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Abstract:
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Cosmology deals with the studies on the structure and evolution
of the universe. The model of the universe formulated by Friedmann,
Lemaitre, Robertson andWalker known as the standard model
(FLRW model) of the universe, which is based on the Einstein's theory
of gravity, turned out to be the accepted model because of the
various observational supports. The major observational supports
to this model are the explanation for the Hubble's law, primordial
nucleosynthesis, microwave back ground radiation etc.
Recent observations on Type Ia supernovae by teams led by S
Perlmutter, Brian P Schmidt and Adam G Riess led to the discovery
that the present universe is expanding in an accelerated manner. The
exotic form of matter which causes the acceleration is termed as dark
energy which produce negative pressure. Understanding the nature
and evolution of dark energy is a challenge for the cosmologists. In
addition to the evidences from supernovae, the anisotropy in CMBR
spectra, large scale structures and Baryon acoustic oscillations are
also supporting the discovery.
To explain dark energy, various theoretical models have been proposed.
One such model is the CDM model, in which the universe
is assumed to be composed of dark energy and dark matter. In this
model, Einstein's cosmological constant is considered as dark energy.
It has a constant equation of state; ! = p
= 1: The model predicts
the values of cosmological parameters such as the Hubble parameter,
transition redshift and present deceleration parameter, having a very
good agreement with the observational constraints. But this model
has two major
aws, which are:
1. Cosmological constant problem:- Theoretically predicted value
of dark energy density as the vacuum constant is,
1074GeV 4; while the observed value is 1047GeV 4: The
predicted value is greater than the observed value by 120 orders
of magnitude. This discrepancy between the theoretical
and observational values is known as the cosmological constant
problem.
2. Cosmological coincidence problem:- Energy densities of dark energy
and dark matter are found to be of the same order even
though their evolutionary nature are di erent. This is known as
the coincidence problem which is not explained by the CDM
model.
These led to the proposals of dynamical dark energy models by considering
that the equation of state parameter is evolving with the expanding
universe. Scalar models of dark energy such as Quintessence,
K-essence, Phantom model, Chaplygin gas model and holographicdark energy model are examples of dynamic dark energy models.
Holographic dark energy model is based on the holographic principle
developed by Susskind and 't Hooft. The principle says that
the degrees of freedom of a system resides on its surface rather than
in its volume. The total energy inside a region of size L must not
exceed the mass of a black hole of the same size. The holographic
dark energy density can then be formulated as, = 3c2M2
plL2 (1)
where 3c2 is a numerical constant, M2
pl = 8 G is the reduced Planck
mass. Possible choices for L; the IR cut-o , are Hubble horizon, particle
horizon and event horizon. The choices for the IR cut-o whether
it be Hubble horizon or particle horizon will not support an accelerating
universe, while the third choice, the event horizon, violates
causality. Another alternative for the IR cut-o is the Ricci scalar,
which was rst introduced by Gao et al. Later modi ed holographic
Ricci dark energy was proposed by Granda and Oliveros.
In the present thesis, the modi ed Ricci dark energy is studied
by considering its interaction with the dark matter present in the
universe. Owing to the lack of knowledge about the microscopic origin
of such an interaction, phenomenological interaction forms of nongravitational
nature is assumed. |