. Finally, the so-obtained results are shown to be in astounding agreement with all previous theoretical analysis as well as with actual accurate cosmic measurements.

Matter Loops Corrected Modified Gravity in Palatini Formulation

Recently,corrections to the standard Einstein Hilbert action were proposed to explain the current cosmicacceleration in stead of introducing dark energy.In the Palatini formulation of those modified gravity models,thereis an important observation due to Arkani Hamed:matter loops will give rise to a correction to the modified gravityaction proportional to the Ricci scalar of the metric.In the presence of such a term,we show that the current formsof modified gravity models in Palatini formulation,specifically,the 1/R gravity and in R gravity,will have phantoms.Then we study the possible instabilities due to the presence of phantom fields.We show that the strong instability inthe metric formulation of 1/R gravity indicated by Dolgov and Kawasaki will not appear and the decay timescales forthe phantom fields may be long enough for the theories to make sense as effective field theory.On the other hand,if wechange the sign of the modification terms to eliminate the phantoms,some other inconsistencies will arise for the variousversions of the modified gravity models.Finally,we comment on the universal property of the Palatini formulation ofthe matter loops corrected modified gravity models and its implications.

Non-Rotating Black Holes, Dark Matter and Dark Energy in a Unifying Theory

The theory here developed, makes use of the decomposition of matter (mass) in different spatial frequencies k’s using spatial Fourier transforms, and the posterior use of modified inverse Fourier transforms to construct an accurate description of the classical Newtonian gravitational field. Introducing the concept of quantization of the spatial frequency k, which means allowing only discrete values, such as km, 2km, 3km, leads to the appearance of extra gravitational force regions that occur at distances equally spaced apart in 2π/km. These areas of extra gravitational force decrease inscribed in an inverse of the distance envelope (1/r). The value of 2π/km can be adjusted to be of the order of kiloparsec (kpc), being this way a plausible explanation for the effect of the dark matter since this causes practically flat rotation curves for most of the galaxies. As these regions of extra gravitational force also have adjacent areas of negative values (repulsive gravitational force), it is possible to show that any mass placed in the gravitational field far from the galaxy center will acquire, on average, a null acceleration, thereby remains the “light push,” or in other words, the “mean luminosity density” between galaxies as an explanation for the accelerating expansion of the universe, today being considered mainly due to dark energy. Along with the article, it is showed that the effect of light push is sufficient to explain the expansion of the universe. The present work also explains the nonlinear behavior of gravitational fields near massive objects such as blackholes, not contradicting the theory of general relativity, instead giving a complementary description of how black holes work, even describing the gravitational field internally to it, which is not available in the GR theory.