6,848 research outputs found
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Euclidean Theory
We study the large-j asymptotics of the Euclidean EPRL/FK spin foam amplitude
on a 4d simplicial complex with arbitrary number of simplices. We show that for
a critical configuration (j_f, g_{ve}, n_{ef}) in general, there exists a
partition of the simplicial complex into three regions: Non-degenerate region,
Type-A degenerate region and Type-B degenerate region. On both the
non-degenerate and Type-A degenerate regions, the critical configuration
implies a non-degenerate Euclidean geometry, while on the Type-B degenerate
region, the critical configuration implies a vector geometry. Furthermore we
can split the Non-degenerate and Type-A regions into sub-complexes according to
the sign of Euclidean oriented 4-simplex volume. On each sub-complex, the spin
foam amplitude at critical configuration gives a Regge action that contains a
sign factor sgn(V_4(v)) of the oriented 4-simplices volume. Therefore the Regge
action reproduced here can be viewed as a discretized Palatini action with
on-shell connection. The asymptotic formula of the spin foam amplitude is given
by a sum of the amplitudes evaluated at all possible critical configurations,
which are the products of the amplitudes associated to different type of
geometries.Comment: 27 pages, 5 figures, references adde
Asymptotics of Spinfoam Amplitude on Simplicial Manifold: Lorentzian Theory
The present paper studies the large-j asymptotics of the Lorentzian EPRL
spinfoam amplitude on a 4d simplicial complex with an arbitrary number of
simplices. The asymptotics of the spinfoam amplitude is determined by the
critical configurations. Here we show that, given a critical configuration in
general, there exists a partition of the simplicial complex into three type of
regions R_{Nondeg}, R_{Deg-A}, R_{Deg-B}, where the three regions are
simplicial sub-complexes with boundaries. The critical configuration implies
different types of geometries in different types of regions, i.e. (1) the
critical configuration restricted into R_{Nondeg} is degenerate of type-A in our definition of degeneracy, but implies
a nondegenerate discrete Euclidean geometry on R_{Deg-A}, (3) the critical
configuration restricted into R_{Deg-B} is degenerate of type-B, and implies a
vector geometry on R_{Deg-B}. With the critical configuration, we further make
a subdivision of the regions R_{Nondeg} and R_{Deg-A} into sub-complexes (with
boundary) according to their Lorentzian/Euclidean oriented 4-simplex volume
V_4(v), such that sgn(V_4(v)) is a constant sign on each sub-complex. Then in
the each sub-complex, the spinfoam amplitude at the critical configuration
gives the Regge action in Lorentzian or Euclidean signature respectively on
R_{Nondeg} or R_{Deg-A}. The Regge action reproduced here contains a sign
factor sgn(V_4(v)) of the oriented 4-simplex volume. Therefore the Regge action
reproduced here can be viewed a discretized Palatini action with on-shell
connection. Finally the asymptotic formula of the spinfoam amplitude is given
by a sum of the amplitudes evaluated at all possible critical configurations,
which are the products of the amplitudes associated to different type of
geometries.Comment: 54 pages, 2 figures, reference adde
Euclidean three-point function in loop and perturbative gravity
We compute the leading order of the three-point function in loop quantum
gravity, using the vertex expansion of the Euclidean version of the new spin
foam dynamics, in the region of gamma<1. We find results consistent with Regge
calculus in the limit gamma->0 and j->infinity. We also compute the tree-level
three-point function of perturbative quantum general relativity in position
space, and discuss the possibility of directly comparing the two results.Comment: 16 page
Semi-classical States in Homogeneous Loop Quantum Cosmology
Semi-classical states in homogeneous loop quantum cosmology (LQC) are
constructed by two different ways. In the first approach, we firstly construct
an exponentiated annihilation operator. Then a kind of semi-classical
(coherent) state is obtained by solving the eigen-equation of that operator.
Moreover, we use these coherent states to analyze the semi-classical limit of
the quantum dynamics. It turns out that the Hamiltonian constraint operator
employed currently in homogeneous LQC has correct classical limit with respect
to the coherent states. In the second approach, the other kind of
semi-classical state is derived from the mathematical construction of coherent
states for compact Lie groups due to Hall.Comment: 13 pages, submitted to CQ
Cosmological evolution of interacting phantom (quintessence) model in Loop Quantum Gravity
The dynamics of interacting dark energy model in loop quantum cosmology (LQC)
is studied in this paper. The dark energy has a constant equation of state
and interacts with dark matter through a form . We
find for quintessence model () the cosmological evolution in LQC is the
same as that in classical Einstein cosmology; whereas for phantom dark energy
(), although there are the same critical points in LQC and classical
Einstein cosmology, loop quantum effect reduces significantly the parameter
spacetime () required by stability. If parameters and satisfy
the conditions that the critical points are existent and stable, the universe
will enter an era dominated by dark energy and dark matter with a constant
energy ratio between them, and accelerate forever; otherwise it will enter an
oscillatory regime. Comparing our results with the observations we find at
confidence level the universe will accelerate forever.Comment: 15 pages, 8 figures, to appear in JCA
Ashtekar's New Variables and Positive Energy
We discuss earlier unsuccessful attempts to formulate a positive
gravitational energy proof in terms of the New Variables of Ashtekar. We also
point out the difficulties of a Witten spinor type proof. We then use the
special orthonormal frame gauge conditions to obtain a locally positive
expression for the New Variables Hamiltonian and thereby a ``localization'' of
gravitational energy as well as a positive energy proof.Comment: 12 pages Plain Te
Inflationary universe in loop quantum cosmology
Loop quantum cosmology provides a nice solution of avoiding the big bang
singularity through a big bounce mechanism in the high energy region. In loop
quantum cosmology an inflationary universe is emergent after the big bounce, no
matter what matter component is filled in the universe. A super-inflation phase
without phantom matter will appear in a certain way in the initial stage after
the bounce; then the universe will undergo a normal inflation stage. We discuss
the condition of inflation in detail in this framework. Also, for slow-roll
inflation, we expect the imprint from the effects of the loop quantum cosmology
should be left in the primordial perturbation power spectrum. However, we show
that this imprint is too weak to be observed.Comment: 21 pages, 4 figures; accepted for publication in JCA
Inverse volume corrections to emergent tachyonic inflation in loop quantum cosmology
The emergent model in the context of loop quantum cosmology with a tachyon
scalar field is studied. We find that there is a center equilibrium point in
the semiclassical region and a saddle point in the classical region. If the
potential of the tachyon field satisfies some conditions, the universe can stay
at the center equilibrium point past-eternally and then oscillate infinitely
around this point with the tachyon climbing up its potential. Once the
potential reaches a critical value, these two equilibrium points coincide with
each other and the oscillation phase is broken by an emergent inflation. In
order to obtain a successful emergent tachyon inflation, a constraint on
of tachyon is required.Comment: 13 pages, 5 figures, a reference adde
Interacting entropy-corrected new agegraphic tachyon, K-essence and dilaton scalar field models of dark energy in non-flat universe
We present the new agegraphic dark energy model by introducing the quantum
corrections to the entropy-area relation in the setup of loop quantum gravity.
Employing this new form of dark energy, we investigate the model of interacting
dark energy and derive its equation of state. We study the correspondence
between the tachyon, K-essence and dilaton scalar field models with the
interacting entropy-corrected new agegraphic dark energy model in the non-flat
FRW universe. Moreover, we reconstruct the corresponding scalar potentials
which describe the dynamics of the scalar field models.Comment: 11 pages, typos fixe
Early Universe Dynamics in Semi-Classical Loop Quantum Cosmology
Within the framework of loop quantum cosmology, there exists a semi-classical
regime where spacetime may be approximated in terms of a continuous manifold,
but where the standard Friedmann equations of classical Einstein gravity
receive non-perturbative quantum corrections. An approximate, analytical
approach to studying cosmic dynamics in this regime is developed for both
spatially flat and positively-curved isotropic universes sourced by a
self-interacting scalar field. In the former case, a direct correspondence
between the classical and semi-classical field equations can be established
together with a scale factor duality that directly relates different expanding
and contracting universes. Some examples of non-singular, bouncing cosmologies
are presented together with a scaling, power-law solution.Comment: 14 pages, In Press, JCA
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