Cosmological Density Perturbations from Matter Domination to Recombination in Newtonian and MONDian Gravity Scenarios
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Cosmological Density Perturbations from Matter Domination to Recombination in Newtonian and MONDian Gravity Scenarios Aritra Ganguly1 and Amitava Choudhuri1* 1
Department of Physics, The University of Burdwan, Golapbag 713104, West Bengal, India Received December 2, 2019; revised December 22, 2019; accepted May 20, 2020
Abstract—Cosmological density perturbations governed by Newtonian and MONDian force laws scenarios for the period from matter domination to recombination have been investigated. Particularly, we find solutions for the density contrast equations obtained for both cases with respect to a homogeneous spatially flat Friedman-Lema ˆıtre-Robertson-Walker (FLRW) background using the Lie symmetry approach. Numerical solutions of the density contrast equations for both cases also have been provided in order to study the evolution of the density contrast. For the Newtonian case we find a limiting mass that dictates whether the growth of the density contrast is possible or not. Interestingly, in the Newtonian case, physical growth of the density contrast is not possible since the horizon mass is smaller than the limiting mass. On the other hand, growth of the density contrast is possible depending on the initial condition and the fluctuation mass of the MOND-dominated region despite the radiation pressure that leads to future structure formation. DOI: 10.1134/S020228932003007X
1. INTRODUCTION The origin and evolution of the cosmological structure formation is one of the challenging problems in the field of cosmology for the researchers. It is quite natural to assume that the perturbations started off from an extremely homogeneous and isotropic state, with initial conditions provided by an era of accelerated expansion called inflation [1]. In this context inflation not only solves the initial-condition problems, but also provides the seed for the formation of density perturbations. The slow-roll inflation predicts almost scale-invariant density perturbations consistent with the observation on CMB anisotropy. The initial quantum fluctuation of a scalar field blows up very rapidly during inflation. Once the scale becomes larger than the horizon scale, quantum fluctuations are frozen in and behave as classical seed perturbations. It is established that the large-scale structure in the distribution of matter in the present universe arose due to gravitational instability from the primordial perturbations seen in the CMB anisotropy at the epoch of the recombination [2]. In this context, as the very early universe was hot and dense, the interactions among particles were more frequent, and consequently the mean free path of a photon was very small, almost about the dimension of an atom [3]. These resulted in multiple interactions and kept the constituents of the universe in equilibrium up to one second after the Big Bang. *
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At a temperature of about 5 × 109 K, four seconds after Big Bang, the electron-positron pairs began to annihilate, leaving as the dominant constituents of the universe only phot
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