Astronomia

Dynamics of Dark Matter in Baryon-Radiation Plasma:
Perspectives using Meschersky equation
Himanshu kumar∗ and Sharf Alam

arXiv:1211.0154v1 [astro-ph.CO] 1 Nov 2012

Jamia Millia Islamia, New Delhi, India
With an aim to argue for the truly collisionless nature of cold dark matter between epochs of
equality and recombination, we assume a model, wherein strongly coupled baryon-radiationplasma
ejects out of small regions of concentrated cold dark matter without losing its equilibrium. We use
the Meschersky equation to describe the dynamics of cold dark matter in the presence of varying
mass of strongly coupled baryon-radiation plasma. Based on this model, we discuss the growth of
perturbations in cold dark matter both in the Jeans theory and in the expanding universe usingNewton’s theory. We see the effect of the perturbations in the cold dark matter potential on
the cosmic microwave background anisotropy that originated at redshifts between equality and
recombination i.e. 1100 < z < zeq . Also we obtain an expression for the Sachs-Wolfe effect, i.e.
the CMB temperature anisotropy at decoupling in terms of the perturbations in cold dark matter
potential. We obtainsimilar solutions both in the static and in the expanding universe, for epochs
of recombination. From this, we infer about the time scale when the dark energy starts to dominate.

Meschersky equation, Cold Dark matter, Collisionless, Baryon-Radiation plasma, Cosmic Microwave background, SachsWolfe effect

I.

INTRODUCTION

Flat cosmological models with a mixture of ordinary baryonic matter,cold dark matter, and cosmological constant(or quintessence) and a nearly scale-invariant, adiabatic spectrum of density fluctuations are consistent with
standard inflationary cosmology. They provide an excellent fit to current observations on large scales(>> 1 Mpc).
Currently, the constitution of the universe is 4% baryons, 23% dark matter and 73% dark energy [1–6].
In the standard hot Big Bangmodel, the universe is initially hot and the energy density is dominated by radiation.
The transition to matter domination occurs at z ≈ 104 . In the epochs after equality and before recombination, the
universe remains hot enough. Thus the gas is ionized, and the electron-photon scattering effectively couples the matter
and radiation [7]. At z ≈ 1200, the temperature drops below ≈ 3300 K. Theprotons and electrons now recombine
to form neutral hydrogen and neutral helium. This event is usually known as recombination [8–10]. The photons
then decouple and travel freely. These photons which keep on travelling till present times are observed as the cosmic
microwave background(CMB). The cold dark matter theory including cosmic inflation is the basis of standard modern
cosmology. This isfavoured by the CMB data and the large scale structure data [11, 12]. The CDM model is based
on the assumption that the mass of the universe now is dominated by dark matter, which is non-baryonic [13, 14].
Also it acts like a gas of massive, weakly interacting(collisionless)particles [15]. They have negligibly small primeval
velocty dispersion. Also they are electromagnetically neutral [16, 17].T
The word Cold here means that the ratio M < φ, the gravitation potential, where T and M represent the temperature
and mass of the dark matter particle. There is remarkably good agreement between standard CDM models and the
observed power spectrum of Lyman α observers [18]. This rules out the warm dark matter candidates. The CDM
model predicts the power spectrum of the angular distributionof the temperature of the 3K cosmic microwave
background radiation and the flat Friedmann model. A low density CDM model with a density parameter of around
0. 3 to 0. 4 with cosmological constant actually matches all available data fairly well [19, 20]. The stable CDM
paradigms predict all structure formation [21, 22].
The existence of clusters(≤ 50 mpc) and groups of galaxies suggests that...