2,007 research outputs found
Cosmological Perturbations in Renormalization Group Derived Cosmologies
A linear cosmological perturbation theory of an almost homogeneous and
isotropic perfect fluid Universe with dynamically evolving Newton constant
and cosmological constant is presented. A gauge-invariant formalism
is developed by means of the covariant approach, and the acoustic propagation
equations governing the evolution of the comoving fractional spatial gradients
of the matter density, , and are thus obtained. Explicit solutions
are discussed in cosmologies where both and vary according to
renormalization group equations in the vicinity of a fixed point.Comment: 22 pages, revtex, subeqn.sty, to appear on IJMP
Dynamical System Analysis of Cosmologies with Running Cosmological Constant from Quantum Einstein Gravity
We discuss a mechanism that induces a time-dependent vacuum energy on
cosmological scales. It is based on the instability induced renormalization
triggered by the low energy quantum fluctuations in a Universe with a positive
cosmological constant. We employ the dynamical systems approach to study the
qualitative behavior of Friedmann-Robertson-Walker cosmologies where the
cosmological constant is dynamically evolving according with this
nonperturbative scaling at low energies. It will be shown that it is possible
to realize a "two regimes" dark energy phases, where an unstable early phase of
power-law evolution of the scale factor is followed by an accelerated expansion
era at late times.Comment: 26 pages, 4 figures. To appear in New Journal of Physic
Dynamic asset trees and Black Monday
The minimum spanning tree, based on the concept of ultrametricity, is
constructed from the correlation matrix of stock returns. The dynamics of this
asset tree can be characterised by its normalised length and the mean
occupation layer, as measured from an appropriately chosen centre called the
`central node'. We show how the tree length shrinks during a stock market
crisis, Black Monday in this case, and how a strong reconfiguration takes
place, resulting in topological shrinking of the tree.Comment: 6 pages, 3 eps figues. Elsevier style. Will appear in Physica A as
part of the Bali conference proceedings, in pres
Flow Equations for U_k and Z_k
By considering the gradient expansion for the wilsonian effective action S_k
of a single component scalar field theory truncated to the first two terms, the
potential U_k and the kinetic term Z_k, I show that the recent claim that
different expansion of the fluctuation determinant give rise to different
renormalization group equations for Z_k is incorrect. The correct procedure to
derive this equation is presented and the set of coupled differential equations
for U_k and Z_k is definitely established.Comment: 5 page
Spacetime Structure of an Evaporating Black Hole in Quantum Gravity
The impact of the leading quantum gravity effects on the dynamics of the
Hawking evaporation process of a black hole is investigated. Its spacetime
structure is described by a renormalization group improved Vaidya metric. Its
event horizon, apparent horizon, and timelike limit surface are obtained taking
the scale dependence of Newton's constant into account. The emergence of a
quantum ergosphere is discussed. The final state of the evaporation process is
a cold, Planck size remnant.Comment: 23 pages, BibTeX, revtex4, 7 figure
The role of Background Independence for Asymptotic Safety in Quantum Einstein Gravity
We discuss various basic conceptual issues related to coarse graining flows
in quantum gravity. In particular the requirement of background independence is
shown to lead to renormalization group (RG) flows which are significantly
different from their analogs on a rigid background spacetime. The importance of
these findings for the asymptotic safety approach to Quantum Einstein Gravity
(QEG) is demonstrated in a simplified setting where only the conformal factor
is quantized. We identify background independence as a (the ?) key prerequisite
for the existence of a non-Gaussian RG fixed point and the renormalizability of
QEG.Comment: 2 figures. Talk given by M.R. at the WE-Heraeus-Seminar "Quantum
Gravity: Challenges and Perspectives", Bad Honnef, April 14-16, 2008; to
appear in General Relativity and Gravitatio
Wegner-Houghton equation and derivative expansion
We study the derivative expansion for the effective action in the framework
of the Exact Renormalization Group for a single component scalar theory. By
truncating the expansion to the first two terms, the potential and the
kinetic coefficient , our analysis suggests that a set of coupled
differential equations for these two functions can be established under certain
smoothness conditions for the background field and that sharp and smooth
cut-off give the same result. In addition we find that, differently from the
case of the potential, a further expansion is needed to obtain the differential
equation for , according to the relative weight between the kinetic and
the potential terms. As a result, two different approximations to the
equation are obtained. Finally a numerical analysis of the coupled equations
for and is performed at the non-gaussian fixed point in
dimensions to determine the anomalous dimension of the field.Comment: 15 pages, 3 figure
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