Australia: The Land Where Time Began 

Hysteresis in the Sky
Hysteresis is a phenomenon that occurs naturally in several magnetic and
electric materials in condensed matter physics. It has interesting,
vivid implications for the scenario of a cyclic bouncy Universe when it
is applied to cosmology, i.e.
cosmological hysteresis. The most important feature of this physical
prescription is that it can be treated as an alternative proposal to an
inflationary paradigm. The asymmetry in the equation of state parameter
during expansion and contraction phase of the Universe causes
cosmological hysteresis, as a consequence of a single scalar field. This
process is purely thermodynamical in nature, resulting in a
nonvanishing integral in cosmology. When applied to variants of
modified gravity models:
1)
DvaliGabadadzPorrati (DGP) brane world gravity,
2)
Einstein gravity dominated by the cosmological constant,
3)
Loop Quantum Gravity (LQG),
4)
EinsteinGaussBonnet brane world gravity,
5)
Randall Sundrum single brane world gravity (RSII), in certain
circumstances, this phenomenon leads to the increase of amplitude of the
consecutive cycles as well as to a universe with older and larger
successive cycles provided we have physical mechanisms to make the
universe bounce and turnaround.
An arrow of time is inculcated in a dissipationless cosmology by this.
It is said to be remarkable that it appears this phenomenon is
widespread in several cosmological potentials in variants of modified
gravity background, which Choudhury et
al. explicitly study for
i)
Hilltop,
ii)
Natural and
iii)
ColemanWeinberg potentials, in this paper.
It is shown by semianalytical analysis of these models, for different
potentials with minimum/minima that the conditions which creates a
universe with an ever increasing expansion, depend on the signature of
the hysteresis loop integral as well as on the variants of model
parameters.
The phenomenon of hysteresis arises in systems where there is a lag
between input and output. Hysteresis occurs when the lag is dynamic,
i.e. changing over time. It can be evaluated by purely thermodynamical
expressions where the output is dependent on the current and past
inputs. In many lab systems such as ferromagnetic and ferroelectric
materials such a phenomenon occurs naturally and is incorporated
artificially in several electrical systems.
In cosmology, analogously with hysteresis, there is a phenomenon of
cyclic universes where the Universe repeatedly comes into existence
after each cycle. As occurs in hysteresis, where the material goes
through the same process repeatedly, in a cyclic universe the Universe
starts from big bang and ends in a big crunch repeatedly. There have
been several proposals for cyclic universes in the literature (Eliade,
1934; Jaki, 1974; Starobinsky, 1979). In exact solutions of Einstein’s
equations for a closed Universe filled with perfect fluid such models of
cyclic universe also arise. In most of these models, however, all the
cycles are identical to one another. Also, all of these models do not
provide any prescription for avoiding a singularity. Therefore these
models have failed to be successful for solving some of the major
problems with the big bang model, such as the flatness and horizon
problem, and avoidance of a singularity. In his paper Tolman (Tolman,
1934) used a radically different approach in which an oscillating
universe could be obtained with increasing maximum expansion after each
cycle. In other cyclic universe models that have been proposed
(Steinhardt & Turok, 2002; Lehners, 2008), the same phenomenon occurs
naturally. Tolman has proposed the presence of a viscous fluid which
gave rise to an asymmetric, irreversible equation of motion. This
generated an inequality between the pressures at the time of expansion
and contraction phases which resulted in the growth of both energy and
entropy. He therefore demonstrated a novel way for linking
thermodynamical principals to the model of a cyclic universe. The
solving of the flatness and horizons was helped by this unusual
approach. But none of these models avoided a big bang singularity. Also,
Tolman’s proposed model led to an increase in entropy with each cycle
which was inevitable.
A method has been proposed (Kanekar, Sahni & Shtanov, 2001; Sahni &
Toporensky, 2012) of both avoiding the presence of a singularity and
increasing entropy by the use of a cosmological analogue model of
hysteresis. The basic idea of generating the cyclical universe with an
increasing maximum remains unchanged. According to Tolman if there is a
tendency for the pressure to be greater during a compression than during
a previous expansion, as he suggests would be expected with a lag
following equilibrium conditions, an element of fluid can return to the
volume it had originally with energy that had increased. Chaudhary et
al. used the scalar field
dynamics that were generated during the inflationary paradigm to
generate the pressure asymmetry in order to maintain the symmetric
nature of the equation of motion and thereby avoiding the production of
entropy. It was originally proposed (Kanekar, Sahni & Shtanov, 2001) and
extended later (Sahni & Toporensky, 2012) Chaudhary et
al. demonstrated that “a
universe filled with a scalar field possesses the intriguing property of
‘hysteresis’.” According to
Chaudhary et al. the central
idea was to show that in the presence of a massive scalar field under
certain reasonable conditions when the bounce occurred (Cai et al.,
2013; Cai, Brandenberger & Peter, 2013; Cai, Gao & Saridakis, 2012; Cai.
Easson & Brandenberger, 2012; Li, Brandenberger & Cheung, 2014;
Brandenberger, ????; Cai, Brandenberger & Zhang, 2011; Lilley & Peter,
????; Falciano, Lilley & Peter, ????; Lilley, Di Marco, Martin & Peter,
2010; Lilley, Lorenz & Clesse, ????; Battefeld & Peter, 2015; Graham et
al., 2014; Koehn, Lehners & Ovrut, 2014), growing expansion cycles
arise, the increase in amplitude of the expansion being related to the
work done by/on the scalar field during the expansion/contraction of the
universe. This leads to the production of a hysteresis loop defined to
as
∮ pdV=0
during each oscillatory cycle. But the phenomenon of hysteresis is
independent of the nature of potential, i.e. generic. Any potential
which has a proper minima that randomises the phase of the scaler field
as it oscillates around the minima during expansion, and thereby makes
all possible values of ϕ
probable at turnaround, is capable of causing the phenomenon of
hysteresis. Potentials that have no proper minimum, however, will result
in a unique value of ϕ which
will make
Ƥexp =
Ƥcont,
Thereby making:
∮
pdV = 0
According to Choudhury et al.
such potentials are not suitable candidates for causing hysteresis. The
authors have used existing models such as brane world scenario in the
early universe so as to avoid a big bang and big crunch, as well as the
presence of negative density or phantomlike density in the early
universe. In these models a bounce replaces the big bang singularity,
and recollapse or turnaround replaces the big crunch.
This paper is based on an analysis carried out (Sahni & Toporensky,
2001). Choudhury et al. have
investigated further the phenomenon of hysteresis in different models
such as variants of a cosmological constant model that includes ACDM,
higher dimensional models such as DvaliGabadadzPorrati (DGP) brane
world gravity model in brane world. Models in which the dynamics of the
scalar field are modified were used, which can be achieved by making the
cosmological constant field dependent. The aim of the study was to study
the phenomenon of hysteresis in different models as well as well as to
constrain the models by using hysteresis. Models which can give rise to
bounce in the early universe and turnaround in the late universe were
studied. Also, Choudhury et al.
investigated the equivalent conditions required to achieve such bounding
and recollapsing scenarios. It was shown that their analysis holds true
for any form of the potential of the scalar field with a proper minimum.
They have also shown that the phenomenon of hysteresis or the asymmetry
in pressure can be achieved whether or not the slow roll conditions of
inflation are satisfied. An increase in expansion maximum following each
cycle depends on the sign of
∮
pdV as well as the parameters
of the models that have been considered is a notable feature of this
analysis. It is therefore can be seen that by using the remarkable
cosmological effect of hysteresis as proposed (Kanekar, Sahni & Shtanov,
2001; Sahni & Toporensky, 2001), there are many methods and models in
which a cyclical universe in which there is an ever increasing amplitude
maximum can be achieved.
In this paper Choudhury et
al. have drawn various
physical conclusions by explicitly solving the equations that govern the
dynamics of the system by the use of semianalytical techniques. They
have studied the detailed features for 3 different potentials – hilltop
potential, natural potential and ColemannWeinberg potential; though the
analysis is perfectly true for any kind of cosmological potential that
has a proper minimum/minima. All of these potentials have minimum/minima
that are well defined and have free parameters which can be adjusted to
obtain the required results. This analysis therefore helps to apply
stringent constraints to the characteristic parameters of these models
in the bounding scenario along with cosmological hysteresis. According
to Choudhury et al. they can
at least show mathematically if there are any limiting cases in which
these potentials combined with the models that can give rise to the
phenomenon of cosmological hysteresis, i.e. Make
∮
pdV nonzero, though the analysis they carried out holds good under
certain approximations that are physically acceptable and limiting
cases. In this study we have explicitly derived the expression for work
done in 1 complete cycle of expansion and contraction, and have shown
that it is nonzero. But the sign of the integral depends on how the
sign and magnitudes of the parameters of the models used in the study
have been chosen. That there are
several models capable of giving rise to a cyclical universe with an
increasing expansion magnitude is the most interesting result of their
analysis.




Author: M.H.Monroe Email: admin@austhrutime.com Sources & Further reading 