光子场的运动学：暗物质的可能来源
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Eur. Phys. J. C (2016) 76:648
DOI 10.1140/epjc/s10052-016-4512-z
Regular Article - Theoretical Physics
Kinematics of radion field: a possible source of dark matter
Sumanta Chakraborty
1,a
, Soumitra SenGupta
2,b
1
IUCAA, Post Bag 4, Ganeshkhind, Pune University Campus, Pune 411 007, India
2
Department of Theoretical Physics, Indian Association for the Cultivation of Science, Kolkata 700032, India
Received: 11 July 2016 / Accepted: 11 November 2016 / Published online: 25 November 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract The discrepancy between observed virial and
baryonic mass in galaxy clusters have lead to the missing
mass problem. To resolve this, a new, non-baryonic mat-
ter field, known as dark matter, has been invoked. However,
till date no possible constituents of the dark matter compo-
nents are known. This has led to various models, by modi-
fying gravity at large distances to explain the missing mass
problem. The modification to gravity appears very naturally
when effective field theory on a lower-dimensional mani-
fold, embedded in a higher-dimensional spacetime is con-
sidered. It has been shown that in a scenario with two lower-
dimensional manifolds separated by a finite distance is capa-
ble to address the missing mass problem, which in turn deter-
mines the kinematics of the brane separation. Consequences
for galactic rotation curves are also described.
1 Introduction
Recent astrophysical observations strongly suggest the exis-
tence of non-baryonic dark matter at the galactic as well
as extra-galactic scales (if the dark matter is baryonic in
nature, the third peak in the Cosmic Microwave Background
power spectrum would have been lower compared to the
observed height of the spectrum [1]). These observations can
be divided into two branches – (a) behavior of galactic rota-
tion curves and (b) mass discrepancy in clusters of galaxies
[2].
The first one, i.e., rotation curves of spiral galaxies, shows
clear evidence of problems associated with Newtonian and
general relativity prescriptions [2–4]. In these galaxies neu-
tral hydrogen clouds are observed much beyond the extent
of luminous baryonic matter. In a Newtonian description,
the equilibrium of these clouds moving in a circular orbit of
radius r is obtained through equality of centrifugal and grav-
a
e-mails: sumantac.physics@gmail.com; sumanta@iucaa.in
b
e-mail: tpssg@iacs.res.in
itational force. For cloud velocity v(r ), the centrifugal force
is given by v
2
/r and the gravitational force by GM(r)/r
2
,
where M(r) stands for total gravitational mass within radius
r. Equating these two will lead to the mass profile of the
galaxy: M(r) = rv
2
/G. This immediately posed serious
problem, for at large distances from the center of the galaxy,
the velocity remains nearly constant v ∼ 200 km/s, which
suggests that mass inside radius r should increase monotoni-
cally with r , even though at large distance very little luminous
matter can be detected [2–4].
The mass discrepancy of galaxy clusters also provides
direct hint for existence of dark matter. The mass of galaxy
clusters, which are the largest virialized structures in the uni-
verse, can be determined in two possible ways – (i) from
the knowledge about motion of the member galaxies one can
estimate the virial mass M
V
, second, (ii) estimating mass of
individual galaxies and then summing over them in order to
obtain total baryonic mass M. Almost without any exception
M
V
turns out to be much large compared to M, typically one
has M
V
/M ∼ 20 − 30 [2–4]. Recently, new methods have
been developed to determine the mass of galaxy clusters;
these are (i) dynamical analysis of hot X-ray emitting gas
[5] and (ii) gravitational lensing of background galaxies [6]
– these methods also lead to similar results. Thus dynamical
mass of galaxy clusters are always found to be in excess com-
pared to their visible or baryonic mass. This missing mass
issue can be explained through postulating that every galaxy
and galaxy cluster is embedded in a halo made up of dark mat-
ter. Thus the difference M
V
−M is originating from the mass
of the dark matter halo the galaxy cluster is embedded in.
The physical properties and possible candidates for dark
matter can be summarized as follows: dark matter is assumed
to be non-relativistic (hence cold and pressure-less), inter-
acting only through gravity. Among many others, the most
popular choice being weakly interacting massive particles.
Among different models, the one with sterile neutrinos (with
masses of several keV) has attracted much attention [7,8].
Despite some success it comes with its own limitations. In
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