Bouncing cosmology from warped extra dimensional scenario
Eur. Phys. J. C
Bouncing cosmology from warped extra dimensional scenario
Ashmita Das 1
Debaprasad Maity 1
Tanmoy Paul 0
Soumitra SenGupta 0
0 Department of Theoretical Physics, Indian Association for the Cultivation of Science , 2A & 2B Raja S.C. Mullick Road, Kolkata 700 032 , India
1 Department of Physics, Indian Institute of Technology , North Guwahati, Guwahati, Assam 781039 , India
From the perspective of four dimensional effective theory on a two brane warped geometry model, we examine the possibility of “bouncing phenomena”on our visible brane. Our results reveal that the presence of a warped extra dimension lead to a non-singular bounce on the brane scale factor and hence can remove the “big-bang singularity”. We also examine the possible parametric regions for which this bouncing is possible.
1 Introduction
Over the last two decades models with extra spatial
dimensions [1–13] have been increasingly playing a central role
in physics beyond the standard model of particle [14] and
cosmological [15] physics. Apart from the
phenomenological approach, higher dimensional scenarios occur naturally
in string theory. Depending on different possible
compactification schemes for the extra dimensions, a large number of
models have been constructed, and their predictions are yet to
be observed in the current experiments. In all these models,
our visible universe is identified as one of the three branes
embedded within a higher dimensional spacetime. The low
energy effective description [16–18] of the dynamical three
brane turned out to be a very powerful tool in studying the
dynamics ranging from particle to cosmology. In our present
work we will take this ansatz to understand cosmological
bouncing phenomena in the early universe cosmology
considering the Randall–Sundrum two brane model.
Among various extra dimensional models proposed over
the last several years, the Randall–Sundrum (RS) warped
extra dimensional model [6] earned special attention since it
can resolve the gauge hierarchy problem without
introducing any intermediate scale (between Planck and TeV) in the
theory. The RS model is a five dimensional AdS space with
S1/Z2 orbifolding along the extra dimension while two three
branes are placed at the orbifold fixed points. The bulk
negative cosmological constant along with appropriate boundary
conditions generate exponentially warped geometry along
the extra dimension. Due to this exponential warping, the
Planck scale on one brane gets suppressed along the extra
dimension and emerges as TeV scale [6] on the visible brane.
In the RS model the interbrane separation (known as
modulus or radion) is ∼ Planck length and generates the required
hierarchy between the branes. Subsequently, Goldberger and
Wise (GW) proposed a modulus stabilzation mechanism
[19] by introducing a massive scalar field in the bulk with
appropriate boundary conditions. Different variants of the RS
model and its modulus stabilization are extensively studied
in [21–28]. In this paper we will consider a specific variant
of RS scenario and study the cosmological dynamics from
the perspective of low energy effective field theory induced
on the visible brane.
It is well known that standard Big Bang scenario is quite
successful in explaining many aspects of cosmological
evolution of our universe. However, the big-bang model is plagued
with a singularity (known as “cosmological singularity”) in
the finite past. Resolving this time like cosmological
singularity is an important issue which is a subject of great research
in theoretical cosmology for the last several decades. It is
widely believed that quantum theory of gravity, if any, should
play very important role in resolving this singularity. One
of the important aspects of all the known non-singular
cosmological models is the existence of pre Big-Bang universe
[29]. In terms of effective theory, different models of
nonsingular cosmologies, such as ekpyrotic universe [30,31],
loop quantum cosmology [32,33], Galileon genesis [34–36],
or the classical bouncing model, can be described by
gravity coupled to a scalar field which generically violates the
null energy condition at the background level. Therefore, the
scale factor of the universe undergoes a non-singular bounce
geometry has S1/Z2 orbifolding along the extra dimension.
Taking ϕ as the extra dimensional angular coordinate, the
branes are situated at orbifolded fixed points i.e. at ϕ = 0
(Planck brane) and ϕ = π (TeV brane), respectively, while
our visible universe is identified with the TeV scale brane.
The proper distance between the branes is considered as a
function of spacetime coordinates. The action of this model
[16] is the following:
1
S = 2κ2
d4x dϕ√−G R(
5
) + (12/ l2)
−
d4x √−ghid Vhid +
√
−gvisVvis
with x μ = (x 0, x 1, x 2, x 3) the brane coordinates. 2κ12 = M 3,
M is the five dimensional Planck mass. R(
5
) and l (∼ Planck
length) are the Ricci scalar and curvature radius of the five
dimensional spacetime, re (...truncated)