Abstract
Motivated by the observed cosmic matter distribution, we present the following conjecture: due to the formation of voids and opaque structures, the average matter density on the path of the light from the well-observed objects changes from Ω M ≃ 1 in the homogeneous early universe to Ω M ≃ 0 in the clumpy late universe, so that the average expansion rate increases along our line of sight from EdS expansion Ht ≃ 2/3 at high redshifts to free expansion Ht ≃ 1 at low redshifts. To calculate the modified observable distance–redshift relations, we introduce a generalized Dyer–Roeder method that allows for two crucial physical properties of the universe: inhomogeneities in the expansion rate and the growth of the nonlinear structures. By treating the transition redshift to the void-dominated era as a free parameter, we find a phenomenological fit to the observations from the CMB anisotropy, the position of the baryon oscillation peak, the magnitude–redshift relations of type Ia supernovae, the local Hubble flow and the nucleosynthesis, resulting in a concordant model of the universe with 90% dark matter, 10% baryons, no dark energy, 15 Gyr as the age of the universe and a natural value for the transition redshift z 0 = 0.35. Unlike a large local void, the model respects the cosmological principle, further offering an explanation for the late onset of the perceived acceleration as a consequence of the forming nonlinear structures. Additional tests, such as quantitative predictions for angular deviations due to an anisotropic void distribution and a theoretical derivation of the model, can vindicate or falsify the interpretation that light propagation in voids is responsible for the perceived acceleration.
Similar content being viewed by others
References
Zel’dovich Ya.B.: Observations in a universe homogeneous in the mean. Sov. Ast. 8, 13 (1964)
Bertotti B.: The luminosity of distant galaxies. Proc. R. Soc. Lond. A 294, 195 (1966)
Gunn J.E.: On the propagation of light in inhomogeneous cosmologies. I. Mean Eff. Astrophys. J. 150, 737 (1967)
Kantowski R.: Corrections in the luminosity-redshift relations of the homogeneous friedmann models. Astrophys. J. 155, 89 (1969)
Dyer C.C., Roeder R.C.: The distance–redshift relation for universes with no intergalactic medium. Astrophys. J. 174, L115 (1972)
Dyer C.C., Roeder R.C.: Distance–redshift relations for universes with some intergalactic medium. Astrophys. J. 180, L31 (1973)
Hoyle F., Vogeley M.S.: Voids in the 2dF galaxy redshift survey. Astrophys. J. 607, 751 (2004) [arXiv:astro-ph/0312533]
Gott J.R.I. et al.: A map of the universe. Astrophys. J. 624, 463 (2005) [arXiv:astro-ph/0310571]
Tikhonov A.V.: Voids in the SDSS galaxy survey. Astron. Lett. 33, 499 (2007) [arXiv:0707.4283 [astro-ph]]
von Benda-Beckmann, A.M., Mueller, V.: Void statistics and void galaxies in the 2dFGRS. arXiv:0710.2783 [astro-ph]
Einasto M., Einasto J., Tago E., Dalton G.B., Andernach H.: The structure of the universe traced by rich clusters of galaxies. Mon. Not. R. Astron. Soc. 269, 301 (1994)
Rudnick L., Brown S., Williams L.R.: Extragalactic radio sources and the WMAP cold spot. Astrophys. J. 671, 40 (2007) [arXiv:0704.0908 [astro-ph]]
Copeland E.J., Sami M., Tsujikawa S.: Dynamics of dark energy. Int. J. Mod. Phys. D 15, 1753 (2006) [arXiv:hep-th/0603057]
Straumann N.: Dark energy: recent developments. Mod. Phys. Lett. A 21, 1083 (2006) [arXiv:hep-ph/0604231]
Sahni V., Starobinsky A.: Reconstructing dark energy. Int. J. Mod. Phys. D 15, 2105 (2006) [arXiv:astro-ph/0610026]
Riess, A.G., et al. [Supernova Search Team Collaboration]: Type Ia supernova discoveries at z > 1 from the Hubble Space telescope: evidence for past deceleration and constraints on dark energy evolution. Astrophys. J. 607, 665 (2004) [arXiv:astro-ph/0402512]
Riess A.G. et al.: New hubble space telescope discoveries of type Ia Supernovae at z > 1: narrowing constraints on the early behavior of dark energy. Astrophys. J. 659, 98 (2007) [arXiv:astro-ph/0611572]
Eisenstein D.J. et al.: Detection of the Baryon acoustic peak in the large-scale correlation function of sdss luminous red galaxies. Astrophys. J. 633, 560 (2005) [arXiv:astro-ph/0501171]
Spergel, D.N., et al. [WMAP Collaboration]: Wilkinson microwave anisotropy probe (WMAP) three year results: implications for cosmology. Astrophys. J. Suppl. 170, 377 (2007) [arXiv:astro-ph/0603449]
Schwarz, D.J.: Accelerated expansion without dark energy. arXiv:astro-ph/0209584
Wetterich C.: Can structure formation influence the cosmological evolution? Phys. Rev. D 67, 043513 (2003) [arXiv:astro-ph/0111166]
Räsänen S.: Dark energy from backreaction. JCAP 0402, 003 (2004) [arXiv:astro-ph/0311257]
Räsänen S.: Accelerated expansion from structure formation. JCAP 0611, 003 (2006) [arXiv:astro-ph/0607626]
Räsänen S.: Evaluating backreaction with the peak model of structure formation. JCAP 0804, 026 (2008) [arXiv:0801.2692 [astro-ph]]
Räsänen S.: Light propagation in statistically homogeneous and isotropic dust universes. JCAP 0902, 011 (2009) [arXiv:0812.2872[astro-ph]]
Buchert T.: Dark energy from structure—a status report. Gen. Relativ. Gravit. 40, 467 (2008) [arXiv:0707.2153 [gr-qc]]
Ishibashi A., Wald R.M.: Can the acceleration of our universe be explained by the effects of inhomogeneities? Class. Quant. Grav. 23, 235 (2006) [arXiv:gr-qc/0509108]
Paranjape A., Singh T.P.: Cosmic inhomogeneities and the average cosmological dynamics. Phys. Rev. Lett. 101, 181101 (2008) [arXiv:0806.3497 [astro-ph]]
Kolb E.W., Marra V., Matarrese S.: On the description of our cosmological spacetime as a perturbed conformal Newtonian metric and implications for the backreaction proposal for the accelerating universe. Phys. Rev. D 78, 103002 (2008) [arXiv:0807.0401 [astro-ph]]
Shirokov M.F., Fisher I.Z.: Isotropic space with discrete gravitational-field sources. on the theory of a nonhomogeneous isotropic universe. Sov. Ast. 6, 699 (1963)
Ellis G.F.R.: Relativistic cosmology: Its nature, aims and problems. In: Bertotti, B., Felice, F., Pascolini, A. (eds) General Relativity and Gravitation, pp. 215. Reidel D Publishing Company, Dordrecht (1984)
Ellis G.F.R., Stoeger W.: The fitting problem in cosmology. Class. Quant. Grav. 4, 1697 (1987)
Ellis G.F.R.: 83 years of general relativity and cosmology: progress and problems. Class. Quant. Grav. 16, A37 (1999)
Ellis G.F.R., Buchert T.: The universe seen at different scales. Phys. Lett. A 347, 38 (2005) [arXiv:gr-qc/0506106]
Buchert T.: On average properties of inhomogeneous fluids in general relativity. I: Dust cosmologies. Gen. Relativ. Gravit. 32, 105 (2000) [arXiv:gr-qc/9906015]
Mattsson T., Ronkainen M.: Exploiting scale dependence in cosmological averaging. JCAP 0802, 004 (2008) [arXiv:0708.3673 [astro-ph]]
Apostolopoulos P.S., Brouzakis N., Tetradis N., Tzavara E.: Cosmological acceleration and gravitational collapse. JCAP 0606, 009 (2006) [arXiv:astro-ph/0603234]
Kai T., Kozaki H., Nakao K.I., Nambu Y., Yoo C.M.: Can inhomogeneties accelerate the cosmic volume expansion? Prog. Theor. Phys. 117, 229 (2007) [arXiv:gr-qc/0605120]
Paranjape A., Singh T.P.: The possibility of cosmic acceleration via spatial averaging in Lemaître–Tolman–Bondi models. Class. Quant. Gravit. 23, 6955 (2006) [arXiv:astro-ph/0605195]
Wiltshire D.L.: Cosmic clocks, cosmic variance and cosmic averages. New J. Phys. 9, 377 (2007) [arXiv:gr-qc/0702082]
Wiltshire D.L.: Exact solution to the averaging problem in cosmology. Phys. Rev. Lett. 99, 251101 (2007) [arXiv:0709.0732 [gr-qc]]
Leith B.M., Ng S.C.C., Wiltshire D.L.: Gravitational energy as dark energy: concordance of cosmological tests. Astrophys. J. 672, L91 (2008) [arXiv:0709.2535 [astro-ph]]
Wiltshire D.L.: Gravitational energy and cosmic acceleration. Int. J. Mod. Phys. D 17, 641 (2008) [arXiv:0712.3982 [gr-qc]]
Wiltshire, D.L.: Dark energy without dark energy. arXiv:0712.3984 [astro-ph]
Wiltshire D.L.: Cosmological equivalence principle and the weak-field limit. Phys. Rev. D 78, 084032 (2008) [arXiv:0809.1183 [gr-qc]]
Smith, K.M., Huterer, D.: No evidence for the cold spot in the NVSS radio survey. arXiv:0805.2751 [astro-ph]
Moffat, J.W., Tatarski, D.C.: Cosmological observations in a local void. arXiv:astro-ph/9407036
Zehavi I., Riess A.G., Kirshner R.P., Dekel A.: A local hubble bubble from SNe Ia? Astrophys. J. 503, 483 (1998) [arXiv:astro-ph/9802252]
Tomita K.: A local void and the accelerating universe. Mon. Not. R. Astron. Soc. 326, 287 (2001) [arXiv:astro-ph/0011484]
Frith W.J., Metcalfe N., Shanks T.: New H-band galaxy number counts: a large local hole in the galaxy distribution? Mon. Not. R. Astron. Soc. 371, 1601 (2006) [arXiv:astro-ph/0509875]
Lemaître, G.: Annales Soc. Sci. Brux. Ser. I Sci. Math. Astron. Phys. A 53 51 (1933) (For an English translation, see: G. Lemaître, The Expanding Universe. Gen. Relativ. Gravit. 29, 641 (1997))
Plebanski J., Krasinski A.: An Introduction to General Relativity and Cosmology. Cambridge University Press, London (2006)
Mustapha N., Hellaby C., Ellis G.F.R.: Large scale inhomogeneity versus source evolution: can we distinguish them observationally? Mon. Not. R. Astron. Soc. 292, 817 (1997) [arXiv:gr-qc/9808079]
Celerier M.N.: Do we really see a cosmological constant in the supernovae data? Astron. Astrophys. 353, 63 (2000) [arXiv:astro-ph/9907206]
Alnes H., Amarzguioui M., Grøn Ø.: An inhomogeneous alternative to dark energy? Phys. Rev. D 73, 083519 (2006) [arXiv:astro-ph/0512006]
Enqvist K., Mattsson T.: The effect of inhomogeneous expansion on the supernova observations. JCAP 0702, 019 (2007) [arXiv:astro-ph/0609120]
Iguchi H., Nakamura T., Nakao K.I.: Is dark energy the only solution to the apparent acceleration of the present universe? Prog. Theor. Phys. 108, 809 (2002) [arXiv:astro-ph/0112419]
Biswas T., Mansouri R., Notari A.: Nonlinear structure formation and apparent acceleration: an investigation. JCAP 0712, 017 (2007) [arXiv:astro-ph/0606703]
Tanimoto M., Nambu Y.: Luminosity distance-redshift relation for the LTB solution near the center. Class. Quant. Grav. 24, 3843 (2007) [arXiv:gr-qc/0703012]
Alexander, S., Biswas, T., Notari, A., Vaid, D.: Local void vs dark energy: confrontation with WMAP and Type Ia Supernovae. arXiv:0712.0370 [astro-ph]
Garcia-Bellido J., Haugboelle T.: Confronting Lemaître–Tolman–Bondi models with observationalcosmology. JCAP 0804, 003 (2008) [arXiv:0802.1523 [astro-ph]]
Garcia-Bellido, J., Haugboelle, T.: The radial BAO scale and cosmic shear, a new observable for inhomogeneous cosmologies. arXiv:0810.4939 [astro-ph].
Zibin J.P.: Scalar perturbations on Lemaître–Tolman–Bondi spacetimes. Phys. Rev.D 78, 043504 (2008) [ar-Xiv:0804.1787[astro-ph]]
Alnes H., Amarzguioui M.: CMB anisotropies seen by an off-center observer in a spherically symmetric inhomogeneous universe. Phys. Rev. D 74, 103520 (2006) [arXiv:astro-ph/0607334]
Pain, R., et al. [Supernova cosmology project collaboration]: The distant Type Ia supernova rate. Astrophys. J. 577, 120 (2002) [arXiv:astro-ph/0205476]
Tonry J.L.: Supernovae and dark energy. Phys. Scr. T 117, 11–16 (2005)
Weinberg S.: Apparent luminosities in a locally inhomogeneous universe. Astrophys. J. 208, L1–L3 (1976)
Ellis G.F.R., Bassett B.A., Dunsby P.K.S.: Lensing and caustic effects on cosmological distances. Class. Quant. Grav. 15, 2345 (1998) [arXiv:gr-qc/9801092]
Linder E.V.: Light propagation in generalized Friedmann universes. Astron. Astrophys. 206, 190 (1988)
Kantowski R., Vaughan T., Branch D.: The effects of inhomogeneities on evaluating the deceleration parameter q0. Astrophys. J. 447, 35 (1995) [arXiv:astro-ph/9511108]
Kantowski, R.: The effects of inhomogeneities on evaluating the mass parameter Ω m and the cosmological constant Λ. arXiv:astro-ph/9802208
Kantowski R.: The Lamé equation for distance-redshift in partially filled Beam Friedmann- Lemaître–Robertson-Walker cosmology. Phys. Rev. D 68, 123516 (2003) [arXiv:astro-ph/0308419]
Sachs R.K.: Gravitational waves in general relativity. VI. The outgoing radiation condition. Proc. R. Soc. Lond. A 264, 309 (1961)
Etherington I.M.H.: On the definition of distance in general relativity. Philos. Mag. ser. 7(15), 761 (1933)
Ellis G.F.R.: Relativistic cosmology. In: Sachs, R.K. (eds) Proceeding of School Enrico Fermi, General Relativity and Cosmology, p. 104. Academic Press, New York (1971)
Santos R.C., Lima J.A.S.: Clustering, angular size and dark energy. Phys. Rev. D 77, 083505 (2008) [ar-Xiv:0803.1865[astro-ph]]
Peacock J.A.: Cosmological Physics. Cambridge University Press, London (1999)
Springel V. et al.: Simulating the joint evolution of quasars, galaxies and their large-scale distribution. Nature 435, 629 (2005) [arXiv:astro-ph/0504097]
Sarkar S.: Is the evidence for dark energy secure? Gen. Relat. Gravit. 40, 269 (2008) [arXiv:0710.53071191 [astro-ph]]
Blanchard A., Douspis M., Rowan-Robinson M., Sarkar S.: An alternative to the cosmological ‘concordance model’. Astron. Astrophys. 412, 35 (2003) [arXiv:astro-ph/0304237]
Blanchard A., Douspis M., Rowan-Robinson M., Sarkar S.: Large-scale galaxy correlations as a test for dark energy. Astron. Astrophys. 449, 925 (2006) [arXiv:astro-ph/0512085]
Hunt P., Sarkar S.: Multiple inflation and the WMAP ‘glitches’. Phys. Rev. D 70, 103518 (2004) [ar-Xiv:astro-ph/0408138]
Hunt P., Sarkar S.: Multiple inflation and the WMAP ‘glitches’ II. Data analysis and cosmological parameter extraction. Phys. Rev. D 76, 123504 (2007) [arXiv:0706.2443[astro-ph]]
Hunt, P., Sarkar, S.: Constraints on large scale voids from WMAP-5 and SDSS. arXiv:0807.4508 [astro-ph]
Adams J.A., Ross G.G., Sarkar S.: Multiple inflation. Nucl. Phys. B 503, 405 (1997) [arXiv:hepph/9704286]
Yao W.M. et al.: Review of particle physics. [Particle Data Group]. J. Phys. G 33, 1 (2006)
Drexlin G.: [KATRIN Collaboration], KATRIN: direct measurement of a sub-eV neutrino mass. Nucl. Phys. Proc. Suppl. 145, 263 (2005)
Elgarøy Lahav O.: The role of priors in deriving upper limits on neutrino masses from the 2dFGRS and WMAP. JCAP 0304, 004 (2003) [arXiv:astro-ph/0303089]
Singh S., Ma C.P.: Neutrino clustering in cold dark matter halos: implications for ultra high energy cosmic rays. Phys. Rev. D 67, 023506 (2003) [arXiv:astro-ph/0208419]
Hu W., Sugiyama N.: Small scale cosmological perturbations: an analytic approach. Astrophys. J. 471, 542 (1996) [arXiv:astro-ph/9510117]
Rakic A., Schwarz D.J.: Correlating anomalies of the microwave sky: the good, the evil and the axis. Phys. Rev. D 75, 103002 (2007) [arXiv:astro-ph/0703266]
Gurzadyan V.G., Kashin A., Bianco C.L., Khachatryan H., Yegorian G.: On axial and plane–mirror inhomogeneities in the WMAP3 cosmic microwave background maps. Mod. Phys. Lett. A 22, 2955 (2007) [arXiv:0709.0886 [astro-ph]]
Freedman W.L. et al.: Final results from the hubble space telescope key project to measure the Hubble constant. Astrophys. J. 553, 47 (2001) [arXiv:astro-ph/0012376]
Sandage A., Tammann G.A., Saha A., Reindl B., Macchetto F.D., Panagia N.: The Hubble constant: a summary of the HST Program for the luminosity calibration of Type Ia Supernovae by means of cepheids. Astrophys. J. 653, 843 (2006) [arXiv:astro-ph/0603647]
Hasinger G., Schartel N., Komossa S.: Discovery of an ionized Fe-K edge in the z = 3.91 broad absorption line Quasar APM08279+5255 with XMM-Newton. Astrophys. J. 573, L77 (2002) [arXiv:astroph/0207005]
Komossa, S., Hasinger, G.: The X-ray evolving universe: (ionized) absorption and dust, from nearby Seyfert galaxies to high-redshift quasars. arXiv:astro-ph/0207321
Jain D., Dev A.: Age of high redshift objects—a Litmus Test for the dark energy models. Phys. Lett. B 633, 436 (2006) [arXiv:astro-ph/0509212]
Fields, B., Sarkar, S.: Big-bang nucleosynthesis (PDG mini-review). arXiv:astro-ph/0601514
Krauss L.M., Chaboyer B.: Age Estimates of Globular Clusters in the Milky Way: Constraints on Cosmology. Science 299, 65 (2003)
Wang X.F., Wang L.F., Pain R., Zhou X., Li Z.W.: Determination of the Hubble constant, the intrinsic scatter of luminosities of Type Ia SNe, and evidence for non-standard dust in other galaxies. Astrophys. J. 645, 488 (2006) [arXiv:astro-ph/0603392]
Schwarz, D.J., Weinhorst, B.: (An)isotropy of the Hubble diagram: comparing hemispheres. arXiv:0706.0165 [astro-ph]
Seikel M., Schwarz D.J.: Howstrong is the evidence for accelerated expansion? JCAP 0802, 007 (2008) [ar- Xiv:0711.3180[astro-ph]]
McClure M.L., Dyer C.C.: Anisotropy in the Hubble constant as observed in the HST Extragalactic Distance Scale Key Project results. New Astron 12, 533 (2007) [arXiv:astro-ph/0703556]
Gurzadyan, V.G., et al.: Kolmogorov CMB Sky. arXiv:0811.2732 [astro-ph]
Kutschera M., Dyrda M.: Coincidence of universe age in LambdaCDMandMilne cosmologies. Acta Phys. Pol. B 38, 215 (2007) [arXiv:astro-ph/0605175]
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Mattsson, T. Dark energy as a mirage. Gen Relativ Gravit 42, 567–599 (2010). https://doi.org/10.1007/s10714-009-0873-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10714-009-0873-z