Physics Letters B 797 (2019) 134796
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Physics Letters B
www.elsevier.com/locate/physletb
Linear growth index of matter perturbations in Rastall gravity
Wompherdeiki Khyllep
a,b
, Jibitesh Dutta
c,d,∗
a
Department of Mathematics, North-Eastern Hill University, Shillong, Meghalaya 793022, India
b
Department of Mathematics, St. Anthony’s College, Shillong, Meghalaya 793001, India
c
Mathematics Division, Department of Basic Sciences and Social Sciences, North-Eastern Hill University, Shillong, Meghalaya 793022, India
d
Visiting Associate, Inter University Centre for Astronomy and Astrophysics, Pune 411 007, India
a r t i c l e i n f o a b s t r a c t
Article history:
Received
15 March 2019
Received
in revised form 19 June 2019
Accepted
19 July 2019
Available
online 24 July 2019
Editor: M.
Trodden
Rastall gravity theory shows notable features consistent with physical observations in comparison to the
standard Einstein theory. Recently, there has been a debate about the equivalence of Rastall gravity and
general relativity. Motivated by this open issue, in the present work, we attempt to shed some light on
this debate by analyzing the evolution of the Rastall based cosmological model at the background as
well as perturbation level. Employing the dynamical system techniques, we found that at late times, the
dynamics of the model resembles the CDM model at the background level irrespective of the choice of
Rastall’s parameter. However, at the perturbation level, we found that the evolution of the growth index
heavily depends on the Rastall’s parameter and displays a significant deviation from the CDM model.
© 2019 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
The inability of the standard theory of gravity to describe var-
ious
observational evidence has led to the need for extending the
theory of general relativity (GR). The structure of extended theories
of gravity provides a useful approach to alleviate the fundamental
problems such as dark matter (DM) and dark energy (DE) associ-
ated
with the standard model of GR [1–3].
One
of the extended theories of gravity was proposed by Rastall
in 1972 [4,5]. In his theory, Rastall assumed the violation of the
conservation of energy-momentum tensor in curved spacetime
without dropping the Bianchi identities. As the usual particle cre-
ation
phenomenon violates the energy-momentum conservation
law, therefore, this theory can also be regarded as a classical for-
mulation
of a particle creation process [6–9]. Rastall gravity is
one of the most promising non-conservative modified theory of
gravity supporting various cosmological and astrophysical observa-
tions.
Recently, it got a lot of attention in the physics community
[10–14]. For instance, this theory fits well with observational data
related to the age of the Universe, Hubble parameter and helium
nucleosynthesis [15,16]. Further, this theory can possibly circum-
vent
the entropy and age problems of standard cosmology [17].
From Mach’s principle perspective, this theory is more ‘Machian’
than the standard theory of GR [18].
*
Corresponding author.
E-mail
addresses: sjwomkhyllep@gmail.com (W. Khyllep), jibitesh@nehu.ac.in
(J. Dutta).
It has been claimed by Visser in [19] that the theory of Rastall
gravity is completely equivalent to GR and further supported by
[20]from a thermodynamical perspective. However, this result
has been recently denied by [21,22]leaving an open debate that
whether this theory is a modified gravity theory or it is equiva-
lent
to GR with an additional modified matter content. Earlier, the
non-equivalence of Rastall gravity from GR has also been pointed
by Smalley in Ref. [23].
In Ref. [11]it has been shown that Rastall cosmology is equiv-
alent
to the CDM at both background and linear perturbation
level except that DE cluster for the former model. The growth of
matter perturbations provides an efficient approach to predict the
matter distribution of the Universe and also to discriminate vari-
ous
gravitational theories [24,25]. One of the simple observational
tools used to study the growth history of a model is the so-called
growth index of matter perturbations (denoted by γ ) [26]. The ac-
curate
estimation of the growth index is one of the basic tasks
from the cosmological point of view as it can be used as a tool
to test the validity of GR on extragalactic scales. It is a usual pro-
cedure
that for each cosmological model, one requires to analyze
its background evolution and the growth index of matter pertur-
bations.
This task helps one to get an overall effect of the model
at the cosmological and astrophysical level. For instance, those DE
models based on GR, the value of the constant growth index can
be reduced to that of the CDM model (i.e. γ =
6
11
) irrespective
of the choice of model parameters. However, in the case of modi-
fied
gravity based models, the value shows a significant deviation
from
6
11
. Recently, there are various works in the literature where
https://doi.org/10.1016/j.physletb.2019.134796
0370-2693/
© 2019 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
.
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