Algorithms for Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation can be explained numerically in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and α. Furthermore, every equation can also be explained in terms of the Avogadro number and the number of electrons at 1 C. We show that every equation can be described in terms of the Planck constant. Then, the ratio of the gravitational force to the electric force can be uniquely determined with the assumption of minimum mass. In this report, we describe the algorithms used to explain these equations in detail. Thus, there are no dimension mismatch problems.

Ratio of Gravitational Force to Electric Force from Empirical Equations in Terms of the Cosmic Microwave Background Temperature

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature. Next, we propose an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10−11 m3∙kg−1∙s−2, respectively. Every equation could be explained in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and a. Furthermore, every equation could also be explained in terms of Avogadro’s number and the number of electrons in 1 C. However, the ratio of the gravitational force to the electric force cannot be uniquely determined when the unit of the Planck constant (Js) is changed. In this study, we showed that every equation can be described in terms of Planck constant. From the assumption of minimum mass, the ratio of gravitational force to electric force could be elucidated.

Correspondence Principle for Empirical Equations in Terms of the Cosmic Microwave Background Temperature with Solid-State Ionics

Previously, we presented several empirical equations using the cosmic microwave background (CMB) temperature that were mathematically connected. Next, we proposed an empirical equation for the fine-structure constant. Considering the compatibility among these empirical equations, the CMB temperature (Tc) and gravitational constant (G) were calculated to be 2.726312 K and 6.673778 × 10-11 m3·kg-1·s-2, respectively. Every equation can be explained in terms of the Compton length of an electron (λe), the Compton length of a proton (λp) and α. However, these equations are difficult to follow. Using the correspondence principle with the thermodynamic principles in solid-state ionics, we propose a canonical ensemble to explain these equations in this report. For this purpose, we show that every equation can be explained in terms of Avogadro’s number and the number of electrons in 1 C.

The Origin of Cosmic Microwave Background Radiation

This paper explains the Olbers paradox and the origin of cosmic microwave background radiation (CMBR) from the viewpoint of the quantum redshift effect. The derived formula dispels the Olbers paradox, confirming that the CMBR originates from the superposition of light radiated by stars in the whole universe, not the relic of the Big Bang. The dark-night sky and CMBR are all caused by Hubble redshift—the physical mechanism is the quantum redshift of the photon rather than cosmic expansion. So this theory supports the infinite and steady cosmology.

Possible Relations of Cosmic Microwave Background with Gravity and Fine-Structure Constant

Gravity is the only force that cannot be explained by the Standard Model (SM), the current best theory describing all the known fundamental particles and their forces. Here we reveal that gravitational force can be precisely given by mass of objects and microwave background (CMB) radiation. Moreover, using the same strategy we reveal a relation by which CMB can also precisely define fine-structure constant α.

The Derivation of the Cosmic Microwave Background Radiation Peak Spectral Radiance, Planck Time, and the Hubble Constant from the Neutron and Hydrogen

Purpose: The cosmic microwave background radiation, CMB, is fundamental to observational cosmology, and is believed to be a remnant from the Big Bang. The CMB, Planck time, tP, and the Hubble constant, H0, are important cosmologic constants. The goal is to accurately derive and demonstrate the inter-relationships of the CMB peak spectral radiance frequency, tP, and H0 from neutron and hydrogen quantum data only. Methods: The harmonic neutron hypothesis, HNH, evaluates physical phenomena within a finite consecutive integer and exponential power law harmonic fraction series that are scaled by a fundamental frequency of the neutron as the exponent base. The CMB and the H0 are derived from a previously published method used to derive tP. Their associated integer exponents are respectively +1/2, −3/4, and −128/35. Results: Precise mathematical relationships of these three constants are demonstrated. All of the derived values are within their known observational values. The derived and known values are: νCMB, 160.041737 (06) × 109 Hz, ~160 × 109 Hz;2.72519 K, 2.72548 ± 0.00057 K, H0 2.29726666 (11) × 10−18 s−1, ~2.3 × 10−18 s−1;and tP 5.3911418 (3) × 10−44 s, 5.39106 (32) × 10−44 s. Conclusion: The cosmic fundamental constants tP, H0, and CMB are mathematically inter-related constants all defined by gravity. They are also directly derivable from the quantum properties of the neutron and hydrogen within a harmonic power law.

Cosmic microwave background constraints on the tensor-to-scalar ratio

One of the main goals of modern cosmic microwave background （CMB） missions is to measure the tensor-to-scalar ratio r accurately to constrain inflation models. Due to ignorance about the reionization history Xe （z）, this analysis is usu- ally done by assuming an instantaneous reionization Xe （z） which, however, can bias the best-fit value of r. Moreover, due to the strong mixing of B-mode and E-mode polarizations in cut-sky measurements, multiplying the sky coverage fraction fsky by the full-sky likelihood would not give satisfactory results. In this work, we forecast constraints on r for the Planck mission taking into account the general reionization scenario and cut-sky effects. Our results show that by applying an N-point interpo- lation analysis to the reionization history, the bias induced by the assumption of in- stantaneous reionization is removed and the value of r is constrained within 5% error level, if the true value of r is greater than about 0.1.

Various Empirical Equations for the Electromagnetic Force in Terms of the Cosmic Microwave Background Temperature

Previously, we proposed an empirical equation describing the relationship between the gravitational force and the temperature of the cosmic microwave background (CMB). After evaluating our equation, we discovered many empirical equations describing the electromagnetic force in terms of the CMB, including equations for the Rydberg constant, the Bohr radius, the Compton wavelength, the classical electron radius, the Hartree energy, the Coulomb’s law with distance, and the ratio between the gravitational force and electric force. The background theory is not yet complete. However, we can justify why the discovered empirical equations should not be coincidence.

COSMIC MICROWAVE BACKGROUND

Revised September 2013 by D. Scott （University of British Columbia） and G.F. Smoot （UCB/LBNL）. Appendix A, describing the BICEP2 B-mode polarization result, added April 2014.

Introducing a 2nd Universal Space-Time Constant Can Explain the Observed Age of the Universe and Dark Energy

The purpose of this paper is to introduce new theoretical concepts as opposed to accepting the existence of dark entities, such as dark energy. This research sought to introduce a 2nd universal space-time constant, besides having a finite speed constant (speed of light in vacuum c). A finite universal age constant b is introduced. Namely, this paper shows that the changes in the Earth’s anomalistic year duration over time support the hypothesis of the age of the universe correlating with a maximum number of orbital revolutions constant. Neglecting the gravitational influence of other cosmological entities in the proximity of the Earth, the constant maximum number of revolutions is herewith determined solely by the Earth’s orbital revolutions around the Sun. The value of the universal age constant b is calculated to be around 13.8 billion orbital revolutions, derived out of an equation related to the changes in the Earth’s anomalistic year duration over time and the so-called Hubble tension. The above-mentioned calculated value b correlates well with the best fit to measured data of the cosmic microwave background radiation (CMBR) by the Planck spacecraft, the age of the observed universe is measured to be approximately 13.787 ± 0.020 billion years (2018 final data release). Developing a theory with this 2nd universal space-time constant b, being covariant with respect to the Lorentz transformations when time spans are large, gives results such as: A confirmation of the measured CMBR value of 13.787 ± 0.020 billion years. Correlating well with the observed expansion rate of the universe (dark energy). The universe’s expansion accelerating over the last four to five billion years.

How the Flat Space Cosmology Model Correlates the Recombination CMB Temperature of 3000 K with a Redshift of 1100

This paper shows how the Flat Space Cosmology model correlates the recom-bination epoch CMB temperature of 3000 K with a cosmological redshift of 1100. This proof is given in support of the recent publication that the Tatum and Seshavatharam Hubble temperature formulae can be derived using the Stephan-Boltzmann dispersion law. Thus, as explained herein, the era of high precision Planck scale quantum cosmology has arrived.

The Speed of Light Is Not Constant in Basic Big Bang Theory

Starting from the basic assumptions and equations of Big Bang theory, we present a simple mathematical proof that this theory implies a varying (decreasing) speed of light, contrary to what is generally accepted. We consider General Relativity, the first Friedmann equation and the Friedmann-Lema?tre- Robertson-Walker (FLRW) metric for a Comoving Observer. It is shown explicitly that the Horizon and Flatness Problems are solved, taking away an important argument for the need of Cosmic Inflation. A decrease of 2.1 cm/s per year of the present-day speed of light is predicted. This is consistent with the observed acceleration of the expansion of the Universe, as determined from high-redshift supernova data. The calculation does not use any quantum processes, and no adjustable parameters or fine tuning are introduced. It is argued that more precise laboratory measurements of the present-day speed of light (and its evolution) should be carried out. Also it is argued that the combination of the FLRW metric and Einstein’s field equations of General Relativity is inconsistent, because the FLRW metric implies a variable speed of light, and Einstein’s field equations use a constant speed of light. If we accept standard Big Bang theory (and thus the combination of General Relativity and the FLRW metric), a variable speed of light must be allowed in the Friedmann equation, and therefore also, more generally, in Einstein’s field equations of General Relativity. The explicit form of this time dependence will then be determined by the specific problem.

Variable Physical Constants and Beyond

We previously revealed that the speed of light in vacuum c, the gravitational constant G, the vacuum permittivity ε, and the vacuum permeability μ can be defined by the temperature T (or the expected average frequency f) of cosmic microwave background (CMB) radiation. Given that CMB is continuously cooling, that is, T is continuously decreasing, we proposed that the above “constants” are variable and their values at some space-time with CMB temperature T (cT, GT, εT, and μT) can be described using their values (c0, G0, ε0, and μ0) and the temperature (T0) of CMB at present space-time. Based on the above observation, a number of physical equations related with these constants are re-described in this study, including relativity equation, mass-energy equation, and Maxwell’s equations, etc.

Explanation of the Necessity of the Empirical Equations That Relate the Gravitational Constant and the Temperature of the CMB

In previous papers, we proposed an empirical equation for the fine-structure constant. Using this equation, we proposed a refined version of our own former empirical equations about the electromagnetic force and gravity in terms of the temperature of the cosmic microwave background. The calculated values of the temperature of the cosmic microwave background (Tc) and the gravitational constant (G) were 2.726312 K and 6.673778 × 10-11 m3⋅kg-1⋅ s-2, respectively. Then, for the values of the factors 9/2 and π in our equations, we used 4.488519503 and 3.132011447, respectively. However, we could not provide a theoretical explanation for the necessity of these empirical equations. In this paper, using the redefinition method for the UNIT, we show the necessity for our empirical equations.

Nonlocal Theory of the Photon Gas Evolution Beginning from the Planck Time

Evolution of the photon gas (PG) in the Planck period is considered as a particular case of the physical vacuum (PV) hydrodynamics. Nonlocal quantum hydrodynamic equations are applied for calculation of the photon gas evolution. In general case, PG hydrodynamics contains gravitation in the explicit form. Exact analytical solutions of PG hydrodynamics are obtained. Solutions show the exponential growth of gradient values for internal energy in time and space. In comparison with phenomenological General Relativistic Theory, Nonlocal quantum hydrodynamics (NQH) does not lead to contradictions in all limit cases. Theory of physical vacuum and the theory of photonic gas are related theories. These theoretical (analytical!) results confirm the result of direct observations (Arno Alan Penzias and Robert Woodrow Wilson, Nobel Prize (1978) for their discovery of cosmic microwave background;John C. Mather and George F. Smoot. Nobel Prize (2006) for their discovery of the blackbody form and anisotropy of the cosmic microwave background radiation).

A Different Cosmology—Thoughts from Outside the Box

In this paper, we present a new cosmology based on the idea of a universe dominated by vacuum energy with time-varying curvature. In this model, the universe began with an exponential Plank era inflation before transitioning to a spacetime described by Einstein’s equations. While no explicit model of the Plank era is yet known, we do establish a number of properties that the vacuum of that time must have exhibited. In particular, we show that structures came into existence during that inflation that were later responsible for all cosmic structures. A new solution of Einstein’s equations incorporating time-varying curvature is presented which predicts that the scaling was initially power law with a parameter of y=1/2 before transitioning to an exponential acceleration of the present-day scaling. A formula relating the curvature to the vacuum energy density is also a part of the solution. A non-conventional model of nucleosynthesis provides a solution for the matter/antimatter asymmetry problem and a non-standard origin of the CMB. The CMB power spectrum is shown to be a consequence of uncertainties embedded during the initial inflation and the existence of superclusters. Using Einstein’s equations, we show that so-called dark matter is, in fact, vacuum energy. A number of other issues are discussed.

A special kind of local structure in the CMB intensity maps: duel peak structure

We study the local structure of Cosmic Microwave Background （CMB） temperature maps released by the Wilkinson Microwave Anisotropy Probe （WMAP） team, and find a new kind of structure, which can be described as follows： a peak （or valley） of average temperature is often followed by a peak of temperature fluctuation that is 4° away. This structure is important for the following reasons： both the well known cold spot detected by Cruz et al. and the hot spot detected by Vielva et al. with the same technology （the third spot in their article） have such structure; more spots that are similar to them can be found on CMB maps and they also tend to be significant cold/hot spots; if we change the 4° characteristic into an artificial one, such as 3° or 5°, there will be less ＂similar spots＂, and the temperature peaks or valleys will be less significant. The presented ＂sim- ilar spots＂ have passed a strict consistency test which requires them to be significant on at least three different CMB temperature maps. We hope that this article could arouse some interest in the relationship of average temperature with temperature fluctuation in local areas; meanwhile, we are also trying to find an explanation for it which might be important to CMB observation and theory.

On the Possibility of Describing the Origin of the Big Bang According to the Hypothesis of Primary Particles

In this paper, we have determined the basic physical quantities that describe the very formation of the Big Bang using hypothetical primary particles, in accordance with our Hypothesis of primary particles, as well as with the logically observed smallest increment of speed that can exist, the “speed quantum”. According to the Hypothesis of primary particles, they exist in their basic, dynamic state, in their own flat spacetime, moving mutually at speeds much higher than the speed of light in a vacuum. Hence, a certain probability of a collision among these hypothetical particles exists, during which one of them would be abruptly decelerated to a speed greater than the border speed in our Universe, c, by a speed quantum, εu. As shown in this Hypothesis, such deceleration would increase the energy and the momentum of this particle immensely, so that in a very short period of time, they could tunnel into our Universe through the Big Bang, creating our total energy as well as our spacetime. With this theoretical consideration, we determined the power released during the Big Bang itself, the time period during which it took place, and its radius: PB≈1.63×10183W, tB≈9.51×10-114s and rB≈2.85×10-105m. Evidently, this approach allowed us to theoretically push the boundaries for the description of this singularity to values lesser than the Planck time and the Planck length. We expect that the results for the initial singularity itself will allow a more detailed study of the Big Bang.

On the Possibility of Variable Speed of Light in Vacuum

We previously revealed a quantitative relation by which the fine-structure constant α can be described by the temperature T of cosmic microwave background (CMB) with several other fundamental constants, including the elementary charge e, the Boltzmann constant k, the Planck constant h, and the light of speed in vacuum c. Given that the value of α is quite conserved but T is variable across CMBs, we propose that c changes with T and can be given by T, the present CMB temperature T0 and the present light speed c0. As T is continuously decreasing, c is thus predicted to decrease at a rate of ~2.15 centimeters/second (cm/s) per year. Moreover, we provide a lot of evidence to support this finding. In conclusion, this study suggests a possibility of variable speed of light in vacuum.

Reconstruction of Gas Temperature and Density Profiles of the Galaxy Cluster RX J1347.5–1145

We use observations of Sunyaev-Zel＇dovich effect and X-ray surface brightness to reconstruct the radial profiles of gas temperature and density under the assumption of a spherically symmetric distribution of the gas. The method of reconstruction, first raised by Silk ＆ White, depends directly on the observations of the Sunyaev-Zel＇dovich effect and the X-ray surface brightness, without involving additional assumptions such as the equation of state of the gas or the conditions of hydrostatic equilibrium. We applied this method to the cluster RX J1347.5-1145, which has both the Sunyaev-Zel＇dovich effect and X-ray observa- tions with relative high precision. It is shown that it will be an effective method to obtain the gas distribution in galaxy clusters. Statistical errors of the derived temperature and density profiles of gas were estimated according to the observational uncertainties.