Skip to main content
Log in

Linear expansion models vs. standard cosmologies: a critical and historical overview

  • Review Article
  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

Numerous linear expansion cosmological models are critically revised and compared with standard cosmologies from a historical perspective. There are two major classes of such models: those strictly linear along the expansion history (coasting) and those linear at late times, but not in the early Universe (quasi-linear). Their merits and weaknesses, theoretical foundations and compatibility with diverse observational constraints are assessed. The ways the different models, a number of them avoiding inflation, try to solve the cosmological problems of Big Bang cosmology are also considered. Some severe tensions, model-dependent analyses, inconclusive data and unsettled controversy after two decades since the \(\varLambda \)CDM model became the standard cosmology are pointed out. All in all, at least quasi-linear models cannot be definitely ruled out so far. Certainly, \(\varLambda \)CDM continues dominating the landscape, but the growing evidence here reported advises paying some attention to the (quasi-)linear expansion scenario as an alternative cosmology.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  • Abdel-Rahman, A.M.: Singularity-free decaying-vacuum cosmologies. Phys. Rev. D 45(10), 3497 (1992)

    ADS  Google Scholar 

  • Abdel-Rahman, A.M., Riad, I.F.: Astron. J. 134, 1391 (2007)

    ADS  Google Scholar 

  • Aghanim, N., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A.J., et al.: Planck intermediate results-XLVI. Reduction of large-scale systematic effects in HFI polarization maps and estimation of the reionization optical depth. Astron. Astrophys. 596, A107 (2016)

    Google Scholar 

  • Alam, S., Ata, M., Bailey, S., et al.: Mon. Not. R. Astron. Soc. 470, 2617 (2017). arXiv:1607.03155

    ADS  Google Scholar 

  • Allen, R.E.: Four testable predictions of instanton cosmology. In: AIP Conference Proceedings, vol. 478, pp. 204–207. AIP, New York (1999). No. 1

    Google Scholar 

  • Amanullah, R., Lidman, C., Rubin, D., Aldering, G., Astier, P., Barbary, K., et al.: Spectra and Hubble Space Telescope light curves of six type Ia supernovae at \(0.511< z< 1.12\) and the Union2 compilation. Astrophys. J. 716(1), 712 (2010)

    ADS  Google Scholar 

  • Amendola, L., Tocchini-Valentini, D.: Phys. Rev. D 64, 043509 (2001)

    ADS  Google Scholar 

  • Amendola, L., Tsujikawa, S., Sami, M.: Phys. Lett. B 632, 155 (2006)

    ADS  Google Scholar 

  • Avelino, A., Kirshner, R.P.: The dimensionless age of the Universe: a riddle for our time. Astrophys. J. 828(1), 35 (2016)

    ADS  Google Scholar 

  • Batra, A., Lohiya, D., Mahajan, S., Mukherjee, A.: Nucleosynthesis in a universe with a linearly evolving scale factor. Int. J. Mod. Phys. D 9(06), 757–773 (2000)

    ADS  Google Scholar 

  • Bautista, J.E., Guy, J., Rich, J., Blomqvist, M., Des Bourboux, H.D.M., Pieri, M.M., et al.: Measurement of baryon acoustic oscillation correlations at \(z= 2.3\) with SDSS DR12 Ly\(\alpha \)-Forests. Astron. Astrophys. 603, A12 (2017)

    Google Scholar 

  • Benoit-Lévy, A., Chardin, G.: Introducing the Dirac-Milne universe. Astron. Astrophys. 537, A78 (2012)

    ADS  Google Scholar 

  • Bilicki, M., Seikel, M.: We do not live in the Rh = ct universe. Mon. Not. R. Astron. Soc. 425, 1664 (2012)

    ADS  Google Scholar 

  • Blumenthal, G.R., Faber, S.M., Primack, J.R., Rees, M.J.: Formation of galaxies and large-scale structure with cold dark matter. Nature 311(5986), 517 (1984)

    ADS  Google Scholar 

  • Casado, J.: (2004). ArXiv preprint, arXiv:astro-ph/0404130v1

  • Casado, J.: Modeling the expansion of the Universe by a steady flow of space-time. Apeiron16(2) (2009)

  • Casado, J., Jou, D.: Steady Flow cosmological model. Astrophys. Space Sci. 344(2), 513–520 (2013)

    ADS  Google Scholar 

  • Chen, G., Ratra, B.: Median statistics and the Hubble constant. Publ. Astron. Soc. Pac. 123(907), 1127 (2011)

    ADS  Google Scholar 

  • Chen, W., Wu, Y.S.: Implications of a cosmological constant varying as R−2. Phys. Rev. D 41(2), 695 (1990)

    ADS  MathSciNet  Google Scholar 

  • Cimatti, A., Daddi, E., Renzini, A., Cassata, P., Vanzella, E., Pozzetti, L., et al.: Old galaxies in the young Universe. Nature 430(6996), 184 (2004)

    ADS  Google Scholar 

  • Coles, P., Lucchin, F.: Cosmology: The Origin and Evolution of Cosmic Structure. John Wiley & Sons, New York (2003)

    MATH  Google Scholar 

  • Delubac, T., Bautista, J.E., Rich, J., Kirkby, D., Bailey, S., Font-Ribera, A., et al.: Baryon acoustic oscillations in the Ly\(\alpha \) forest of BOSS DR11 quasars. Astron. Astrophys. 574, A59 (2015)

    Google Scholar 

  • Dev, A., Sethi, M., Lohiya, D.: Linear coasting in cosmology and SNe Ia. Phys. Lett. B 504(3), 207–212 (2001)

    ADS  MATH  Google Scholar 

  • Dev, A., Safonova, M., Jain, D., Lohiya, D.: Cosmological tests for a linear coasting cosmology. Phys. Lett. B 548(1–2), 12–18 (2002)

    ADS  MATH  Google Scholar 

  • Dolgov, A.D.: In: Gibbons, G.W., Hawking, S.W., Siklos, S.T.C. (eds.) The Very Early Universe, p. 449. Cambridge University Press, Cambridge (1983)

    Google Scholar 

  • Dolgov, A.D.: Higher spin fields and the problem of the cosmological constant. Phys. Rev. D 55(10), 5881 (1997)

    ADS  Google Scholar 

  • Einstein, A., De Sitter, W.: On the relation between the expansion and the mean density of the universe. Proc. Natl. Acad. Sci. 18(3), 213–214 (1932)

    ADS  MATH  Google Scholar 

  • Ellis, G.F.R.: Gen. Relativ. Gravit. 32, 1135 (2000)

    ADS  Google Scholar 

  • Farooq, O., Madiyar, F.R., Crandall, S., Ratra, B.: Astrophys. J. 835, 26 (2017). arXiv:1607.03537

    ADS  Google Scholar 

  • Feng, C., Wang, B., Abdalla, E., Su, R.: Phys. Lett. B 665, 111 (2008)

    ADS  Google Scholar 

  • Ford, L.H.: Cosmological-constant damping by unstable scalar fields. Phys. Rev. D 35(8), 2339 (1987)

    ADS  Google Scholar 

  • Friaça, A.C.S., Alcañiz, J.S., Lima, J.A.S.: An old quasar in a young dark energy-dominated universe? Mon. Not. R. Astron. Soc. 362(4), 1295–1300 (2005)

    ADS  Google Scholar 

  • Funkhouser, S.: A new large-number coincidence and a scaling law for the cosmological constant. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 464, pp. 1345–1353 (2008). The Royal Society. No. 2093

    Google Scholar 

  • Gehlaut, S., Kumar, P., Lohiya, D.: A concordant “Freely Coasting Cosmology” (2003). ArXiv preprint, astro-ph/0306448

  • Gómez-Valent, A., Amendola, L.: H0 from cosmic chronometers and Type Ia supernovae, with Gaussian Processes and the novel Weighted Polynomial Regression method. J. Cosmol. Astropart. Phys. 2018(04), 051 (2018)

    Google Scholar 

  • Gott, J.R. III, Vogeley, M.S., Podariu, S., Ratra, B.: Median statistics, H0, and the accelerating universe. Astrophys. J. 549(1), 1 (2001)

    ADS  Google Scholar 

  • Gumjudpai, B.: Quintessential power-law cosmology: dark energy equation of state. Mod. Phys. Lett. A 28(29), 1350122 (2013)

    ADS  MathSciNet  Google Scholar 

  • Guth, A.H., Lightman, A.P.: The Inflationary Universe: The Quest for a New Theory of Cosmic Origins. Perseus Publishing, ??? (1997)

    Google Scholar 

  • Haridasu, B.S., Luković, V.V., D’Agostino, R., Vittorio, N.: Strong evidence for an accelerating Universe. Astron. Astrophys. 600, L1 (2017)

    ADS  Google Scholar 

  • Haridasu, B.S., Luković, V.V., Moresco, M., Vittorio, N.: An improved model-independent assessment of the late-time cosmic expansion (2018a). ArXiv preprint, arXiv:1805.03595

  • Haridasu, B.S., Luković, V.V., Vittorio, N.: Isotropic vs. anisotropic components of BAO data: a tool for model selection. J. Cosmol. Astropart. Phys. 2018(05), 033 (2018b)

    Google Scholar 

  • Hasinger, G., Schartel, N., Komossa, S.: Discovery of an ionized Fe K edge in the \(z=3.91\) broad absorption line quasar APM 08279+ 5255 with XMM-Newton. Astrophys. J. Lett. 573(2), L77 (2002)

    ADS  Google Scholar 

  • Hu, Y., Turner, M.S., Weinberg, E.J.: Phys. Rev. D 49, 3830 (1994)

    ADS  Google Scholar 

  • Jain, D., Dev, A., Alcañiz, J.S.: Class. Quantum Gravity 20, 4485 (2003)

    ADS  Google Scholar 

  • Jain, D., Alcañiz, J.S., Dev, A.: Nucl. Phys. B 732, 379 (2006)

    ADS  Google Scholar 

  • John, M.V.: Exact classical correspondence in quantum cosmology. Gravit. Cosmol. 21(3), 208–215 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  • John, M.V.: Realistic coasting cosmology from the Milne model (2018). ArXiv preprint, arXiv:1610.09885

  • John, M.V., Joseph, K.B.: A modified Ozer-Taha type cosmological model. Phys. Lett. B 387(3), 466–470 (1996)

    ADS  MathSciNet  Google Scholar 

  • John, M.V., Joseph, K.B.: Generalized Chen-Wu type cosmological model. Phys. Rev. D 61(8), 087304 (2000)

    ADS  MathSciNet  Google Scholar 

  • John, M.V., Narlikar, J.V.: Phys. Rev. D 65, 043506 (2002)

    ADS  MathSciNet  Google Scholar 

  • Kaplinghat, M., Steigman, G., Tkachev, I., Walker, T.P.: Observational constraints on power-law cosmologies. Phys. Rev. D 59(4), 043514 (1999)

    ADS  Google Scholar 

  • Keller, S.C., Bessell, M.S., Frebel, A., Casey, A.R., Asplund, M., Jacobson, H.R., et al.: A single low-energy, iron-poor supernova as the source of metals in the star SMSS J031300.36-670839.3. Nature 506(7489), 463 (2014). https://doi.org/10.1038/nature12990

    Article  ADS  Google Scholar 

  • Kelly, P.L., Hicken, M., Burke, D.L., Mandel, K.S., Kirshner, R.P.: Hubble residuals of nearby type Ia supernovae are correlated with host galaxy masses. Astrophys. J. 715(2), 743 (2010)

    ADS  Google Scholar 

  • Kolb, E.W.: A coasting cosmology. Astrophys. J. 344, 543–550 (1989)

    ADS  Google Scholar 

  • Kragh, H.: Contemporary history of cosmology and the controversy over the multiverse. Ann. of Sci. 66(4), 529–551 (2009)

    Google Scholar 

  • Krauss, L.M.: Astrophys. J. 480, 466 (1997)

    ADS  Google Scholar 

  • Kumar, S.: Observational constraints on Hubble constant and deceleration parameter in power-law cosmology. Mon. Not. R. Astron. Soc. 422(3), 2532–2538 (2012)

    ADS  Google Scholar 

  • Kumar, R.: A New Class of Cosmologically ‘Viable’ \(f (R)\) Models (2016). ArXiv preprint, arXiv:1611.03728

  • Lemons, D.S., Peter, W.: Gravitational instability in a coasting universe. Astron. Astrophys. 265, 373 (1992)

    ADS  Google Scholar 

  • Lewis, G.F.: Matter matters: unphysical properties of the Rh = ct universe. Mon. Not. R. Astron. Soc. 432(3), 2324–2330 (2013)

    ADS  Google Scholar 

  • Lohiya, D., Sethi, M.: A programme for a problem-free cosmology within the framework of a rich class of scalar-tensor theories. Class. Quantum Gravity 16(5), 1545 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  • Mamon, A.A., Bamba, K.: Observational constraints on the jerk parameter with the data of the Hubble parameter (2018). ArXiv preprint, arXiv:1805.02854

  • Maoz, D.: Quasar lensing statistics and omega_lambda: what went wrong? In: Mellier, Y., Meylan, G. (eds.) Impact of Gravitational Lensing on Cosmology. Proceedings of the IAU Symposium, vol. 225 (2005). arXiv:astro-ph/0501491v1

    Google Scholar 

  • Marugán, G., Carneiro, S.: Phys. Rev. D 65, 087303 (2002). arXiv:gr-qc/0111034v2

    ADS  Google Scholar 

  • Melia, F.: High-z quasars in the Rh = ct universe. Astrophys. J. 764(1), 72 (2013)

    ADS  Google Scholar 

  • Melia, F.: The premature formation of high-redshift galaxies. Astron. J. 147(5), 120 (2014a)

    ADS  Google Scholar 

  • Melia, F.: On recent claims concerning the Rh = ct Universe. Mon. Not. R. Astron. Soc. 446(2), 1191–1194 (2014b)

    ADS  Google Scholar 

  • Melia, F.: Constancy of the cluster gas mass fraction in the Rh = ct Universe. Proc. R. Soc. A 472(2186), 20150765 (2016)

    ADS  Google Scholar 

  • Melia, F.: The linear growth of structure in the Rh = ct universe. Mon. Not. R. Astron. Soc. 464(2), 1966–1976 (2017)

    ADS  Google Scholar 

  • Melia, F., López-Corredoira, M.: Alcock–Paczyński test with model-independent BAO data. Int. J. Mod. Phys. D 26(06), 1750055 (2017)

    ADS  Google Scholar 

  • Melia, F., Maier, R.S.: Mon. Not. R. Astron. Soc. 432, 2669 (2013)

    ADS  Google Scholar 

  • Melia, F., McClintock, T.M.: Astron. J. 150, 119 (2015)

    ADS  Google Scholar 

  • Melia, F., Shevchuk, A.S.H.: The Rh = ct universe. Mon. Not. R. Astron. Soc. 419(3), 2579–2586 (2012)

    ADS  Google Scholar 

  • Méndez, V., Pavón, D.: Expanding models with a varying cosmological term and bulk stress. Gen. Relativ. Gravit. 28(6), 679–689 (1996)

    ADS  MATH  Google Scholar 

  • Milne, E.A.: Relativity, Gravitation and World Structure. Oxford University Press, Oxford (1935)

    MATH  Google Scholar 

  • Mishra, B., Ray, P.P., Myrzakulov, R.: Bulk viscous embedded hybrid dark energy models. Eur. Phys. J. C 79(1), 34 (2019)

    ADS  Google Scholar 

  • Mitra, A.: Mon. Not. R. Astron. Soc. 442, 382 (2014)

    ADS  Google Scholar 

  • Nielsen, J.T., Guffanti, A., Sarkar, S.: Marginal evidence for cosmic acceleration from Type Ia supernovae. Nat. Sci. Rep. 6, 35596 (2016)

    ADS  Google Scholar 

  • Olson, T.S., Jordan, T.F.: Ages of the Universe for decreasing cosmological constants. Phys. Rev. D 35(10), 3258 (1987)

    ADS  Google Scholar 

  • Ostriker, J.P., Steinhardt, P.J.: The observational case for a low-density Universe with a non-zero cosmological constant. Nature 377(6550), 600 (1995)

    ADS  Google Scholar 

  • Overduin, J.M., Cooperstock, F.I.: Phys. Rev. D 58, 043506 (1998). arXiv:astro-ph/9805260v1

    ADS  Google Scholar 

  • Özer, M., Taha, M.O.: A possible solution to the main cosmological problems. Phys. Lett. B 171(4), 363–365 (1986)

    ADS  Google Scholar 

  • Padmanabhan, T.: Cosmological constant—the weight of the vacuum. Phys. Rep. 380(5–6), 235–320 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  • Pavón, D.: Nonequilibrium fluctuations in cosmic vacuum decay. Phys. Rev. D 43(2), 375 (1991)

    ADS  Google Scholar 

  • Pavón, D., Bafaluy, J., Jou, D.: Causal Friedmann-Robertson-Walker cosmology. Class. Quantum Gravity 8(2), 347 (1991)

    ADS  MathSciNet  Google Scholar 

  • Peebles, P.J.E., Ratra, B.: The cosmological constant and dark energy. Rev. Mod. Phys. 75(2), 559 (2003)

    ADS  MathSciNet  MATH  Google Scholar 

  • Perlmutter, S., Aldering, G., Goldhaber, G., Knop, R.A., Nugent, P., Castro, P.G., et al.: Measurements of \(\varOmega \) and \(\varLambda \) from 42 high-redshift supernovae. Astrophys. J. 517(2), 565 (1999)

    ADS  MATH  Google Scholar 

  • Petri, M.: Holographic spherically symmetric metrics. Int. J. Mod. Phys. E 16(06), 1603–1641 (2007)

    ADS  Google Scholar 

  • Pimentel, L.O., Diaz-Rivera, L.M.: Coasting cosmologies with time dependent cosmological constant. Int. J. Mod. Phys. A 14(10), 1523–1529 (1999)

    ADS  MathSciNet  MATH  Google Scholar 

  • Rácz, G., Dobos, L., Beck, R., Szapudi, I., Csabai, I.: Concordance cosmology without dark energy. Mon. Not. R. Astron. Soc. Lett. 469(1), L1–L5 (2017)

    ADS  Google Scholar 

  • Rani, S., Altaibayeva, A., Shahalam, M., Singh, J.K., Myrzakulov, R.: Constraints on cosmological parameters in power-law cosmology. J. Cosmol. Astropart. Phys. 2015(03), 031 (2015)

    Google Scholar 

  • Riess, A.G., Filippenko, A.V., Challis, P., Clocchiatti, A., Diercks, A., Garnavich, P.M., et al.: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116(3), 1009 (1998)

    ADS  Google Scholar 

  • Riess, A.G., Filippenko, A.V., Li, W., Schmidt, B.P.: Is there an indication of evolution of type Ia supernovae from their rise times? Astron. J. 118(6), 2668 (1999)

    ADS  Google Scholar 

  • Riess, A.G., Strolger, L.G., Tonry, J., Casertano, S., Ferguson, H.C., Mobasher, B., et al.: 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(2), 665 (2004)

    ADS  MATH  Google Scholar 

  • Riess, A.G., Strolger, L.G., Casertano, S., Ferguson, H.C., Mobasher, B., Gold, B., et al.: New Hubble space telescope discoveries of type Ia supernovae at \(z \geq 1\): narrowing constraints on the early behavior of dark energy. Astrophys. J. 659(1), 98 (2007)

    ADS  Google Scholar 

  • Riess, A.G., Rodney, S.A., Scolnic, D.M., Shafer, D.L., Strolger, L.G., Ferguson, H.C., et al.: Type Ia supernova distances at redshift >1.5 from the Hubble Space Telescope multi-cycle treasury programs: the early expansion rate. Astrophys. J. 853(2), 126 (2018a)

    ADS  Google Scholar 

  • Riess, A.G., Casertano, S., Yuan, W., Macri, L., Anderson, J., MacKenty, J.W., et al.: New parallaxes of galactic cepheids from spatially scanning the hubble space telescope: implications for the hubble constant. Astrophys. J. 855(2), 136 (2018b)

    ADS  Google Scholar 

  • Rubin, D., Hayden, B.: Is the expansion of the universe accelerating? All signs point to yes. Astrophys. J. Lett. 833(2), L30 (2016)

    ADS  Google Scholar 

  • Sahni, V., Starobinsky, A.: The case for a positive cosmological \(\varLambda \)-term. Int. J. Mod. Phys. D 9(04), 373–443 (2000)

    ADS  Google Scholar 

  • Sattar, A., Vishwakarma, R.G.: Some FRW models with variable G and \(\varLambda \). Class. Quantum Gravity 14(4), 945 (1997)

    ADS  MathSciNet  Google Scholar 

  • Schmidt, B.P., Suntzeff, N.B., Phillips, M.M., Schommer, R.A., Clocchiatti, A., Kirshner, R.P., et al.: The high-Z supernova search: measuring cosmic deceleration and global curvature of the universe using type Ia supernovae. Astrophys. J. 507(1), 46 (1998)

    ADS  Google Scholar 

  • Seikel, M., Schwarz, D.J.: How strong is the evidence for accelerated expansion? J. Cosmol. Astropart. Phys. 2008(02), 007 (2008)

    Google Scholar 

  • Sen, A.A., Pavón, D.: Phys. Lett. B 664, 7–11 (2008)

    ADS  Google Scholar 

  • Sethi, G., Dev, A., Jain, D.: Cosmological constraints on a power law universe. Phys. Lett. B 624(3–4), 135–140 (2005)

    ADS  Google Scholar 

  • Shafer, D.L.: Robust model comparison disfavors power law cosmology. Phys. Rev. D 91(10), 103516 (2015)

    ADS  Google Scholar 

  • Shafieloo, A., Sahni, V., Starobinsky, A.A.: Phys. Rev. D 80, 101301(R) (2009)

    ADS  Google Scholar 

  • Silveira, V., Waga, I.: Decaying \(\varLambda \) cosmologies and power spectrum. Phys. Rev. D 50(8), 4890 (1994)

    ADS  Google Scholar 

  • Silveira, V., Waga, I.: Cosmological properties of a class of \(\varLambda \) decaying cosmologies. Phys. Rev. D 56(8), 4625 (1997)

    ADS  Google Scholar 

  • Singh, P., Lohiya, D.: Constraints on lepton asymmetry from nucleosynthesis in a linearly coasting cosmology. J. Cosmol. Astropart. Phys. 2015(05), 061 (2015)

    Google Scholar 

  • Solà, J., Gómez-Valent, A., de Cruz Pérez, J.: The H0 tension in light of vacuum dynamics in the Universe. Phys. Lett. B 774, 317–324 (2017)

    ADS  Google Scholar 

  • Spergel, D.N., Verde, L., Peiris, H.V., Komatsu, E., Nolta, M.R., Bennett, C.L., et al.: First-year Wilkinson Microwave Anisotropy Probe (WMAP)* observations: determination of cosmological parameters. Astrophys. J. Suppl. Ser. 148(1), 175 (2003)

    ADS  Google Scholar 

  • Sultana, J.: The \(R _{{h}} = \mathit{ct}\) universe and quintessence. Mon. Not. R. Astron. Soc. 457(1), 212–216 (2016). https://doi.org/10.1093/mnras/stv3012

    Article  ADS  MathSciNet  Google Scholar 

  • Tonry, J.L., Schmidt, B.P., Barris, B., Candia, P., Challis, P., Clocchiatti, A., et al.: Cosmological results from high-\(z\) supernovae. Astrophys. J. 594(1), 1 (2003)

    ADS  Google Scholar 

  • Tutusaus, I., Lamine, B., Blanchard, A.: Model-independent cosmic acceleration and type Ia supernovae intrinsic luminosity redshift dependence (2018). ArXiv preprint, arXiv:1803.06197

  • Uzan, J-P.: Rev. Mod. Phys. 75, 403 (2003)

    ADS  Google Scholar 

  • Wang, B., Gong, Y-g., Abdalla, E.: Phys. Lett. B 624, 141 (2005)

    ADS  Google Scholar 

  • Wang, B., Zang, J., Lin, C.Y., Abdalla, E., Micheletti, S.: Interacting dark energy and dark matter: observational constraints from cosmological parameters. Nucl. Phys. B 778(1–2), 69–84 (2007)

    ADS  Google Scholar 

  • Watson, D.F., Berlind, A.A., Zentner, A.R.: A cosmic coincidence: the power-law galaxy correlation function. Astrophys. J. 738(1), 22 (2011)

    ADS  Google Scholar 

  • Wei, J.J., Wu, X.F., Melia, F.: A comparison of cosmological models using time delay lenses. Astrophys. J. 788(2), 190 (2014a)

    ADS  Google Scholar 

  • Wei, J.J., Wu, X.F., Melia, F., Wei, D.M., Feng, L.L.: Cosmological tests using gamma-ray bursts, the star formation rate and possible abundance evolution. Mon. Not. R. Astron. Soc. 439(4), 3329–3341 (2014b)

    ADS  Google Scholar 

  • Wei, J.J., Wu, X.F., Melia, F., Maier, R.S.: A comparative analysis of the supernova legacy survey sample with \(\varLambda \)CDM and the Rh = ct Universe. Astron. J. 149(3), 102 (2015)

    ADS  Google Scholar 

  • Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61(1), 1 (1989)

    ADS  MathSciNet  MATH  Google Scholar 

  • Weinberg, S.: The Cosmological Constant Problems (Talk given at Dark Matter 2000, Marina del Rey, CA, February 2000). ArXiv preprint, arXiv:astro-ph/0005265

  • Williams, J.G., Newall, X.X., Dickey, J.O.: Phys. Rev. D 53, 6730 (1996)

    ADS  Google Scholar 

  • Yang, W., Pan, S., Di Valentino, E., Paliathanasis, A., Lu, J.: Challenging bulk viscous unified scenarios with cosmological observations (2019). ArXiv preprint, arXiv:1906.04162

  • Yennapureddy, M.K., Melia, F.: A cosmological solution to the Impossibly Early Galaxy Problem. Phys. Dark Universe 20, 65–71 (2018)

    ADS  Google Scholar 

  • Yu, H., Ratra, B., Wang, F.Y.: Hubble parameter and Baryon acoustic oscillation measurement constraints on the Hubble constant, the deviation from the spatially flat \(\varLambda \)CDM model, the deceleration–acceleration transition redshift, and spatial curvature. Astrophys. J. 856(1), 3 (2018)

    ADS  Google Scholar 

  • Zhao, G.B., Raveri, M., Pogosian, L., Wang, Y., Crittenden, R.G., Handley, W.J., et al.: Dynamical dark energy in light of the latest observations. Nat. Astron. 1(9), 627 (2017)

    ADS  Google Scholar 

  • Zhu, Z.H., Hu, M., Alcañiz, J.S., Liu, Y.X.: Astron. Astrophys. 483, 15 (2008). arXiv:0712.3602v1

    ADS  Google Scholar 

  • Zimdahl, W., Pavón, D., Chimento, L.P.: Phys. Lett. B 521, 133 (2001)

    ADS  Google Scholar 

  • Zlatev, I., Wang, L., Steinhardt, P.J.: Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett. 82(5), 896 (1999)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Juan Casado.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Casado, J. Linear expansion models vs. standard cosmologies: a critical and historical overview. Astrophys Space Sci 365, 16 (2020). https://doi.org/10.1007/s10509-019-3720-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10509-019-3720-z

Keywords

Navigation