1,390 research outputs found
On the Holografic Bound in Newtonian Cosmology
[EN] The holographic principle sets an upper bound on the total (Boltzmann) entropy content of
the Universe at around 10123kB (kB being Boltzmann¿s constant). In this work we point out the existence
of a remarkable duality between nonrelativistic quantum mechanics on the one hand, and Newtonian
cosmology on the other. Specifically, nonrelativistic quantum mechanics has a quantum probability fluid
that exactly mimics the behaviour of the cosmological fluid, the latter considered in the Newtonian
approximation. One proves that the equations governing the cosmological fluid (the Euler equation
and the continuity equation) become the very equations that govern the quantum probability fluid
after applying the Madelung transformation to the Schroedinger wavefunction. Under the assumption
that gravitational equipotential surfaces can be identified with isoentropic surfaces, this model
allows for a simple computation of the gravitational entropy of a Newtonian Universe. In a first
approximation, we model the cosmological fluid as the quantum probability fluid of free Schroedinger
waves. We find that this model Universe saturates the holographic bound. As a second approximation,
we include the Hubble expansion of the galaxies. The corresponding Schroedinger waves lead to a
value of the entropy lying three orders of magnitude below the holographic bound. Current work
on a fully relativistic extension of our present model can be expected to yield results in even better
agreement with empirical estimates of the entropy of the Universe.This research was supported by grant no. ENE2015-71333-R (Spain).Isidro San Juan, JM.; Fernández De Córdoba, P. (2018). On the Holografic Bound in Newtonian Cosmology. Entropy. 20(83):1-8. https://doi.org/10.3390/e20020083S18208
Boltzmann entropy of a Newtonian Universe
A dynamical estimate is given for the Boltzmann entropy of the Universe,
under the simplifying assumptions provided by Newtonian cosmology. We first
model the cosmological fluid as the probability fluid of a quantum-mechanical
system. Next, following current ideas about the emergence of spacetime, we
regard gravitational equipotentials as isoentropic surfaces. Therefore
gravitational entropy is proportional to the vacuum expectation value of the
gravitational potential in a certain quantum state describing the matter
contents of the Universe. The entropy of the matter sector can also be
computed. While providing values of the entropy that turn out to be somewhat
higher than existing estimates, our results are in perfect compliance with the
upper bound set by the holographic principle.Comment: 15 page
Role of the cosmological constant in the holographic description of the early universe
We investigate the role of the cosmological constant in the holographic
description of a radiation-dominated universe with a positive
cosmological constant . In order to understand the nature of
cosmological term, we first study the newtonian cosmology. Here we find two
aspects of the cosmological term: entropy () and
energy (). Also we solve the Friedmann equation
parametrically to obtain another role. In the presence of the cosmological
constant, the solutions are described by the Weierstrass elliptic functions on
torus and have modular properties. In this case one may expect to have a
two-dimensional Cardy entropy formula but the cosmological constant plays a
role of the modular parameter of torus. Consequently the
entropy concept of the cosmological constant is very suitable for establishing
the holographic entropy bounds in the early universe. This contrasts to the
role of the cosmological constant as a dark energy in the present universe.Comment: 15 page
The Friedmann equation in modified entropy-area relation from entropy force
According to the formal holographic principle, a modification to the
assumption of holographic principle in Verlinder's investigation of entropy
force is obtained. A more precise relation between entropy and area in the
holographic system is proposed. With the entropy corrections to the
area-relation, we derivate Newton's laws and Einstein equation with a static
spherically symmetric holographic screen. Furthermore we derived the correction
terms to the modified Friedmann equation of the FRW universe starting from the
holographic principle and the Debye model.Comment: Mod. Phys. Lett. A26, 489-500 (2011
Does entropic force always imply the Newtonian force law?
We study the entropic force by introducing a bound between
entropy and area which was derived by imposing the non-gravitational collapse
condition. In this case, applying a modified entropic force to this system does
not lead to the Newtonian force law.Comment: 11 pages, version to appear in EPJ
Towards a holographic theory of cosmology -- threads in a tapestry
In this Essay we address several fundamental issues in cosmology: What is the
nature of dark energy and dark matter? Why is the dark sector so different from
ordinary matter? Why is the effective cosmological constant non-zero but so
incredibly small? What is the reason behind the emergence of a critical
acceleration parameter of magnitude in galactic dynamics? We
suggest that the holographic principle is the linchpin in a unified scheme to
understand these various issues.Comment: 8 pages, LaTeX; This Essay, dedicated to the memory of Hendrik van
Dam, received Honorable Mention in the 2013 Essay Competition of the Gravity
Research Foundatio
Quantum UV/IR Relations and Holographic Dark Energy from Entropic Force
We investigate the implications of the entropic force formalism proposed by
Verlinde. We show that an UV/IR relation proposed by Cohen et al, as well as an
uncertainty principle proposed by Hogan can be derived from the entropic force
formalism. We show that applying the entropic force formalism to cosmology,
there is an additional term in the Friedmann equation, which can be identified
as holographic dark energy. We also propose an intuitive picture of holographic
screen, which can be thought of as an improvement of Susskind's holographic
screen.Comment: 12 pages, 4 figures; v2: typos corrected, references added; v3:
references added; v4: final version to appear on PL
Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology
[EN] The holographic principle sets an upper bound on the total (Boltzmann) entropy content
of the Universe at around 10123kB (kB being Boltzmann¿s constant). In this work we point out
the existence of a remarkable duality between nonrelativistic quantum mechanics on the one
hand, and Newtonian cosmology on the other. Specifically, nonrelativistic quantum mechanics
has a quantum probability fluid that exactly mimics the behaviour of the cosmological fluid,
the latter considered in the Newtonian approximation. One proves that the equations governing the
cosmological fluid (the Euler equation and the continuity equation) become the very equations that
govern the quantum probability fluid after applying the Madelung transformation to the Schroedinger
wavefunction. Under the assumption that gravitational equipotential surfaces can be identified
with isoentropic surfaces, this model allows for a simple computation of the gravitational entropy
of a Newtonian Universe.This research was supported by grant no. ENE2015-71333-R (Spain).Fernández De Córdoba, P.; Isidro, J. (2018). Boltzmann Entropy, the Holographic Bound and Newtonian Cosmology. Proceedings. 2(4):155-159. https://doi.org/10.3390/ecea-4-050081551592
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