Using a rigorous mathematical approach, we demonstrate how the Cosmic Microwave Background (CMB) temperature could simply be a form of geometric mean temperature between the minimum time-dependent Hawking Hubble tempe...Using a rigorous mathematical approach, we demonstrate how the Cosmic Microwave Background (CMB) temperature could simply be a form of geometric mean temperature between the minimum time-dependent Hawking Hubble temperature and the maximum Planck temperature of the expanding universe over the course of cosmic time. This mathematical discovery suggests a re-consideration of Rh=ctcosmological models, including black hole cosmological models, even if it possibly could also be consistent with the Λ-CDM model. Most importantly, this paper contributes to the growing literature in the past year asserting a tightly constrained mathematical relationship between the CMB temperature, the Hubble constant, and other global parameters of the Hubble sphere. Our approach suggests a solid theoretical framework for predicting and understanding the CMB temperature rather than solely observing it.1.展开更多
In the Hubble sphere,we assume that the wavelength of pure energy spreads out in all directions.The maximum wavelength in the Hubble sphere is then the circumference of the Hubble sphere.We assume the minimum waveleng...In the Hubble sphere,we assume that the wavelength of pure energy spreads out in all directions.The maximum wavelength in the Hubble sphere is then the circumference of the Hubble sphere.We assume the minimum wavelength occurs in a Planck mass black hole,which is given by,4πR_(s,p)= 8πl_(p).Here,we build further on the geometric mean CMB approach by Haug and Tatum and based on new analysis given in this paper1 we conclude that the CMB temperature is simply given as:cmb min max T_(cmb)=T_(min)T_(max),which is the geometric mean of the minimum and maximum physically possible temperatures in the Hubble sphere.This again means the CMB temperature simply is the geometric mean of the Hawking temperature of the Hubble sphere(in black hole cosmology)and the Hawking temperature of the Planck mass black hole,se we have also T_(cmb)=T_(Haw,H) T_(Haw,p).展开更多
Based on recent progress in quantum gravity and quantum cosmology, we are also presenting a way to estimate the temperature in the cosmos, the Hubble sphere, from a relation between the Planck temperature and the Hubb...Based on recent progress in quantum gravity and quantum cosmology, we are also presenting a way to estimate the temperature in the cosmos, the Hubble sphere, from a relation between the Planck temperature and the Hubble scale. Our analysis predicts the Hubble sphere temperature of 2.72 K with the one standard deviation confidence interval between 2.65 K and 2.80 K, which corresponds well with the measured temperature observed from the cosmic microwave background (CMB) of about 2.72 K. This adds evidence that there is a close connection between the Planck scale, gravity, and the cosmological scales as anticipated by Eddington already in 1918.1.展开更多
This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper su...This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.展开更多
We are proposing a temperature formula for the Cosmic Neutrino back-ground(CνB)temperature that can be derived from the Stefan-Boltzman law under certain assumptions,such as R_(H_(t))=ct cosmology.Our derived for-mul...We are proposing a temperature formula for the Cosmic Neutrino back-ground(CνB)temperature that can be derived from the Stefan-Boltzman law under certain assumptions,such as R_(H_(t))=ct cosmology.Our derived for-mula gives a prediction of the CνB temperature of 1.9336 K±0.0072 K which is in line with the current literature on the topic.展开更多
Based on the latest Planck surveys, the universe is close to being remarkably flat, and yet, within observational error, there is still room for a slight curvature. If the curvature is positive, then this would lead t...Based on the latest Planck surveys, the universe is close to being remarkably flat, and yet, within observational error, there is still room for a slight curvature. If the curvature is positive, then this would lead to a closed universe, as well as allow for a big bounce scenario. Working within these assumptions, and using a simple model, we predict that the cosmos may have a positive curvature in the amount, <span style="white-space:nowrap;"><span style="white-space:nowrap;">Ω<sub>0</sub>=1.001802</span></span>, a value within current observational bounds. For the scaling laws associated with the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" style="white-space:normal;" />, equals the smeared cosmic susceptibility. If we allow the <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" /> to <em>decrease with increasing</em> cosmic scale parameter, “<em>a</em>”, then we can predict a maximum Hubble volume, with minimum CMB temperature for the voids, before contraction begins, as well as a minimum volume, with maximum CMB temperature, when expansion starts. A specific heat engine model for the cosmos is also entertained for this model of a closed universe.展开更多
We present how the Bekenstein-Hawking entropy of a growing black hole variant of R_(h)=ct cosmology model can be re-written as a function of the Cosmic Microwave Background(CMB)radiation temperature or Hubble paramete...We present how the Bekenstein-Hawking entropy of a growing black hole variant of R_(h)=ct cosmology model can be re-written as a function of the Cosmic Microwave Background(CMB)radiation temperature or Hubble parameter,rather than the Hubble radius,as first pointed out by Tatum and Seshavatharam[1].We then show how our CMB temperature formulae lead to much higher precision in the estimated entropy of the Hubble radius universe,since the CMB temperature can be measured with great precision.We also briefly discuss how the Schwarzschild metric can be re-written as a function of the Bekenstein-Hawking entropy,and how the entropy of the universe can be directly linked to recent estimates of the number of quantum operations in the universe since its beginning.展开更多
Making use of a CMB temperature formula derivable from the Stefan-Boltzmann law, we have discovered a duality between the Particle Data Group (PDG) CMB temperature of 2.7255 K and its implied Hubble constant H0value o...Making use of a CMB temperature formula derivable from the Stefan-Boltzmann law, we have discovered a duality between the Particle Data Group (PDG) CMB temperature of 2.7255 K and its implied Hubble constant H0value of approximately 66.9 km/s/Mpc, which can be used to predict the 2287 observed supernova redshifts in the PantheonPlusSH0ES database. Both values of this duality fall within constraints set for these cosmological parameters by the Particle Data Group. Notably, because our solution requires a rigorous mathematical derivation of a cosmological distance-vs-redshift formula pertaining to a variant of the RH=ctcosmology model, our supernova redshift-matching solution fits only within the H0constraints of the 2018 Planck Collaboration and the PDG. It is our conclusion that, by matching the entire PantheonPlusSH0ES dataset of 2287 observations with the Planck Collaboration H0constraints, such a dataset provides strong support for a H0value of H0=66.8943−0.0287+0.0287km/s/Mpc based on the Fixsen (2009) observation of T0=2.72548−0.00057+0.00057K.展开更多
This paper provides a brief historical summary of recent progress made with respect to the Upsilon constant linkage between the time-dependent Hubble parameter and the time-dependent cosmic temperature.We discuss how ...This paper provides a brief historical summary of recent progress made with respect to the Upsilon constant linkage between the time-dependent Hubble parameter and the time-dependent cosmic temperature.We discuss how our original RH=ct variant model,called Flat Space Cosmology(FSC),has evolved,including how it has recently been used as an approach to resolving the Hubble tension,to extend the cosmic age to alleviate the early galaxy formation problem,and to provide highly useful Friedmann equations in thermodynamic form.A new and tantalizing cosmic rotation resolution of the Hubble tension using FSC is also briefly discussed,including whether it could also explain“dark energy”observations.展开更多
Haug and Tatum have recently outlined a possible path to solving the Hubble tension within R_(H_(t))=ct cosmology models using a trial-and-error algorithm for redshift scaling,specifically z=(R_(H_(0))/R_(H_(t)))-1 an...Haug and Tatum have recently outlined a possible path to solving the Hubble tension within R_(H_(t))=ct cosmology models using a trial-and-error algorithm for redshift scaling,specifically z=(R_(H_(0))/R_(H_(t)))-1 and z=(R_(H_(0))/R_(H_(t)))^(1/2)-1.Their algorithm demonstrates that one can start with the measured CMB temperature and a rough estimate of H_(0).Based on this approach,they nearly perfectly match the entire distance ladder of observed supernovae by identifying a single value for H_(0).This work replaces a previous numerical approach with a formal,closed-form mathematical solution.Furthermore,we will prove that this solution is valid for a much more general case of any cosmological redshift scaling consistent with:z=(R_(H_(0))/R_(H_(t)))^(x)-1.Haug and Tatum have only considered the most common assumptions of x=1 and x=1/2.Our solution involves simply solving an equation to determine the correct value of H_(0).This is possible because an exact mathematical relation between H_(0)and the CMB temperature has recently been established,in combination with the linearity in an R_(H_(t))=ct model.We also demonstrate that a thermodynamic form of the Friedmann equation is consistent with a wide range of redshift scalings,namely:z=(R_(H_(0))/R_(H_(t)))^(x)-1.展开更多
A naive toy model that the fermion sea offers the dark matter density is discussed here.If the fermion sea fills the total space and the temperature equals the temperature of CMB,we can get the mass of the fermion is ...A naive toy model that the fermion sea offers the dark matter density is discussed here.If the fermion sea fills the total space and the temperature equals the temperature of CMB,we can get the mass of the fermion is about 4.7×10 38 kg (0.026 eV).展开更多
文摘Using a rigorous mathematical approach, we demonstrate how the Cosmic Microwave Background (CMB) temperature could simply be a form of geometric mean temperature between the minimum time-dependent Hawking Hubble temperature and the maximum Planck temperature of the expanding universe over the course of cosmic time. This mathematical discovery suggests a re-consideration of Rh=ctcosmological models, including black hole cosmological models, even if it possibly could also be consistent with the Λ-CDM model. Most importantly, this paper contributes to the growing literature in the past year asserting a tightly constrained mathematical relationship between the CMB temperature, the Hubble constant, and other global parameters of the Hubble sphere. Our approach suggests a solid theoretical framework for predicting and understanding the CMB temperature rather than solely observing it.1.
文摘In the Hubble sphere,we assume that the wavelength of pure energy spreads out in all directions.The maximum wavelength in the Hubble sphere is then the circumference of the Hubble sphere.We assume the minimum wavelength occurs in a Planck mass black hole,which is given by,4πR_(s,p)= 8πl_(p).Here,we build further on the geometric mean CMB approach by Haug and Tatum and based on new analysis given in this paper1 we conclude that the CMB temperature is simply given as:cmb min max T_(cmb)=T_(min)T_(max),which is the geometric mean of the minimum and maximum physically possible temperatures in the Hubble sphere.This again means the CMB temperature simply is the geometric mean of the Hawking temperature of the Hubble sphere(in black hole cosmology)and the Hawking temperature of the Planck mass black hole,se we have also T_(cmb)=T_(Haw,H) T_(Haw,p).
文摘Based on recent progress in quantum gravity and quantum cosmology, we are also presenting a way to estimate the temperature in the cosmos, the Hubble sphere, from a relation between the Planck temperature and the Hubble scale. Our analysis predicts the Hubble sphere temperature of 2.72 K with the one standard deviation confidence interval between 2.65 K and 2.80 K, which corresponds well with the measured temperature observed from the cosmic microwave background (CMB) of about 2.72 K. This adds evidence that there is a close connection between the Planck scale, gravity, and the cosmological scales as anticipated by Eddington already in 1918.1.
文摘This paper introduces the two Upsilon constants to the reader. Their usefulness is described with respect to acting as coupling constants between the CMB temperature and the Hubble constant. In addition, this paper summarizes the current state of quantum cosmology with respect to the Flat Space Cosmology (FSC) model. Although the FSC quantum cosmology formulae were published in 2018, they are only rearrangements and substitutions of the other assumptions into the original FSC Hubble temperature formula. In a real sense, this temperature formula was the first quantum cosmology formula developed since Hawking’s black hole temperature formula. A recent development in the last month proves that the FSC Hubble temperature formula can be derived from the Stephan-Boltzmann law. Thus, this Hubble temperature formula effectively unites some quantum developments with the general relativity model inherent in FSC. More progress towards unification in the near-future is expected.
文摘We are proposing a temperature formula for the Cosmic Neutrino back-ground(CνB)temperature that can be derived from the Stefan-Boltzman law under certain assumptions,such as R_(H_(t))=ct cosmology.Our derived for-mula gives a prediction of the CνB temperature of 1.9336 K±0.0072 K which is in line with the current literature on the topic.
文摘Based on the latest Planck surveys, the universe is close to being remarkably flat, and yet, within observational error, there is still room for a slight curvature. If the curvature is positive, then this would lead to a closed universe, as well as allow for a big bounce scenario. Working within these assumptions, and using a simple model, we predict that the cosmos may have a positive curvature in the amount, <span style="white-space:nowrap;"><span style="white-space:nowrap;">Ω<sub>0</sub>=1.001802</span></span>, a value within current observational bounds. For the scaling laws associated with the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" style="white-space:normal;" />, equals the smeared cosmic susceptibility. If we allow the <img src="Edit_18751d6f-dbfa-47ba-be7c-8298073a34fd.png" alt="" /> to <em>decrease with increasing</em> cosmic scale parameter, “<em>a</em>”, then we can predict a maximum Hubble volume, with minimum CMB temperature for the voids, before contraction begins, as well as a minimum volume, with maximum CMB temperature, when expansion starts. A specific heat engine model for the cosmos is also entertained for this model of a closed universe.
文摘We present how the Bekenstein-Hawking entropy of a growing black hole variant of R_(h)=ct cosmology model can be re-written as a function of the Cosmic Microwave Background(CMB)radiation temperature or Hubble parameter,rather than the Hubble radius,as first pointed out by Tatum and Seshavatharam[1].We then show how our CMB temperature formulae lead to much higher precision in the estimated entropy of the Hubble radius universe,since the CMB temperature can be measured with great precision.We also briefly discuss how the Schwarzschild metric can be re-written as a function of the Bekenstein-Hawking entropy,and how the entropy of the universe can be directly linked to recent estimates of the number of quantum operations in the universe since its beginning.
文摘Making use of a CMB temperature formula derivable from the Stefan-Boltzmann law, we have discovered a duality between the Particle Data Group (PDG) CMB temperature of 2.7255 K and its implied Hubble constant H0value of approximately 66.9 km/s/Mpc, which can be used to predict the 2287 observed supernova redshifts in the PantheonPlusSH0ES database. Both values of this duality fall within constraints set for these cosmological parameters by the Particle Data Group. Notably, because our solution requires a rigorous mathematical derivation of a cosmological distance-vs-redshift formula pertaining to a variant of the RH=ctcosmology model, our supernova redshift-matching solution fits only within the H0constraints of the 2018 Planck Collaboration and the PDG. It is our conclusion that, by matching the entire PantheonPlusSH0ES dataset of 2287 observations with the Planck Collaboration H0constraints, such a dataset provides strong support for a H0value of H0=66.8943−0.0287+0.0287km/s/Mpc based on the Fixsen (2009) observation of T0=2.72548−0.00057+0.00057K.
文摘This paper provides a brief historical summary of recent progress made with respect to the Upsilon constant linkage between the time-dependent Hubble parameter and the time-dependent cosmic temperature.We discuss how our original RH=ct variant model,called Flat Space Cosmology(FSC),has evolved,including how it has recently been used as an approach to resolving the Hubble tension,to extend the cosmic age to alleviate the early galaxy formation problem,and to provide highly useful Friedmann equations in thermodynamic form.A new and tantalizing cosmic rotation resolution of the Hubble tension using FSC is also briefly discussed,including whether it could also explain“dark energy”observations.
文摘Haug and Tatum have recently outlined a possible path to solving the Hubble tension within R_(H_(t))=ct cosmology models using a trial-and-error algorithm for redshift scaling,specifically z=(R_(H_(0))/R_(H_(t)))-1 and z=(R_(H_(0))/R_(H_(t)))^(1/2)-1.Their algorithm demonstrates that one can start with the measured CMB temperature and a rough estimate of H_(0).Based on this approach,they nearly perfectly match the entire distance ladder of observed supernovae by identifying a single value for H_(0).This work replaces a previous numerical approach with a formal,closed-form mathematical solution.Furthermore,we will prove that this solution is valid for a much more general case of any cosmological redshift scaling consistent with:z=(R_(H_(0))/R_(H_(t)))^(x)-1.Haug and Tatum have only considered the most common assumptions of x=1 and x=1/2.Our solution involves simply solving an equation to determine the correct value of H_(0).This is possible because an exact mathematical relation between H_(0)and the CMB temperature has recently been established,in combination with the linearity in an R_(H_(t))=ct model.We also demonstrate that a thermodynamic form of the Friedmann equation is consistent with a wide range of redshift scalings,namely:z=(R_(H_(0))/R_(H_(t)))^(x)-1.
基金supported by the National Natural Science Foundation of China (Grant Nos.10805002 and 11075011)the Foundation for the Author of National Excellent Doctoral Dissertation of China (Grant No.201020)the Fundamental Research Funds for the Central Universities
文摘A naive toy model that the fermion sea offers the dark matter density is discussed here.If the fermion sea fills the total space and the temperature equals the temperature of CMB,we can get the mass of the fermion is about 4.7×10 38 kg (0.026 eV).
