108 research outputs found
Cosmological model from the holographic equipartition law with a modified R\'{e}nyi entropy
Cosmological equations were recently derived by Padmanabhan from the
expansion of cosmic space due to the difference between the degrees of freedom
on the surface and in the bulk in a region of space. In this study, a modified
R\'{e}nyi entropy is applied to Padmanabhan's `holographic equipartition law',
by regarding the Bekenstein--Hawking entropy as a nonextensive Tsallis entropy
and using a logarithmic formula of the original R\'{e}nyi entropy.
Consequently, the acceleration equation including an extra driving term (such
as a time-varying cosmological term) can be derived in a homogeneous,
isotropic, and spatially flat universe. When a specific condition is
mathematically satisfied, the extra driving term is found to be constant-like
as if it is a cosmological constant. Interestingly, the order of the
constant-like term is naturally consistent with the order of the cosmological
constant measured by observations, because the specific condition constrains
the value of the constant-like term.Comment: Final version accepted for publication in EPJC. The titile is revised
and references are added. [12 pages, 4 figures
General form of entropy on the horizon of the universe in entropic cosmology
Entropic cosmology assumes several forms of entropy on the horizon of the
universe, where the entropy can be considered to behave as if it were related
to the exchange (the transfer) of energy. To discuss this exchangeability, the
consistency of the two continuity equations obtained from two different methods
is examined, focusing on a homogeneous, isotropic, spatially flat, and
matter-dominated universe. The first continuity equation is derived from the
first law of thermodynamics, whereas the second equation is from the Friedmann
and acceleration equations. To study the influence of forms of entropy on the
consistency, a phenomenological entropic-force model is examined, using a
general form of entropy proportional to the -th power of the Hubble horizon.
In this formulation, the Bekenstein entropy (an area entropy), the
Tsallis--Cirto black-hole entropy (a volume entropy), and a quartic entropy are
represented by , , and , respectively. The two continuity equations
for the present model are found to be consistent with each other, especially
when , i.e., the Bekenstein entropy. The exchange of energy between the
bulk (the universe) and the boundary (the horizon of the universe) should be a
viable scenario consistent with the holographic principle.Comment: Final version accepted for publication in PRD. Several pasragraphs
and references are added and corrected. [10 pages
Cosmological model based on both holographic-like connection and Padmanabhan's holographic equipartition law
A cosmological model based on holographic scenarios is formulated in a flat
Friedmann-Robertson-Walker universe. To formulate this model, the cosmological
horizon is assumed to have a general entropy and a general temperature
(including Bekenstein-Hawking entropy and Gibbons-Hawking temperature,
respectively). In addition, a holographic-like connection [Eur. Phys. J. C 83,
690 (2023) (arXiv:2212.05822)] and Padmanabhan's holographic equipartition law
are assumed for the entropy and temperature, and the Friedmann and acceleration
equations are derived from these. The derived Friedmann and acceleration
equations include both the entropy and the temperature and are slightly
complicated, but can be combined into a single simple equation, corresponding
to a similar equation that describes the background evolution of the universe
in time-varying cosmologies. The simple equation depends on the
entropy but not on the temperature because the temperatures in the Friedmann
and acceleration equations cancel each other. These results imply that the
holographic-like connection should be consistent with Padmanabhan's holographic
equipartition law through the present model and that the entropy plays a more
important role. When the Gibbons-Hawking temperature is used as the
temperature, the Friedmann and acceleration equations are found to be
equivalent to those for a model. A particular case of the present
model is also examined, applying a power-law corrected entropy.Comment: 12 pages, 1 figur
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