f（R，T）Brane模型中的构型熵
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Eur. Phys. J. C (2016) 76:100
DOI 10.1140/epjc/s10052-016-3952-9
Regular Article - Theoretical Physics
Configurational entropy in f (R, T) brane models
R. A. C. Correa
1,a
, P. H. R. S. Moraes
2,b
1
CCNH, Universidade Federal do ABC, Santo André, São Paulo 09210-580, Brazil
2
ITA, Instituto Tecnológico de Aeronáutica, São José dos Campos, São Paulo 12228-900, Brazil
Received: 3 September 2015 / Accepted: 17 February 2016 / Published online: 25 February 2016
© The Author(s) 2016. This article is published with open access at Springerlink.com
Abstract In this work we investigate generalized theories
of gravity in the so-called configurational entropy (CE) con-
text. We show, by means of this information-theoretical mea-
sure, that a stricter bound on the parameter of f (R, T ) brane
models arises from the CE. We find that these bounds are
characterized by a valley region in the CE profile, where the
entropy is minimal. We argue that the CE measure can play
a new role and might be an important additional approach to
selecting parameters in modified theories of gravitation.
1 Introduction
Although CDM cosmological model provides a great
match between theory and observation [1], which is why
it usually is referred to as the “concordance model”, a num-
ber of shortcomings, as the cosmological constant and hier-
archy problems, still await convincing explanations. While
by assuming general relativity as the gravitational theory,
those problems cannot be solve straightforwardly, higher
order derivative and extradimensional theories might con-
tribute efficiently to solving these issues.
Note that f (R) and f (R, T ) cosmological models [2–
10], with R and T being, respectively, the Ricci scalar and the
trace of the energy-momentum tensor, are able to describe the
cosmic acceleration our universe is undergoing [11,12] with
no need of invoking a cosmological constant. On the other
hand, the hierarchy problem can be solved by assuming that
our observable universe is a sub-manifold which is embedded
in an anti-de Sitter five-dimensional space (AdS
5
), called the
bulk, as in the Randall–Sundrum braneworld model [13]. In
fact, it has been shown in [14] that braneworld models can
explain the cosmic acceleration as an effect of the leaking of
gravity to the extra dimension.
a
e-mails: fis04132@gmail.com; rafael.couceiro@ufabc.edu.br
b
e-mail: moraes.phrs@gmail.com
In this work we will deal with braneworld models in the
presence of scalar fields [15–18]. Departing from the orig-
inal Randall and Sundrum proposal, which leads to a thin
braneworld scenario, the coupling with scalar fields leads
to thick braneworlds. The presence of a scalar field lets the
warp function behave smoothly, yielding such a thickness.
This possibility has opened a new area of study, and here we
quote Refs. [19–26] for some work on the subject.
Specifically, we will consider the f (R, T ) gravity in such
a thick braneworld scenario. Note that although f (R) brane
models have already been presented in the literature [27–
35], due to its recent elaboration, f (R, T ) gravity still lacks
a significant number of applications in the braneworld. Any-
how, it is a remarkable the fact that in [36], the authors have
pioneered such an approach.
Here, rather than a cosmological approach, we will investi-
gate f (R, T ) brane models from the configurational entropy
(CE) perspective. Gleiser and Stamatopoulos (GS) have pro-
posed in [37] such a new physical quantity, which brings
about additional information as regards some parameters of
a given model for which the energy density is localized. They
have shown that the higher the energy that approximates the
actual solution, the higher its relative CE, which is defined as
the absolute difference between the actual function CE and
the trial function CE. The CE is able to solve situations where
the energies of the configurations are degenerate. In this case,
it can be used to select the best system configuration.
Although it has been recently proposed, the CE has already
been used to study the non-equilibrium dynamics of sponta-
neous symmetry breaking [38], to obtain the stability bound
for compact objects [39], to investigate the emergence of
localized objects during inflationary preheating [40], and
to distinguish configurations with energy-degenerate spatial
profiles [41]. Solitons, Lorentz symmetry breaking, super-
symmetry, and entropy were employed using the CE concept
[42–45]. The CE for traveling solitons reveals that the best
value of the parameter responsible for breaking the Lorentz
symmetry is that where the energy density is distributed
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