3,297 research outputs found
Simple equation of state for hard disks on the hyperbolic plane
A simple equation of state for hard disks on the hyperbolic plane is
proposed. It yields the exact second virial coefficient and contains a pole at
the highest possible packing. A comparison with another very recent theoretical
proposal and simulation data is presented.Comment: 3 pages, 1 figur
Viable Inflationary Evolution from Loop Quantum Cosmology Scalar-Tensor Theory
In this work we construct a bottom-up reconstruction technique for Loop
Quantum Cosmology scalar-tensor theories, from the observational indices.
Particularly, the reconstruction technique is based on fixing the functional
form of the scalar-to-tensor ratio as a function of the -foldings number.
The aim of the technique is to realize viable inflationary scenarios, and the
only assumption that must hold true in order for the reconstruction technique
to work is that the dynamical evolution of the scalar field obeys the slow-roll
conditions. We shall use two functional forms for the scalar-to-tensor ratio,
one of which corresponds to a popular inflationary class of models, the
-attractors. For the latter, we shall calculate the leading order
behavior of the spectral index and we shall demonstrate that the resulting
inflationary theory is viable and compatible with the latest Planck and
BICEP2/Keck-Array data. In addition, we shall find the classical limit of the
theory, and as we demonstrate, the Loop Quantum Cosmology corrected theory and
the classical theory are identical at leading order in the perturbative
expansion quantified by the parameter , which is the critical density
of the quantum theory. Finally, by using the formalism of slow-roll
scalar-tensor Loop Quantum Cosmology, we shall investigate how several
inflationary potentials can be realized by the quantum theory, and we shall
calculate directly the slow-roll indices and the corresponding observational
indices. In addition, the gravity frame picture is presented.Comment: PRD Accepte
Qualitative study in Loop Quantum Cosmology
This work contains a detailed qualitative analysis, in General Relativity and
in Loop Quantum Cosmology, of the dynamics in the associated phase space of a
scalar field minimally coupled with gravity, whose potential mimics the
dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with
the orbits (solutions) of the system, we will see that there are analytic ones,
which lead to the same dynamics as the perfect fluid, and our goal is to check
their stability, depending on the value of the EoS parameter, i.e., to show
whether the other orbits converge or diverge to these analytic solutions at
early and late times.Comment: 12 pages, 7 figures. Version accepted for publication in CQ
On the radial distribution function of a hard-sphere fluid
Two related approaches, one fairly recent [A. Trokhymchuk et al., J. Chem.
Phys. 123, 024501 (2005)] and the other one introduced fifteen years ago [S. B.
Yuste and A. Santos, Phys. Rev. A 43, 5418 (1991)], for the derivation of
analytical forms of the radial distribution function of a fluid of hard spheres
are compared. While they share similar starting philosophy, the first one
involves the determination of eleven parameters while the second is a simple
extension of the solution of the Percus-Yevick equation. It is found that the
{second} approach has a better global accuracy and the further asset of
counting already with a successful generalization to mixtures of hard spheres
and other related systems.Comment: 3 pages, 1 figure; v2: slightly shortened, figure changed, to be
published in JC
Possible polarisation and spin dependent aspects of quantum gravity
We argue that quantum gravity theories that carry a Lie algebraic
modification of the Poincare' and Heisenberg algebras inevitably provide
inhomogeneities that may serve as seeds for cosmological structure formation.
Furthermore, in this class of theories one must expect a strong polarisation
and spin dependence of various quantum-gravity effects.Comment: Awarded an "honourable mention" in the 2007 Gravity Research
Foundation Essay Competitio
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Dual gravitons in AdS <inf>4</inf>/CFT <inf>3</inf> and the holographic Cotton tensor
We argue that gravity theories in AdS4 are holographically dual to either of
two three-dimensional CFT's: the usual Dirichlet CFT1 where the fixed graviton
acts as a source for the stress-energy tensor, and a dual CFT2 with a fixed
dual graviton which acts as a source for a dual stress-energy tensor. The dual
stress-energy tensor is shown to be the Cotton tensor of the Dirichlet CFT. The
two CFT's are related by a Legendre transformation generated by a gravitational
Chern-Simons coupling. This duality is a gravitational version of
electric-magnetic duality valid at any radius r, where the renormalized
stress-energy tensor is the electric field and the Cotton tensor is the
magnetic field. Generic Robin boundary conditions lead to CFT's coupled to
Cotton gravity or topologically massive gravity. Interaction terms with CFT1
lead to a non-zero vev of the stress-energy tensor in CFT2 coupled to gravity
even after the source is removed. We point out that the dual graviton also
exists beyond the linearized approximation, and spell out some of the details
of the non-linear construction
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