1,606 research outputs found
Growth index of matter perturbations in the light of Dark Energy Survey
We study how the cosmological constraints from growth data are improved by
including the measurements of bias from Dark Energy Survey (DES). In
particular, we utilize the biasing properties of the DES Luminous Red Galaxies
(LRGs) and the growth data provided by the various galaxy surveys in order to
constrain the growth index () of the linear matter perturbations.
Considering a constant growth index we can put tight constraints, up to accuracy, on . Specifically, using the priors of the Dark Energy
Survey and implementing a joint likelihood procedure between theoretical
expectations and data we find that the best fit value is in between
and . On the other hand utilizing the
Planck priors we obtain and . This
shows a small but non-zero deviation from General Relativity (), nevertheless the confidence level is in the range . Moreover, we find that the estimated mass of the dark-matter halo
in which LRGs survive lies in the interval and , for the different bias
models. Finally, allowing to evolve with redshift [Taylor expansion:
] we find that the
parameter solution space accommodates the GR
prediction at levels.Comment: 8 pages, 3 figures, discussion added, to appear in European Physical
Journal C (EPJC
Non-Linear Sigma Model and asymptotic freedom at the Lifshitz point
We construct the general O(N)-symmetric non-linear sigma model in 2+1
spacetime dimensions at the Lifshitz point with dynamical critical exponent
z=2. For a particular choice of the free parameters, the model is
asymptotically free with the beta function coinciding to the one for the
conventional sigma model in 1+1 dimensions. In this case, the model admits also
a simple description in terms of adjoint currents.Comment: 23 pages, 2 figure
The Ising Model on a Quenched Ensemble of c = -5 Gravity Graphs
We study with Monte Carlo methods an ensemble of c=-5 gravity graphs,
generated by coupling a conformal field theory with central charge c=-5 to
two-dimensional quantum gravity. We measure the fractal properties of the
ensemble, such as the string susceptibility exponent gamma_s and the intrinsic
fractal dimensions d_H. We find gamma_s = -1.5(1) and d_H = 3.36(4), in
reasonable agreement with theoretical predictions. In addition, we study the
critical behavior of an Ising model on a quenched ensemble of the c=-5 graphs
and show that it agrees, within numerical accuracy, with theoretical
predictions for the critical behavior of an Ising model coupled dynamically to
two-dimensional quantum gravity, provided the total central charge of the
matter sector is c=-5. From this we conjecture that the critical behavior of
the Ising model is determined solely by the average fractal properties of the
graphs, the coupling to the geometry not playing an important role.Comment: 23 pages, Latex, 7 figure
Unitary One Matrix Models: String Equations and Flows
We review the Symmetric Unitary One Matrix Models. In particular we discuss
the string equation in the operator formalism, the mKdV flows and the Virasoro
Constraints. We focus on the \t-function formalism for the flows and we
describe its connection to the (big cell of the) Sato Grassmannian \Gr via
the Plucker embedding of \Gr into a fermionic Fock space. Then the space of
solutions to the string equation is an explicitly computable subspace of
\Gr\times\Gr which is invariant under the flows.Comment: 20 pages (Invited talk delivered by M. J. Bowick at the Vth Regional
Conference on Mathematical Physics, Edirne Turkey: December 15-22, 1991.
Abelian gauge fields coupled to simplicial quantum gravity
We study the coupling of Abelian gauge theories to four-dimensional
simplicial quantum gravity. The gauge fields live on dual links. This is the
correct formulation if we want to compare the effect of gauge fields on
geometry with similar effects studied so far for scalar fields. It shows that
gauge fields couple equally weakly to geometry as scalar fields, and it offers
an understanding of the relation between measure factors and Abelian gauge
fields observed so-far.Comment: 20 page
The Area Law in Matrix Models for Large N QCD Strings
We study the question whether matrix models obtained in the zero volume limit
of 4d Yang-Mills theories can describe large N QCD strings. The matrix model we
use is a variant of the Eguchi-Kawai model in terms of Hermitian matrices, but
without any twists or quenching. This model was originally proposed as a toy
model of the IIB matrix model. In contrast to common expectations, we do
observe the area law for Wilson loops in a significant range of scale of the
loop area. Numerical simulations show that this range is stable as N increases
up to 768, which strongly suggests that it persists in the large N limit. Hence
the equivalence to QCD strings may hold for length scales inside a finite
regime.Comment: 12 pages, 4 figure
Singularities of the Partition Function for the Ising Model Coupled to 2d Quantum Gravity
We study the zeros in the complex plane of the partition function for the
Ising model coupled to 2d quantum gravity for complex magnetic field and real
temperature, and for complex temperature and real magnetic field, respectively.
We compute the zeros by using the exact solution coming from a two matrix model
and by Monte Carlo simulations of Ising spins on dynamical triangulations. We
present evidence that the zeros form simple one-dimensional curves in the
complex plane, and that the critical behaviour of the system is governed by the
scaling of the distribution of the singularities near the critical point.
Despite the small size of the systems studied, we can obtain a reasonable
estimate of the (known) critical exponents.Comment: 22 pages, LaTeX2e, 10 figures, added discussion on antiferromagnetic
transition and reference
The Concept of Time in 2D Quantum Gravity
We show that the ``time'' t_s defined via spin clusters in the Ising model
coupled to 2d gravity leads to a fractal dimension d_h(s) = 6 of space-time at
the critical point, as advocated by Ishibashi and Kawai. In the unmagnetized
phase, however, this definition of Hausdorff dimension breaks down. Numerical
measurements are consistent with these results. The same definition leads to
d_h(s)=16 at the critical point when applied to flat space. The fractal
dimension d_h(s) is in disagreement with both analytical prediction and
numerical determination of the fractal dimension d_h(g), which is based on the
use of the geodesic distance t_g as ``proper time''. There seems to be no
simple relation of the kind t_s = t_g^{d_h(g)/d_h(s)}, as expected by
dimensional reasons.Comment: 14 pages, LaTeX, 2 ps-figure
The Flat Phase of Crystalline Membranes
We present the results of a high-statistics Monte Carlo simulation of a
phantom crystalline (fixed-connectivity) membrane with free boundary. We verify
the existence of a flat phase by examining lattices of size up to . The
Hamiltonian of the model is the sum of a simple spring pair potential, with no
hard-core repulsion, and bending energy. The only free parameter is the the
bending rigidity . In-plane elastic constants are not explicitly
introduced. We obtain the remarkable result that this simple model dynamically
generates the elastic constants required to stabilise the flat phase. We
present measurements of the size (Flory) exponent and the roughness
exponent . We also determine the critical exponents and
describing the scale dependence of the bending rigidity () and the induced elastic constants (). At bending rigidity , we find
(Hausdorff dimension ), and . These results are consistent with the scaling relation . The additional scaling relation implies
. A direct measurement of from the power-law decay of
the normal-normal correlation function yields on the
lattice.Comment: Latex, 31 Pages with 14 figures. Improved introduction, appendix A
and discussion of numerical methods. Some references added. Revised version
to appear in J. Phys.
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