An Astrophysical Peek into Einstein’s Static Universe: No Dark Energy

Abhas Mitra

.

DOI: 10.4236/ijaa.2011.14024                

Abstract

It is shown that in order that the fluid pressure and acceleration are uniform and finite in Einstein’s Static Universe (ESU), , the cosmological constant, is zero. being a fundamental constant, should be same everywhere including the Friedman model. Independent proofs show that it must be so. Accordingly, the supposed acceleration of the universe and the attendant concept of “Dark Energy”(DE) could be an illusion; an artifact of explaining cosmological observations in terms of an oversimplified model which is fundamentally inappropriate. Indeed observations show that the actual universe is lumpy and inhomogeneous at the largest scales. Further in order that there is no preferred centre, such inhomogeneity might be expressed in terms of infinite hierarchial fractals. Also, the recent finding that the Friedman model intrinsically corresponds to zero pressure (and hence zero temperature) in accordance with the fact that an ideal Hubble flow implies no collision, no randomness (Mitra, Astrophys. Sp. Sc., 333,351, 2011) too shows that the Friedman model cannot represent the real universe having pressure, temperature and radiation. Dark Energy might also be an artifact of the neglect of dust absorption of distant Type 1a supernovae coupled with likely evolution of supernovae luminosities or imprecise calibration of cosmic distance ladders or other systemetic errors (White, Rep. Prog. Phys., 70, 883, 2007). In reality, observations may not rule out an inhomogeneous static universe (Ellis, Gen. Rel. Grav. 9, 87, 1978).

Keywords

General Relativity, Cosmological Constant, Cosmology, Dark Energy, Fractal Cosmology, Static Universe, Big Bang Theory

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	S. Weinberg, “Gravitation and Cosmology: Principles and Applications of General Theory of Relativity,” John Wi- ley, New York, 1972.
[2]	L. D. Landau and E. M. Lifshitz, “Classical Theory of Fields,” Pergamon Press, Oxford, 1962.
[3]	R. C. Tolman, “Static Solutions of Einstein’s Field Equa- tions for Spheres of Fluid,” Physical Review, Vol. 55, No. 4, 1939, pp. 364-373
[4]	R. C. Tolman, “Relativity, Thermodynamics & Cosmol- ogy,” Clarendon Press, Oxford, 1962.
[5]	H. Nariai, “On a New Cosmological Solution of Ein- stein’s Field Equations of Gravitation, “ General Relativ- ity and Gravitation, Vol. 31, No. 6, 1999, pp. 963-971. doi:10.1023/A:1026602724948
[6]	Z. Stuchlik and S. Hledk, “Some Properties of the Schwar- zschild-de Sitter and Schwarzschild-anti-de Sitter Space- times,” Physical Review D, Vol. 60, No. 4, 2000, Article ID: 044006.
[7]	C. G. Boehmer, “General Relativistic Static Fluid Solu- tions with Cosmological Constant,” Diploma Thesis, Pots- dam University, Potsdam, 2002, gr-qc/0308057.
[8]	C. G. Bohmer and G. Fodor, “Perfect Fluid Spheres with Cosmological Constant,” Physical Review D, Vol. 77, No. 6, 2008, Article ID: 064008
[9]	A. D. Rendall and B. G. Schmidt, “Existence and Proper- ties of Spherically Symmetric Static Fluid Bodies with a Given Equation of State,” Classical & Quantum Gravity, Vol. 8, No. 5, 1991, p. 985. doi:10.1088/0264-9381/8/5/022
[10]	T. W. Baumgarte and A. D. Rendall, “Regularity of Sphe- rically Symmetric Static Solutions of the Einstein Equa- tions,” Classical & Quantum Gravity, Vol. 10, No. 2, 1993, p. 327. doi:10.1088/0264-9381/10/2/014
[11]	A. Einstein, “On a Stationary System with Spherical Sym- metry Consisting of Many Gravitating Masses,” Annals of Mathematics, Vol. 40, No. 4, 1939, pp. 922-936. doi:10.2307/1968902
[12]	P. S. Florides, “A New Interior Schwarzschild Solution,” Proceedings of the Royal Society of London A, Mathematical and Physical Sciences, Vol. 337, No. 1611, 1974, pp. 529-535.
[13]	N. K. Kofinti, “On a New Interior Schwarzschild Solution,” General Relativity and Gravitation, Vol. 17, No. 3, 1985, pp. 245-249. doi:10.1007/BF00760246
[14]	C. G. Bohmer and F. S. N. Lobo, “A New Two-Sphere Singularity in General Relativity,” International Journal of Modern Physics D, Vol. 17, No. 06, 2008, pp. 897-910. doi:10.1142/S0218271808012565
[15]	L. Rudnick, S. Brown and L. R. Williams, “Extragalactic Radio Sources and the WMAP Cold Spot,” The Astro- physical Journal, Vol. 671, No. 1, 2007, pp. 40-44.
[16]	C. Park, et al., “Topology Analysis of the Sloan Digital Sky Survey. I. Scale and Luminosity Dependence,” The Astrophysical Journal, Vol. 633, No. 1, 2005, pp. 11-22. doi:10.1086/452625
[17]	R. R. Caldwell & A. Stebbins, “A Test of the Copernican Principle,” Physical Review Letters, Vol. 100, No. 19, 2008, Article ID: 191302.
[18]	A. Mitra, “No Uniform Density Star in General Relativity,” Astrophysics and Space Science, Vol. 333, No. 1, 2010, pp. 169-174. doi:10.1007/s10509-010-0567-8
[19]	H. A. Buchdahl, “General Relativistic Fluid Spheres,” Physical Review, Vol. 116, No. 4, 1959, pp. 1027-1034. doi:10.1103/PhysRev.116.1027
[20]	N. Rosen, “The Energy of the Universe,” General Relativity and Gravitation, Vol. 26, No. 3, 1994, pp. 319-321. doi:10.1007/BF02108013
[21]	F. I. Cooperstock, “Perspectives on the energy of the universe,” General Relativity and Gravitation, Vol. 26, No. 3, 1994, pp. 323-327. doi:10.1007/BF02108014
[22]	V. B. Johri, D. Kalligas, G. P. Singh and C. W. F. Everitt, “Gravitational Energy in the Expanding Universe,” Gen- eral Relativity and Gravitation, Vol. 27, No. 3, 1995, pp. 313-318. doi:10.1007/BF02109127
[23]	N. Banerjee and N. S. Sen, “Einstein Pseudotensor and Total Energy of the Universe,” Pramana, Vol. 49, No. 6, 1997, pp. 609-615. doi:10.1007/BF02848334
[24]	S. S. Xulu, “Total Energy of the Bianchi Type I Univer- ses,” International Journal of Theoretical Physics, Vol. 39, No. 4, 2000, pp. 1153-1161. doi:10.1023/A:1003670928681
[25]	V. Faraoni and F. I. Cooperstock, “On the Total Energy of Open Friedmann-Robertson-Walker Universes,” The Astrophysical Journal, Vol. 587, No. 2, 2003, pp. 483- 486. doi:10.1086/368258
[26]	A. Mitra, “Why Gravitational Contraction Must Be Ac- companied by Emission of Radiation in Both Newtonian and Einstein Gravity,” Physical Review D, Vol. 74, No. 2, 2006, Article ID: 024010.
[27]	A. Mitra, “Does Pressure Increase or Decrease Active Gravitational Mass Density,” Physics Letters B, Vol. 685, No. 1, 2010, pp. 8-11.
[28]	K. Kleidis and N. K. Spyrou, “A Conventional Approach to the Dark-Energy Concept,” Astronomy & Astrophysics, Vol. 529, No. 1, 2011, Article ID: 529A26.
[29]	S. D. M. White, “Fundamentalist Physics: Why Dark Ener- gy Is Bad for Astronomy,” Reports on Progress in Phys- ics, Vol. 70, No. 6, 2007, pp. 883-897.
[30]	A. Mitra, “The Matter in the Big-Bang Model Is Dust and Not Any Arbitrary Perfect Fluid!” Astrophysics and Space Science, Vol. 333, No. 1, 2011, pp. 351-356. doi:10.1007/s10509-011-0635-8
[31]	A. Mitra, “Einstein Energy Associated with the Friedmann- Robertson-Walker Metric,” General Relativity and Gravi- tation, Vol. 42, No. 3, 2010, pp. 443-469,
[32]	M. Kriele, “A Bound on the Concentration of Matter in Spherically Symmetric Stars & Its Application for the E- xistence of Black-Holes,” Rendiconti del Seminario Ma- tematico (Università e Politecnico di Torino), Vol. 50, No. 1, 1992, pp. 147-152.
[33]	A. Mitra, “Quantum Information Paradox: Real or Fictitious,” Pramana, Vol. 73, No. 3, 2009, pp. 615-620.
[34]	E. W. Kolb, “Backreaction of Inhomogeneities Can Mimic Dark Energy,” Classical and Quantum Gravity, Vol. 28, No. 16, 2011, Article ID: 164009. doi:10.1088/0264-9381/28/16/164009
[35]	B. M. Leith, S. C. C. Ng and D. L. Wiltshire, “Gravita- tional Energy as Dark Energy: Concordance of Cosmological Tests,” The Astrophysical Journal, Vol. 672, No. 2, 2008, pp. L91-L94. doi:10.1086/527034
[36]	C. Clarkson and R. Maartens, “Inhomogeneity and the Foundations of Concordance Cosmology,” Classical and Quantum Gravity, Vol. 27, No. 12, 2010, Article ID: 124008.
[37]	M. Regis and C. Clarkson, “The Cosmic Microwave Back- ground in an Inhomogeneous Universe,” Journal of Cos- mology and Astroparticle Physics, Vol. 2011, No. 2, 2011, Article ID: 013.
[38]	C. Tsagas, “Peculiar Motions, Accelerated Expansion, and the Cosmological Axis,” Physical Review D, Vol. 84, No. 6, 2011, Article ID: 063503.
[39]	B. B. Mandelbrot, “The Fractal Geometry of Nature,” Free- man, New York, 1982.
[40]	Y. Baryshev and P. Teerikopri, “Discovery of Cosmic Frac- tals,” World Scientific, Singapore, 2002. doi:10.1142/9789812388780
[41]	C. V. L. Charlier, “On the Structure of the Universe,” Pub- lications of the Astronomical Society of the Pacific, Vol. 37, 1925, pp. 53-76. doi:10.1086/123477
[42]	G. de Vaucouleurs, “The Case for a Hierarchical Cosmo- logy,” Science, Vol. 167, No. 3922, 1970, pp. 1203-1213. doi:10.1126/science.167.3922.1203
[43]	Yu. V. Baryshev, F. Sylos Labini, M. Montuori, L. Pie- tronero and P. Teerikorpi, “On the Fractal Structure of Galaxy Distribution and Its Implications for Cosmology,” Fractals, Vol. 6, No. 3, 1998, pp. 231-243. doi:10.1142/S0218348X98000286
[44]	V. Martinez, “COSMOLOGY: Is the Universe Fractal?” Science, Vol. 285, No. 5413, 1999, p. 445-446. doi:10.1126/science.284.5413.445
[45]	K. Wu, O. Lahav and M. Rees, “The Large-Scale Smoo- thness of the Universe,” Nature, Vol. 397, No. 6716, 1999, pp. 225-230. doi:10.1038/16637
[46]	F. Sylos Labini, N. L. Vasilyev and Yu. V. Baryshev, “Ab- sence of Anti-Correlations and of Baryon Acoustic Os- cillations in the Galaxy Correlation Function from the Sloan Digital Sky Survey Data Release 7,” Astronomy and Astrophysics, Vol. 505, No. 3, 2009, pp. 981-990. doi:10.1051/0004-6361/200911987
[47]	F. Sylos Labini, N. L. Vasilyev and Yu. V. Baryshev, “Absence of Self-Averaging and of Homogeneity in the Large-Scale Galaxy Distribution,” Europhysics Letters, Vol. 86, No. 4, 2009, Article ID: 49001. doi:10.1209/0295-5075/86/49001
[48]	F. Sylos Labini, N. L. Vasilyev, L. Pietronero and Yu. V. Baryshev, “Persistent Fluctuations in the Distribution of Galaxies from the Two-degree Field Galaxy Redshift Survey,” Europhysics Letters, Vol. 85, No. 2, 2009, Arti- cle ID: 29002. doi:10.1209/0295-5075/85/29002
[49]	F. Sylos Labini and Yu. V. Baryshev, “Testing the Coper- nican and Cosmological Principles in the Local Universe with Galaxy Surveys,” Journal of Cosmology and Astroparticle Physics, Vol. 2010, No. 6, 2010, Article ID: 021.
[50]	F. Sylos Labini and L. Pietronero, “The Complex Universe: Recent Observations and Theoretical Challenges,” Journal of Statistical Mechanics: Theory and Experiment, Vol. 2010, No. 11, 2010, Article ID: 11029
[51]	F. Sylos Labini, “Inhomogeneities in the Universe,” Clas- sical and Quantum Gravity, Vol. 28, No. 16, 2011, Arti- cle ID: 164003.
[52]	F. Sylos Labini, “Very Large Scale Correlations in the Ga- laxy Distribution,” Europhysics Letters, Vol. 96, No. 5, 2011, Article ID: 59001. doi:10.1007/s10509-010-0578-5
[53]	Y. Baryshev and P. Teerikopri, “Fractal Approach to Large- Scale Galaxy Distribution,” Russian Academy of Sciences, Vol. 59, 2005. arXiv.org:astro-ph/0505185
[54]	A. Mitra, “The fallacy of Oppenheimer Snyder Collapse: No General Relativistic Collapse at All, No Black Hole, No Physical Singularity,” Astrophysics and Space Science, Vol. 332, No. 1, 2011 pp. 43-48.
[55]	A. Mitra, “Why the Astrophysical Black Hole Candidates Are Not Rotating Black Holes,” 2004. arXiv:astro-ph/0407501
[56]	A. Mitra, “Why the Astrophysical Black Hole Candidates May Not Be Black Holes at All,” 2004. arXiv:astro-ph/0409049
[57]	A. Mitra, “Comments on ‘The Euclidean Gravitational Ac- tion as Black Hole Entropy, Singularities, and Space- Time Voids’,” Journal of Mathematical Physics, Vol. 50, No. 4, 2009, Article ID: 042502.
[58]	A. Mitra, “Revisiting the Old Problem of General Relati- vistic Adiabatic Collapse of a Uniform Density Self-Gra- vitating Sphere,” Gravitation & Cosmology, Vol. 18, No. 1, 2012, (To be published).
[59]	S. A. Thomas, F. B. Abdalla and O. Lahav, “Excess Clus- tering on Large Scales in the MegaZ DR7 Photometric Redshift Survey,” Physical Review Letters, Vol. 106, No. 24, 2011, Article ID: 241301.
[60]	M. G. Walker, C. Combet, J. A. Hinton, D. Maurin and D. M. I. Wilkinson, “A Method for Measuring (Slopes of) the Mass Profiles of Dwarf Spheroidal Galaxies,” Astrophysical Journal Letters, Vol. 742, No. 1, 2011, Article ID: 20(2011).
[61]	R. E. Schild & M. Dekker, “The Transparency of the Uni- verse limited by Lyman Alpha clouds,” Astronomische Nachrichten, Vol. 327, No. 7, 2006, pp.729-732. doi:10.1002/asna.200510612
[62]	C. H. Gibson and R. E. Schild, “Planets and Dark En- ergy,” Proceedings of the International Conference on Problems in Practical Cosmology, St. Petersburg, 23-27 June 2008, pp. 232-238.
[63]	G. R. F. Ellis, “Is the Universe Expanding?” General Re- lativity and Gravitation, Vol. 9, No. 2, 1978, pp. 87-94. doi:10.1007/BF00760145
[64]	Y. A. Yatsunenk and J. A. Budagov, “Red Shift in a La- boratory Environment,” 2011. arXiv:1103.0808
[65]	A. Brynjolfsson, “Hubble Constant from Lensing in Pla- sma-Redshift Cosmology, and Intrinsic Redshift of Quasars,” 2004. arXiv:astro-ph/0411666
[66]	A. Brynjolfsson, “The Type Ia Supernovae and the Hub- ble’s Constant”, 2004. arXiv:astro-ph/0407430
[67]	A. Brynjolfsson, “Magnitude-Redshift Relation for SNe Ia, Time Dilation, and Plasma Redshift,” 2006. arXiv:astro-ph/0602500
[68]	A. Brynjolfsson, “Surface Brightness in Plasma-Redshift Cosmology,” 2006. arXiv:astro-ph/0605599
[69]	Ashwini Kumar Lal, “Big Bang? A Critical Review,” Journal of Cosmology, Vol. 6, 2010, pp. 1533-1547.
[70]	M. Lopez-Corredoira, “Angular Size Test on the Expan- sion of the Universe,” International Journal of Modern Physics D, Vol. 19, No. 3, 2010, pp. 245-291.
[71]	N. Castro-Rodriguez and M. Lopez-Corredoira, “The Age of Extremely Red and Massive Galaxies at Very High Red- shift,” Astronomy & Astrophysics, 2011 (in press).
[72]	D. Kocevski and V. Petrosian, “On the Lack of Time Dilation Signatures in Gamma-ray Burst Light Curves,” Submitted to The Astrophysical Journal, 2011.
[73]	D. F. Crawford, “No Evidence of Time Dilation in Gamma- Ray Burst Data,” 2009. arXiv:0901.4169
[74]	D. F. Crawford, “Observational Evidence Favors a Static Universe (Part I),” Journal of Cosmology, Vol. 13, 2011, pp. 3875-3946
[75]	D. F. Crawford, “Observations of Type Ia Supernovae Are Consistent with a Static Universe,” 2009. arXiv:0901.4172
[76]	A. Mitra, “Cosmological Properties of Eternally Collaps- ing Objects (ECOs),” Proceedings of International Con- ference on Problems of Practical Cosmology, Vol. 1, St. Petersburg, 23-27 June 2008, pp. 304-313.
[77]	C. I. Christov, “On the Evolution of Localized Wave Packets Governed by a Dissipative Wave Equation,” Wave Motion, Vol. 45, No. 3, 2008, pp. 154-161. doi:10.1016/j.wavemoti.2007.05.004
[78]	J. G. Hartnett, “Is the Universe Really Expanding?” 2011. arXiv:1107.24851