Abstract
We investigate the evolution of linear density contrasts obtained with respect to a homogeneous spatially flat Friedman-Lemaître–Robertson–Walker (FLRW) background by solving the density contrast equations governed by Newtonian and MONDian force laws using symmetry-based approach. We find eight-parameter Lie group symmetries for the linear order density perturbation equation for the Newtonian case whereas the density contrast equation follows only one parameter Lie group symmetry in MONDian case. We use Lie symmetries to find the group invariant solutions from invariant curve condition. The physical features of the evolution for various mode of density contrast with respect to the global cosmic background density in homogeneous isotropic cosmological models have been investigated using analytical group invariant solutions along with their numerical solutions. An account for cosmological density contrast and mass fluctuation also have been provided. We also have shown that the MONDian force law generates higher amplitudes in the density fluctuation, results in a more rapid structure formation that cannot be possible under the Newtonian force law.
Similar content being viewed by others
References
Spergel, D.N., Verde, L., Peiris, H.V., Komatsu, E., Nolta, M.R., Bennett, C.L., Halpern, M., Hinshaw, G., Jarosik, N., Kogut, A., Limon, M., Meyer, S.S., Page, L., Tucker, G.S., Weiland, J.L., Wollack, E., Wright, E.L.: First year Wilkinson Microwave Probe (WMAP) observations: determination of cosmological parameters. Astrophys. J. Suppl. Ser. 148, 175 (2003)
Sachs, R.K., Wolfe, A.M.: Perturbations of a cosmological model and angular variations of the microwave background. Astrophys. J. 147, 73 (1967)
Jeans, J.H.: The stability of spiral nebula. Philos. Trans. 199A, 49 (1902)
Jeans, J.: Astronomy and Cosmogony. Cambridge University Press, Cambridge (1929)
Lifshitz, E.M.: On the gravitational instability of the expanding universe. JETP 16, 987 (1946)
Weinberg, S.: Cosmology. Oxford University Press Inc., New York (2008)
Peebles, P.J.E.: The Large-Scale Structure of the Universe. Princeton Series in Physics. Princeton University Press, Princeton (1980)
Zel’dovich, Ya B., Novikov, I.D.: Relativistic astrophysics. I. Usp. Fiz. Nauk 84, 377 (1965)
Sakharov, A.D.: The initial stage of an Expanding Universe and Appearance of a Nonuniform Distribution of Matter. ZhETF 49, 345 (1965); translation in JETP Lett. 22, 241 (1966)
Guth, A.H.: In: Freedman, W.L. (ed.) Measuring and Modeling the Universe. Carnegie Observatories Astrophysics Series, vol. 2. Cambridge University Press, Cambridge (2004)
Moffat, J.W.: Scalar–tensor–vector gravity theory. JCAP 0603, 004 (2006)
Skordis, C., Mota, D.F., Ferreira, P.G., Boehm, C.: Large scale structure in Bekensteins theory of relativistic modified newtonian dynamics. Phys. Rev. Lett. 96, 011301 (2006)
McGaugh, S.S.: A tale of two paradigms: the mutual incommensurability of \(\Lambda CDM\) and MOND. Can. J. Phys. 93, 250 (2015)
Milgrom, M.: A modification of the Newtonian dynamics as a possible alternative to the hidden mass hypothesis. J. Astrophys. 270, 365 (1983)
Sanders, R.H., McGaugh, S.S.: Modified Newtonian dynamics as an alternative to dark matter. Annu. Rev. Astron. Astrophys. 40, 263 (2002)
McGaugh, S.S., de Blok, E.: High-resolution rotation curves of low surface brightness galaxies. I. Data. Astrophys. J. 499, 66 (1998)
Sanders, R.H.: Clusters of galaxies with modified Newtonian dynamics. Mon. Not. R. Astron. Soc. 342, 901 (2003)
Pointecouteau, E., Silk, J.: New constraints on modified Newtonian dynamics from galaxy clusters. Mon. Not. R. Astron. Soc. 364, 654 (2005)
Fabris, J.C., Velten, H.E.S.: MOND virial theorem applied to a galaxy cluster. Br. J. Phys. 39, 592 (2009)
Clowe, D.: A direct empirical proof of the existence of dark matter. Astrophys. J. Lett 648, L109 (2006)
Milgrom, M.: MOND Particularly as Modified Inertia. (2011). arXiv:1101.5122v1
Calmet, X., Kuntz, I.: What is modified gravity and how to differentiate it from particle dark matter? (2017). arXiv:1702.03832v2
Milgrom, M.: MOND theory. (2014). arXiv:1404.7661v2
Scarpa, R.: Modified Newtonian Dynamics, an Introductory Review. astro-ph/0601478 (2006)
Nusser, A.: Modified Newtonian dynamics of large-scale structure. Mon. Not. R. Astron. Soc. 331, 909 (2002)
Nusser, A., Pointecouteau, E.: Modeling the formation of galaxy clusters in MOND. Mon. Not. R. Astron. Soc. 366, 969 (2006)
Olver, P.J.: Applications of Lie Groups to Differential equations. Springer, New York (1993)
Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley & Sons, Inc., New York (1972)
Bonnor, W.B.: Jeans’ formula for gravitational instability. Mon. Not. R. Astron. Soc. 117, 104 (1957)
Sanders, R. H.: Cluster of galaxies with modified Newtonian dynamics (MOND). (2002). arXiv:astro-ph/0212293v1
Famaey, B., McGaugh, S.S.: Modified Newtonian dynamics (MOND): observational phenomenology and relativistic extension. Living Rev. Relativ. 15, 10 (2012)
Milgrom, M.: New physics at low accelerations (MOND): an alternative to dark matter. (2010). arXiv:0912.2678v2
Acknowledgements
AC acknowledges UGC, The Government of India, for financial support through Project No. F.30-302/2016(BSR).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choudhuri, A., Ganguly, A. Cosmological Density Perturbations in Newtonian- and MONDian Gravity Scenario: A Symmetry-Based Approach. Found Phys 49, 63–82 (2019). https://doi.org/10.1007/s10701-018-00233-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10701-018-00233-z