Dark energy is thought to make up about 70% of the Universe. Although dark energy cannot be directly observed, its effects are seen in the expansion of spacetime that spreads out galaxies. The observable universe appears to be accelerating in expansion, measured by ‘standard candles’ called type Ia supernovae. These supernovae are bright expulsions of extranuclear star material that appear to happen in the same way and with the same brightness each time, making them useful for measuring cosmological distances and the Hubble constant of universal expansion.

In order to further understand dark energy and its effects, scientists have used type Ia supernovae to measure the expansion rate of the universe and the Hubble Constant (Riess et al., 1998). They have also used computer simulations to model the evolution of the universe and test various theories of dark energy (Springel et al., 2005). Additionally, astronomers are using sophisticated observational techniques, such as radio and infrared observations, to observe smaller and more distant objects and improve our understanding of the structure of the universe (de Graauw et al., 2010). By studying the CMB, the Hubble constant, and the growth of large-scale structures, scientists hope to gain new insights into the nature of dark energy.

**The CMB, the Big Bang, and the Hubble Constant**

The CMB is the oldest known light in our universe and provides evidence for the Big Bang theory (Planck Collaboration et al., 2018). The Big Bang theory states that the universe was initially composed of a hot and dense matter-energy, and that it has since expanded and cooled (Gamow, 1946). The peaks and troughs observed in the angular power spectrum of the Cosmic Microwave Background (CMB) can be attributed to baryon acoustic oscillations, which can also be discerned in the distribution of galaxies in the universe. Prior to the combination of electrons and protons to form the transparent gas, hydrogen, the free electrons effectively scattered the CMB photons. The photons formed a high-pressure fluid, which, if subjected to a pressure gradient, would result in the electrons moving down the gradient. The consequent movement of the electrons requires the protons to follow, lest an electric field of significant magnitude be established and pull the protons along with the electrons. This interaction between normal matter, known as “baryons”, and CMB photons constitutes a “baryon-photon” fluid, characterized by a high sound speed due to the photons providing the majority of both density and pressure. This results in a sound speed within the baryon-photon fluid of approximately 170,000 km/s. When an area of high initial density is encountered, the resulting high pressure in the baryon-photon fluid will propagate as a spherical, expanding sound wave (Wright).

By analyzing the CMB, scientists have obtained the Hubble constant, which describes the relationship between the density of the universe and its rate of expansion (Liddle & Lyth, 2000). These equations have been used to calculate the current age and size of the universe and to estimate the amount of matter and energy it contains. However, there is a discrepancy in measurements known as the Hubble Tension (Riess et al., 2019). The Hubble Tension is a discrepancy in measurements related to the expansion of the universe, and suggests that our understanding is incomplete. The Hubble Constant, which is the rate at which the universe is expanding, is estimated to be around 70 km/s/Mpc (km per second per megaparsec). However, measurements of the Cosmic Microwave Background (CMB) suggest that the universe is expanding faster than predicted by the Hubble Constant, at around 74 km/s/Mpc (Planck Collaboration, 2018). This discrepancy can be expressed in LateX using the equation:

**H^2 = \frac{8\pi G}{3}\rho – \frac{kc^2}{a^2} + \Lambda c^2**

where **H** is the Hubble Constant, **G** is the gravitational constant, **\rho** is the density of the universe, **k** is the curvature of space, **a** is the scale factor, **c** is the speed of light, and **\Lambda** is the cosmological constant. The Hubble Tension suggests that there is something missing from our understanding of the universe and its expansion, such as a new type of matter or energy, or even a modification to the laws of gravity. Scientists are currently exploring a variety of observational and theoretical methods to try and explain the Hubble Tension, such as measuring the weak gravitational lensing of distant galaxies (Kilbinger et al., 2015) and mapping the distribution of galaxies in the sky (Hildebrandt et al., 2016). Additionally, astronomers are using computer simulations to model the evolution of the universe and test various theories of dark energy (Springel et al., 2005).

The integrated Sachs-Wolfe effect (1967) is an effect that attempts to explain why the Cosmic Microwave Background (CMB) radiation has areas of temperature variations. It is an effect that occurs when photons from the CMB interact with large-scale structures in the universe, such as clusters of galaxies and superclusters (Komatsu et al., 2009). The effect is caused by a decrease in the gravitational potential of the structures as the photons pass through them, which causes the photons to lose energy and redshift (Bartelmann & Schneider, 2001). This redshift causes the temperature of the CMB to decrease, resulting in small variations in temperature (Gorski et al., 2005). These temperature variations can be observed in the CMB (Planck Collaboration, 2018) and can be used to study the large-scale structure of the universe (Eisenstein et al., 2005).

The effect can be described using the following equation:

**ΔT/T = (Φ_in – Φ_out)/c^2**

where **ΔT/T** is the temperature fluctuation in the CMB, **Φ_in** and **Φ_out** are the gravitational potentials at the surface of last scattering and the observer, respectively, and **c** is the speed of light. The equation shows that the temperature fluctuation in the CMB is proportional to the difference in the gravitational potentials along the line of sight from the surface of last scattering to the observer.

In order to test the predictions of these models, scientists are constructing larger and more powerful telescopes and launching new missions to observe distant galaxies and measure the expansion rate of the universe (Perlmutter et al., 2020). By studying the CMB, the Hubble constant, and the growth of large-scale structures, scientists hope to gain new insights into the nature of dark energy (de Graauw et al., 2010). To further understand the rate of expansion, astronomers continue to use a variety of observational and theoretical methods to refine our understanding of the Hubble constant (Freedman et al., 2020). Freedman et al. (2020) have used large galaxy surveys to study the distribution of matter and the expansion rate of the universe. They have also used computer simulations to model the evolution of the universe and test different theories of dark energy. Perlmutter et al. (2020) have also developed observational techniques to measure the expansion rate of the universe more accurately. These include measuring the weak gravitational lensing of distant galaxies (Kilbinger et al., 2015) and mapping the distribution of galaxies in the sky (Hildebrandt et al., 2016). Additionally, astronomers are using computer simulations to model the evolution of the universe and test various theories of dark energy (Springel et al., 2005). They are also launching new missions to observe distant galaxies and measure the expansion rate of the universe.

**A Brief History of Space-Time…**

Mathematician Hermann Minkowski made an attempt to consolidate modern Western concepts of space-time when in 1907 he wrote that space and time can no longer be considered separate entities, but instead, should be thought of as a single entity referred to as space-time (Minkowski, 1907). This idea of space-time was further developed in 1915 when Albert Einstein published his General Theory of Relativity, which states that the presence of mass alters the structure of space-time (1915). This means that the more massive an object is, the more it warps space-time around it. As a result, objects with a large mass, like stars and planets, are able to exert a gravitational pull on other objects in the universe. This gravitational pull is what keeps planets in orbit around the sun. The theory of relativity has been tested and confirmed through a variety of experiments, including the observation of the deflection of light by the sun (Dyson, Eddington, & Davidson, 1919) and the prediction of the precession of the orbit of Mercury (Le Verrier, 1859). The theory of relativity is a cornerstone of modern physics and is essential for understanding a wide range of phenomena from the behavior of atomic clocks to the expansion of the universe. Thus, we refer to space and time jointly as space-time, conjoined by the Mysteries of relativity in gravitation and this enigma we call dark energy. As the distance between masses increases, the expulsive force of this ‘dark energy’ drives expansion to accelerate at an increasing rate (Perlmutter & Schmidt, 1998). Perlmutter and Schmidt won the Nobel Prize in Physics and received wide recognition for their discoveries, but as of today no one yet understands what exactly dark energy is, let alone how or why it causes said expansion.

Minkowski space is a four-dimensional space that combines three dimensions of space with one dimension of time into a single space-time entity. The Minkowski metric, which is a mathematical function that describes the distance between two points in Minkowski space-time, is given by:

**ds^2 = c^2dt^2 – dx^2 – dy^2 – dz^2**

where **ds** is the interval of space-time, **c** is the speed of light, **t** is time, and **x**, **y**, and **z** are the three spatial dimensions. The Minkowski metric is based on the idea that the laws of physics are the same for all observers, regardless of their relative motion, which is where Einstein procured his ideas about relativity. The Minkowski metric is also closely related to the concept of the vacuum, which is a region of space that is empty of matter. In Minkowski space, the vacuum is described by the Minkowski metric, which is a mathematical representation of the empty space-time. The vacuum energy of Minkowski space is a form of energy that arises from the fluctuations of the vacuum, and it is thought to be related to the presence of virtual particles (Weinberg, 1989). The vacuum energy of Minkowski space may contribute to the overall energy density of the universe and drive the acceleration of its expansion, which is thought to be related to the mysterious phenomenon known as dark energy (Riess et al., 1998).

One possible explanation for how the vacuum energy of Minkowski space may cause the expansion of the universe is through the concept of the cosmological constant. The cosmological constant is a term that was introduced by Einstein in his theory of general relativity to describe the overall energy density of the universe (1917). According to Einstein’s theory of general relativity, and indeed, what sets his theory apart from Minkowski’s, is that the cosmological constant is a property of space-time that determines its overall expansion or contraction. The foundational concept of relativity can be traced back to the work of James Clerk Maxwell in the late 19th century, who developed the theory of electromagnetism and described the relationship between electric and magnetic fields (1864). This theory led to the prediction of the existence of electromagnetic waves, which were later confirmed by the work of Heinrich Hertz (1888). The connection between electromagnetism and dark energy is still a mystery, but some scientists believe that the two may be related. One proposed explanation is that the mass-energy of the vacuum, which is the energy present in empty space between particles, is related to the electromagnetic field (Weinberg, 1989). The electromagnetic field is described mathematically by Maxwell’s equations, a set of four partial differential equations that describe the behavior of both electric and magnetic fields and their interactions with matter and with each other. In LateX: **\mathbf{E}** is the electric field, **\mathbf{B}** is the magnetic field, **\rho** is the charge density, **\epsilon_0** is the electric permittivity of free space, **\mathbf{J}** is the current density, **\mu_0** is the magnetic permeability of free space, and **t** is time.

The first equation is **Gauss’s Law**, which relates the charge density of a system to the electric field:

**\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}**

Where **\nabla** is the gradient operator, **\mathbf{E}** is the electric field, **\epsilon_0** is the electric constant, and **\rho** is the charge density.

The second equation is the **Divergence Theorem** **for magnetic fields**, which states that the magnetic field is a solenoidal vector field, meaning its divergence is equal to 0:

**\nabla \cdot \mathbf{B} = 0**

Where **\mathbf{B}** is the magnetic field.

The third equation is **Faraday’s Law of Electromagnetic Induction**, which relates the rate of change of the magnetic field to the electric field in a closed loop:

\**nabla \times \mathbf{E} = – \frac{\partial \mathbf{B}}{\partial t}**

Where **\nabla\times** is the curl operator, and **\partial/\partial t** is the partial derivative with respect to time.

The fourth equation is **Ampere’s Law**, which relates the magnetic field produced by a current to the current density and the electric field:

**\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)**

Where **\mu_0 **is the magnetic constant, and **\mathbf{J}** is the current density.

These equations suggest that the vacuum energy of Minkowski space could be related to the electromagnetic field, and that the fluctuations in the electromagnetic field could be responsible for the vacuum energy of Minkowski space (Weinberg, 1989). If the vacuum energy is large enough, it can cause the expansion of the universe to accelerate, which is what is observed in the current expansion of the universe (Riess et al., 1998). This could potentially explain the mysterious phenomenon of dark energy, which is thought to be a form of energy that permeates the universe and exerts a negative pressure on the expansion of the universe (Peebles & Ratra, 2003). In his theory of special relativity, Einstein proposed that the laws of physics are the same for all observers regardless of their relative motion (1905). This theory is based on the idea that the speed of light is constant regardless of the motion of the observer. Einstein’s special theory of relativity also introduced the concept of space-time, on the recommendation of Minkowski, which combines space and time into a single entity. According to the general theory of relativity, Einstein proposed that the force of gravity arises from the curvature of space-time caused by massive objects (1915). This theory can be described mathematically using the equation for the Schwarzschild metric, which describes the curvature of space-time around a spherically symmetric object:

**ds^2 = \left(1 – \frac{2GM}{c^2r}\right)c^2dt^2 – \frac{dr^2}{1-\frac{2GM}{c^2r}} – r^2d\Omega^2**

where **ds** is the interval of space-time, **G** is the gravitational constant, **M** is the mass of the object, **c** is the speed of light, **r** is the distance from the object, **t** is time, and **d\Omega** is the solid angle. According to quantum field theory, the vacuum is not completely empty, but is instead filled with virtual particles that are constantly appearing and disappearing (Feynman, 1948). These particles are not observed directly, but they can be detected through their effects on other particles, such as by influencing the energy levels of atoms. These virtual particles are thought to be responsible for the vacuum energy of Minkowski space, which is a form of energy that arises from the fluctuations of the vacuum (Weinberg, 1989). The vacuum energy of Minkowski space may contribute to the overall energy density of the universe and drive the acceleration of its expansion, which is thought to be due to dark energy. If the vacuum energy of Minkowski space contributes to the overall energy density of the universe, it may act as a source of negative pressure that drives the expansion of the universe. This is because the energy of the vacuum is thought to be evenly distributed throughout space, which would result in a uniform negative pressure that pushes all matter away from itself. This negative pressure would cause the expansion of the universe to accelerate, which is consistent with the observed expansion of the universe (Riess et al., 1998).

**Research & Development**

Thus, dark energy appears to have been in place with its defining characteristic (negative pressure) at least 9 billion years ago and was neither missing (as would be expected for a rapidly changing field) nor mimicking the gravitational behavior of matter or radiation. Vacuum energy or Einstein’s cosmological constant passes this test, a test which they could have failed. This is exactly the kind of test we need to perform, only with much enhanced precision in the future. A plethora of new tests and enhancements of older ones are being sharpened to pin down the nature of the ghostly dark energy. As Hubble wrote of the initial quest to measure cosmic expansion, “The search will continue. Not until the empirical resources are exhausted, need we pass on to the dreamy realms of speculation.”

The search to understand dark energy has been ongoing for decades. Astronomers have hypothesized various theories to explain the mechanism behind dark energy, such as scalar fields, vacuum energy, and modified gravity. In order to test and refine these theories, scientists have used a combination of observational and theoretical methods. These include measuring the Hubble Constant, tracking the cosmic microwave background radiation, and analyzing the growth of large-scale structures in the universe. However, the exact nature of dark energy remains a mystery, and scientists are still working to uncover its secrets.

One approach is to use large galaxy surveys to study the distribution of matter and the expansion rate of the universe (Eisenstein et al., 2005). Another approach is to use computer simulations to model the evolution of the universe and test different theories of dark energy (Springel et al., 2005). In order to answer some of the questions posed by dark energy, astronomers have developed sophisticated methods to measure the expansion of the Universe. These include observing the Cosmic Microwave Background (CMB), which is the faint afterglow of the Big Bang, and using Type Ia supernovae as a standard candle to measure distances. The Bolshoi simulation is based on the study of the CMB and the LambdaCDM standard model and is widely accepted as the most accurate model of the large scale structure of the known universe to date (Bolshoi, 2010). Moreover, the National Radio Astronomy Observatory (NRAO) and NASA have launched various initiatives to measure the effects of dark energy. These observations are only possible with radio and infrared observations that can detect minute temperature fluctuations.

In addition, there are a number of ongoing and planned observational programs that are aimed at studying dark energy. For example, the Dark Energy Survey (DES) is a wide-field imaging survey that is using four filters to study the expansion history of the universe and the growth of cosmic structure (Flaugher et al., 2015). The DES is being conducted using the Blanco telescope at the Cerro Tololo Inter-American Observatory in Chile. The VLBA especially finds a way around the standard candle problem by detecting the radio emissions of naturally occurring lasers, called masers (short for microwave lasers) transmitted from other galaxies, in order to precisely clock expansion rates between galaxies. The Green Bank telescope has also very famously presented us with a 3D map of the known universe, thanks to specialized radio receivers that detect the faintest redshifts of light emitted from distant galaxies and cool hydrogen gas clouds that fill what we used to think was only void space. These data provide astronomers with the tools to observe and predict galactic evolution, galactic mergers, the formation of star clusters and supernovae. It also allows theorists to use radio astronomy data to synthesize new theories and ways of describing the properties of and possibly detecting dark matter, dark energy, and their effects. There are also a number of satellite missions that are studying dark energy, such as the Planck mission, which is a space-based observatory that is studying the CMB to learn more about the early universe and the nature of dark energy (Planck Collaboration, 2018). The Euclid mission is another space-based mission that is studying dark energy and the large-scale structure of the universe (Laureijs et al., 2011).

In addition to observational methods, theoretical approaches are also being used to study dark energy. For example, the Lambda-CDM (Cold Dark Matter) model is a theoretical approach to dark energy that attempts to explain the current expansion rate of the universe using a cosmological constant (Weinberg, 1989). This model has become the standard cosmological model and is widely used to explain the structure and evolution of the universe. However, while the Lambda-CDM model is successful in many ways, it is not without its problems. For example, the model predicts a much smoother universe than what is observed (Klypin & Prada, 2019). Additionally, the model does not explain the accelerated expansion rate of the universe (Spergel et al., 2003). To address these issues, researchers are developing alternative theories of dark energy, such as the scalar field model, which postulates that dark energy is made up of a scalar field that permeates all of space (Peebles & Ratra, 2003). Finally, some researchers are exploring the possibility that dark energy is not a property of space, but rather a new type of particle (Cheung, 2014). By studying the properties of known particles, such as neutrinos and axions, some scientists are hoping to identify a new particle that could explain the accelerated expansion of the universe and perhaps even uncover new understanding in thermodynamics and the development of entropy following the Recombination, or provide some otherwise viable explanation or illustration of forces we have yet to determine.

**The appearance of dark matter and dark energy denote the gravitation of expanding space-time:**

“We reason that it is the gravitation of all ordinary matter, extending from the dense distant past to the sparse present, rather than dark matter, that shows up in galaxy rotation and velocity dispersion. Likewise, we argue that it is this gradient in the gravitational energy due to the expansion, rather than dark energy, that explains Type 1a supernovae brightness vs. redshift data. Our conclusions follow from statistical mechanics, the thermodynamic theory based on the atomistic axiom that everything comprises quanta. In line with the Einstein field equations, the vacuum quanta embodying gravitation, geometrized as spacetime, equate in dynamic balance to the quanta embodying the substance of the stress–energy tensor. In accordance with quantum field theory, the proposed ground-state field of paired light quanta complies with Bose–Einstein statistics and assumes an excited state around a particle.”

https://www.frontiersin.org/articles/10.3389/fphy.2022.995977/full

**Dark Energy as a Power Source**

“In theory, it is possible to use the dark energy of the universe as a power source. In practice, the amount of energy that could be liberated in a local setting is many orders of magnitude too small to be useful or even detectable. Nevertheless, in the interests of education and amusement, simple machines that could, in theory, extract local power from the gravitationally repulsive cosmological constant are discussed. The gravitational neutral buoyancy distance — the distance where local Newtonian gravity balances cosmological dark energy in a concordance cosmology — is computed between two point objects of low mass.”

“A theme that has come to the fore in advanced planning for long-range space exploration is the concept of “propellantless propulsion” or “field propulsion.” One version of this concept involves the projected possibility that empty space itself (the quantum vacuum, or space-time metric) might be manipulated so as to provide energy/thrust for future space vehicles. Although such a proposal has a certain science-fiction quality about it, modern theory describes the vacuum as a polarizable medium that sustains energetic quantum fluctuations. Thus the possibility that matter/vacuum interactions might be engineered for space-flight applications is not a priori ruled out, although certain constraints need to be acknowledged. The structure and implications of such a far-reaching hypothesis are considered herein.”

https://arxiv.org/abs/1012.5264

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This model based on ЛСDM is crashing after the JWST deep field,

The new model is exposed briefly on my web site and explain more simply the DM origine in respect of Hubble Sphere and it is named Ea-DE mAm mode:

http://www.bio-astronomia.blogspot.it