×

Particle pair production in cosmological general relativity. (English) Zbl 1264.83038

Summary: The cosmological general relativity (CGR) of Carmeli, a 5-dimensional (5-D) theory of time, space and velocity, predicts the existence of an acceleration \(a _{0}=c/\tau \) due to the expansion of the universe, where \(c\) is the speed of light in vacuum, \(\tau =1/h\) is the Hubble-Carmeli time constant, where \(h\) is the Hubble constant at zero distance and no gravity. The Carmeli force on a particle of mass \(m\) is \(F _{c }=ma _{0}\), a fifth force in nature. In CGR, the effective mass density \(\rho_{\mathrm{eff}}=\rho - \rho _{c }\), where \(\rho \) is the matter density and \(\rho _{c }\) is the critical mass density which we identify with the vacuum mass density \(\rho _{\mathrm{vac}}= - \rho _{c }\).
The fields resulting from the weak field solution of the Einstein field equations in 5-D CGR and the Carmeli force are used to hypothesize the production of a pair of particles. The mass of each particle is found to be \(m=\tau c ^{3}/4G\), where \(G\) is Newton’s constant. The vacuum mass density derived from the physics is \(\rho_{vac }= - \rho_{c}= - 3/8\pi G\tau ^{2}\). We make a connection between the cosmological constant of the Friedmann-Robertson-Walker model and the vacuum mass density of CGR by the relation \(\Lambda = - 8\pi G\rho_{\mathrm{vac}}=3/\tau^{2}\). Each black hole particle defines its own volume of space enclosed by the event horizon, forming a sub-universe.
The cosmic microwave background (CMB) black body radiation at the temperature \(T _{o }=2.72548\) K which fills that volume is found to have a relationship to the ionization energy of the Hydrogen atom. Define the radiation energy \(\varepsilon _{\gamma }=(1 - g)mc ^{2}/N _{\gamma }\), where \((1 - g)\) is the fraction of the initial energy \(mc ^{2}\) which converts to photons, \(g\) is a function of the baryon density parameter \(\Omega _{b }\) and \(N _{\gamma }\) is the total number of photons in the CMB radiation field. We make the connection with the ionization energy of the first quantum level of the Hydrogen atom by the hypothesis \[ \epsilon_{\gamma} = \frac{ ( 1 - g) m c^2 }{ N_{\gamma} } = \frac{\alpha^2 \mu c^2}{2}, \] where \(\alpha \) is the fine-structure constant and \(\mu =m _{p } f/(1+f)\), where \(f=m _{e }/m _{p }\) with \(m _{e }\) the electron mass and \(m _{p }\) the proton mass. We give a model for \(g\approx \Omega _{b }(1+f)m _{p }/m _{n }\), where \(m _{n }\) is the neutron mass. Then ratio \(\eta \) of the number of baryons \(N _{b }\) to photons \(N _{\gamma }\) is given by \[ \eta = \frac{N_b}{N_{\gamma}} \approx \frac{\alpha^2 \varOmega_b f m_p / m_n}{ 2 ( 1 + f) [ 1 - \varOmega_b ( 1 + f) m_p / m_n ] } \] with a value of \(\eta \approx 6.708\times 10^{ - 10}\).
The Bekenstein-Hawking black hole entropy \(S\) is given by \(S=(kc ^{3} A)/(4\hbar G)\), where \(k\) is Boltzmann’s constant, \(\hbar\) is Planck’s constant over \(2\pi \) and \(A\) is the area of the event horizon. For our black hole sub-universe of mass \(m\) the entropy is given by \[ S = \frac{\pi k \tau^2 c^5 }{ \hbar G }, \] which can be put into the form relating to the vacuum mass density \[ \rho_{vac} = \frac{\rho_P }{ ( S / k) }, \] where the cosmological Planck mass density \(\rho_{P} = -\mathcal{M}_{P} / L^{3}_{P}\). The cosmological Planck mass \(\mathcal{M}_{P} = \sqrt{ \sqrt{ 3 / 8 } \hbar c / G}\) and length \(L_{P} = \hbar / \mathcal{M}_{P} c\). The value of \((S/k)\approx 1.980\times 10^{122}\).

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83F05 Relativistic cosmology
83C47 Methods of quantum field theory in general relativity and gravitational theory
85A40 Astrophysical cosmology
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Behar, S., Carmeli, M.: Cosmological relativity: a new theory of cosmology. Int. J. Theor. Phys. 39(5), 1375–1396 (2000). arXiv:astro-ph/0008352 · Zbl 0959.83040 · doi:10.1023/A:1003651222960
[2] Carmeli, M.: Cosmological Relativity. World Scientific, Singapore (2006) · Zbl 1166.83001
[3] Carmeli, M.: Relativity: Modern Large-Scale Spacetime Structure of the Cosmos. World Scientific, Singapore (2008) · Zbl 1170.83001
[4] Carmeli, M.: Derivation of the Tully-Fisher law: doubts about the necessity and existence of Halo dark matter. Int. J. Theor. Phys. 39(5), 1397–1404 (2000) · Zbl 0974.83063 · doi:10.1023/A:1003642921142
[5] Hartnett, J.G.: Extending the Redshift-Distance relation in cosmological general relativity to higher redshifts. Found. Phys. 38(3), 201–215 (2008). doi: 10.1007/s10701-007-9198-5 · Zbl 1138.85306 · doi:10.1007/s10701-007-9198-5
[6] Carmeli, M., Kuzmenko, T.: Value of the cosmological constant in the cosmological relativity theory. Int. J. Theor. Phys. 41(1), 131–135 (2002). arXiv:astro-ph/0110590 · Zbl 0992.83060 · doi:10.1023/A:1013229818403
[7] Costa, M.S., Malcolm, J.P.: Interacting black holes. Nucl. Phys. B 591, 469–487 (2000) · Zbl 1006.83026 · doi:10.1016/S0550-3213(00)00577-0
[8] Reif, F.: Fundamentals of Statistical and Thermal Physics, pp. 373–378. McGraw-Hill, New York (1965)
[9] Akerlof, C.W.: The Planck blackbody spectral distribution and measurement of the solar photosphere temperature (2009). http://instructor.physics.lsa.umich.edu/adv-labs/BBD_Solar_Temp/Solar_Radiometry.pdf . Accessed 22 March 2012
[10] WMAP Cosmological Parameters: Model: lcdm+sz+lens, Data: wmap7+cmb. http://lambda.gsfc.nasa.gov/product/map/current/params/
[11] Fields, B., Sarkar, S.: Big-bang nucleosynthesis (2006). arXiv:astro-ph/0601514
[12] Tolman, R.C.: On the estimation of distances in a curved universe with non-static line element. Proc. Natl. Acad. Sci. 16, 515–520 (1930) · JFM 56.1365.05
[13] Bekenstein, J.D.: Do we understand black hole entropy? In: Proc. of the Seventh Marcel Grossmann Meeting, Part A, pp. 39–58 (1994). arXiv:gr-qc/9409015
[14] Wikipedia: Black hole thermodynamics. en.wikipedia.org/wiki/Black_hole_thermodynamics
[15] Cohen, A.G., De Rújula, A., Glashow, S.L.: A matter-antimatter universe? Astrophys. J. 495, 539–549 (1998) · doi:10.1086/305328
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.