1,253 research outputs found
Inflationary power spectra with quantum holonomy corrections
In this paper we study slow-roll inflation with holonomy corrections from
loop quantum cosmology. Both tensor and scalar power spectra of primordial
perturbations are computed up to the first order in slow-roll parameters and
, where is a potential of the scalar field and is a
critical energy density (expected to be of the order of the Planck energy
density). Possible normalizations of modes at short scales are discussed. In
case the normalization is performed with use of the Wronskian condition applied
to adiabatic vacuum, the tensor and scalar spectral indices are not quantum
corrected in the leading order. However, by choosing an alternative method of
normalization one can obtain quantum corrections in the leading order.
Furthermore, we show that the holonomy-corrected equation of motion for tensor
modes can be derived from an effective background metric. This allows us to
prove that the Wronskian normalization condition for the tensor modes preserves
the classical form.Comment: 21 page
Asymptotic silence in loop quantum cosmology
The state of asymptotic silence, characterized by causal disconnection of the
space points, emerges from various approaches aiming to describe gravitational
phenomena in the limit of large curvatures. In particular, such behavior was
anticipated by Belinsky, Khalatnikov and Lifshitz (BKL) in their famous
conjecture put forward in the early seventies of the last century. While the
BKL conjecture is based on purely classical considerations, one can expect that
asymptotic silence should have its quantum counterpart at the level of a more
fundamental theory of quantum gravity, which is the relevant description of
gravitational phenomena in the limit of large energy densities. Here, we
summarize some recent results which give support to such a possibility. More
precisely, we discuss occurrence of the asymptotic silence due to
polymerization of space at the Planck scale, in the framework of loop quantum
cosmology. In the discussed model, the state of asymptotic silence is realized
at the energy density , where is the maximal allowed
energy density, being of the order of the Planck energy density. At energy
densities , the universe becomes 4D Euclidean space without
causal structure. Therefore, the asymptotic silence appears to be an
intermediate state of space between the Lorentzian and Euclidean phases.Comment: 4 pages, 3 figures, talk presented at the Multiverse and Fundamental
Cosmology Conference, 10-14 September, 2012, Szczecin, Polan
The Observational Implications of Loop Quantum Cosmology
In this paper we consider realistic model of inflation embedded in the
framework of loop quantum cosmology. Phase of inflation is preceded here by the
phase of a quantum bounce. We show how parameters of inflation depend on the
initial conditions established in the contracting, pre-bounce phase. Our
investigations indicate that phase of the bounce easily sets proper initial
conditions for the inflation. Subsequently we study observational effects that
might arise due to the quantum gravitational modifications. We perform
preliminary observational constraints for the Barbero-Immirzi parameter
, critical density and parameter . In the
next step we study effects on power spectrum of perturbations. We calculate
spectrum of perturbations from the bounce and from the joined bounce+inflation
phase. Based on these studies we indicate possible way to relate quantum
cosmological models with the astronomical observations. Using the Sachs-Wolfe
approximation we calculate spectrum of the super-horizontal CMB anisotropies.
We show that quantum cosmological effects can, in the natural way, explain
suppression of the low CMB multipoles. We show that fine-tuning is not required
here and model is consistent with observations. We also analyse other possible
probes of the quantum cosmologies and discuss perspectives of their
implementation.Comment: 11 pages, 7 figure
Loop-deformed Poincar\'e algebra
In this essay we present evidence suggesting that loop quantum gravity leads
to deformation of the local Poincar\'e algebra within the limit of high
energies. This deformation is a consequence of quantum modification of
effective off-shell hypersurface deformation algebra. Surprisingly, the form of
deformation suggests that the signature of space-time changes from Lorentzian
to Euclidean at large curvatures. We construct particular realization of the
loop-deformed Poincar\'e algebra and find that it can be related to curved
momentum space, which indicates the relationship with recently introduced
notion of relative locality. The presented findings open a new way of testing
loop quantum gravity effects.Comment: Essay written for the Gravity Research Foundation 2013 Awards for
Essays on Gravitation, 7 pages, 1 figur
Spectral dimension with deformed spacetime signature
Studies of the effective regime of loop quantum gravity (LQG) revealed that,
in the limit of Planckian curvature scales, spacetime may undergo a transition
from the Lorentzian to Euclidean signature. This effect is a consequence of
quantum modifications of the hypersurface deformation algebra, which in the
linearized case is equivalent to a deformed version of the Poincar\'e algebra.
In this paper the latter relation is applied to the LQG-inspired hypersurface
deformation algebra that is characterized by the above mentioned signature
change.
While the exact form of the deformed Poincar\'e algebra is not uniquely
determined, the algebra under consideration is representative enough to capture
a number of qualitative features. In particular, the analysis reveals that the
signature change can be associated with two symmetric invariant energy scales,
which separate three physically disconnected momentum subspaces.
Furthermore, the invariant measure on momentum space is derived, which allows
to properly define the average return probability, characterizing a fictitious
diffusion process on spacetime. The diffusion is subsequently studied in the
momentum representation for all possible variants of the model. Finally, the
spectral dimension of spacetime is calculated in each case as a function of the
scale parameter. In the most interesting case the deformation is of the
asymptotically ultralocal type and the spectral dimension undergoes a reduction
to in the UV limit.Comment: 13 pages, 4 figures, v2 some extra results, comments and references
adde
Nonlinear Field Space Cosmology
We consider the FRW cosmological model in which the matter content of
universe (playing a role of inflaton or quintessence) is given by a novel
generalization of the massive scalar field. The latter is a scalar version of
the recently introduced Nonlinear Field Space Theory (NFST), where physical
phase space of a given field is assumed to be compactified at large energies.
For our analysis we choose the simple case of a field with the spherical phase
space and endow it with the generalized Hamiltonian analogous to the XXZ
Heisenberg model, normally describing a system of spins in condensed matter
physics. Subsequently, we study both the homogenous cosmological sector and
linear perturbations of such a test field. In the homogenous sector we find
that nonlinearity of the field phase space is becoming relevant for large
volumes of universe and then it can lead to a recollapse, and possibly also at
very high energies, leading to the phase of a bounce. Quantization of the field
is performed in the limit where nontrivial nature of its phase space can be
neglected, while there is a non-vanishing contribution from the Lorentz
symmetry breaking term of the Hamiltonian. As a result, in the leading order of
the XXZ anisotropy parameter, we find that the inflationary spectral index
remains unmodified with respect to the standard case but the total amplitude of
perturbations is subject to a correction. The Bunch-Davies vacuum state also
becomes appropriately corrected. The proposed new approach is bringing
cosmology and condensed matter physics closer together, which may turn out to
be beneficial for both disciplines.Comment: 15 pages, 1 figure, v2 presentation improved and references adde
Asymmetric cyclic evolution in polymerised cosmology
The dynamical systems methods are used to study evolution of the polymerised
scalar field cosmologies with the cosmological constant. We have found all
evolutional paths admissible for all initial conditions on the two-dimensional
phase space. We have shown that the cyclic solutions are generic. The exact
solution for polymerised cosmology is also obtained. Two basic cases are
investigated, the polymerised scalar field and the polymerised gravitational
and scalar field part. In the former the division on the cyclic and non-cyclic
behaviour is established following the sign of the cosmological constant. The
value of the cosmological constant is upper bounded purely from the dynamical
setting.Comment: 10 pages, 4 figs, JHEP3.cl
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