Physics Letters B 769 (2017) 134–140
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Physics Letters B
www.elsevier.com/locate/physletb
Braneworld mimetic cosmology
Naser Sadeghnezhad, Kourosh Nozari
∗
Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran
a r t i c l e i n f o a b s t r a c t
Article history:
Received
10 December 2016
Received
in revised form 18 March 2017
Accepted
22 March 2017
Available
online 23 March 2017
Editor:
N. Lambert
Keywords:
Braneworld
gravity
Bulk
scalar field
Mimetic
gravity
We extend the idea of mimetic gravity to a Randall–Sundrum II braneworld model. As for the
4-dimensional mimetic gravity, we isolate the conformal degree of freedom of 5-dimensional gravity
in a covariant manner. We assume the bulk metric to be made up of a non-dynamical scalar field and
an auxiliary metric
˜
G
AB
so that G
AB
=
˜
G
CD
,C
,D
˜
G
AB
where A, B, ... are the bulk spacetime indices.
Then we show that the induced conformal degree of freedom on the brane as an induced scalar field,
plays the role of a mimetic field on the brane. In fact, we suppose that the scalar degree of freedom
which mimics the dark sectors on the brane has its origin on the bulk scalar field, . By adopting some
suitable mimetic potentials on the brane, we show that this brane mimetic field explains the late time
cosmic expansion in the favor of observational data: the equation of state parameter of this field crosses
the cosmological constant line in near past from quintessence to phantom phase in a redshift well in the
range of observation. We show also that this induced mimetic scalar field has the capability to explain
initial time cosmological inflation. We study parameter space of the models numerically in order to
constraint the models with Planck2015 data set.
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
Recent observational data are in the favor of an accelerating
phase of the Universe expansion. To explain this late time cos-
mic
speed up, one can follow two main approaches. The first
approach is to add some mysterious components (dubbed dark en-
ergy)
in the energy–momentum sector of the Einstein field equa-
tions.
The cosmological constant is a possible candidate for dark
energy. However, some yet unsolved problems such as unknown
origin, lake of dynamics and a huge amount of fine tuning for
its magnitude, have led cosmologist to propose other candidates
for a dynamical dark energy component. In this respect, several
types of scalar fields such as quintessence, phantom, tachyon and
k-essence are considered as possible candidates for dark energy so
far; see for instance [1–12]. The second approach is modification
of the geometric (gravitational) sector of the Einstein field equa-
tions.
In comparison with “dark energy”, this modification is called
usually as the “dark geometry”. Modification of the geometric sec-
tor
is accomplished in several ways like as modification of the
Einstein–Hilbert action by replacing the Ricci scalar with a generic
function of this scalar as f (R) [13–15], considering the Gauss–
*
Corresponding author.
E-mail
addresses: nsadegh@stu.umz.ac.ir (N. Sadeghnezhad), knozari@umz.ac.ir
(K. Nozari).
Bonnet term or even higher order derivative terms in the spirit of
general scalar–tensor theories in the action of the model [16–23]
and
adopting braneworld scenarios [24–30]. Our attention in this
paper is paid to an extension of the braneworld scenarios in the
spirit of recently proposed mimetic gravity.
From
superstring theories, to have a worthwhile theory our
observed universe should be a membrane embedded in a higher
dimensional spacetime called the bulk. Extra spatial dimensions
should be compactified on the scales that compared to usual four
spatial dimensions are so small [31–33]. In this framework, grav-
ity
propagates through the entire spacetime, whereas the ordinary
matters are trapped on the brane. DGP (Dvali–Gabadadze–Porrati)
[25,26] and Randall–Sundrum (RS) (I and II) [29,30] braneworld
models are the ones in which the universe is considered to be a
5D spacetime and our 4D world is embedded in a 5D bulk. The
DGP setup is based on the modification of the gravitational sector
of the theory over large distances in an induced gravity perspec-
tive.
In this model, the bulk is a flat Minkowski spacetime. On the
other hand, in RS (I and II) models the bulk is AdS
5
. RS I model,
which was proposed to solve the hierarchy problem, consists of
two Minkowski brane embedded in AdS
5
bulk. In this model, the
standard matters are confined on the brane with negative tension
(embedded at y = y
c
) and then gravity is confined on the hidden
brane with positive tension (embedded at y =0). Gravity leaks off
the brane and through the bulk reaches to our brane. However,
in this model there are some problems like as the stabilization of
http://dx.doi.org/10.1016/j.physletb.2017.03.039
0370-2693/
© 2017 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.