LOOP QUANTUM COSMOLOGY

ARTIGAS GUIMAREY, Danilo

A minisuperspace model of compact phase space gravity

The phase space of general relativity is flat and unbounded. This allows for infinite values of field variables, associated with singularities of Einstein’s theory of gravity. For this reason, a generalized theory of gravity with compact phase space, which may cure the singularities, could be particularly relevant. In the talk, I will present a minisuperspace gravitational model with spherical phase space. In the affine limit, the de Sitter cosmological with flat phase space is recovered. In the cylindrical phase space limit, the model is equivalent to the case of loop quantum cosmology. As a consequence of the compactness of the phase space the universe is prevented from expanding infinitely. Furthermore, the quantum solution is investigated and exemplary transition amplitude is evaluated.

DAPOR, Andrea

Generalized Coherent States in Loop Quantum Gravity: properites and examples

In this talk I will introduce a family of coherent states that extends the LQG complexifier coherent states. I will argue that such states can be thought of as the quantum equivalent of discrete 3-geometries. Some examples of such geometries will be discussed, with particular interest to isotropic and anisotropic cosmology, as well as the interior of a spherical black hole. Finally, I will discuss the ``effective dynamics conjecture'': the possibility that the dynamics generated by the effective Hamiltonian (i.e., the phase space function obtained as the expectation value of the Hamiltonian operator) be an approximation of the actual quantum dynamics. Application to cosmology and black holes will be discussed.

KOBLER, Michael

Dynamical Properties of the Mukhanov-Sasaki Hamiltonian in the context of adiabatic vacua and the Lewis-Riesenfeld invariant

In the context of linearized cosmological perturbation theory, the Mukhanov-Sasaki equation plays a pivotal role. Each mode of this equation resembles a time-dependent harmonic oscillator. We consider the single-mode Mukhanov-Sasaki Hamiltonian as a toy model in mechanics and use the known Lewis-Riesenfeld invariant and the extended phase space formalism introduced in previous works in order to analyze this system. These techniques allow to classically construct an extended canonical transformation that maps an explicitly time-dependent Hamiltonian into a time-independent one, as well as to implement the corresponding unitary map in the quantum theory. Our further analysis leads us to a closed form of the time-evolution operator for the single-mode Mukhanov-Sasaki Hamiltonian, that is to the associated Dyson series. Finally, we discuss an extension of these techniques to the bosonic Fock space, together with some applications for a quasi-de Sitter background.

LI, Baofei

Towards the Understanding of Quantum Cosmology from Loop Quantum Gravity

Loop quantum cosmology (LQC) provides an elegant resolution of the big bang singularity by a quantum bounce in the deep Planck era. Now an important issue that has remained open is its connection with loop quantum gravity (LQG). To understand it, various approaches have been proposed in the framework of LQG, such as the group field theory and quantum reduced loop gravity.

In this talk, we shall first give a brief review on various different approaches proposed so far, and then present our recent results of a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, lately derived in LQG using Thiemann's regularization and earlier obtained in  LQC, but by keeping the Lorentzian term explicit in the Hamiltonian constraint. Although the resulted quantum difference equation is of the fourth-order, in contrast to the second-order difference equation in LQC, a non-singular bounce occurs generically. The corresponding dynamics can be described by either the Hamilton's or the Friedmann-Raychaudhuri equations, but the map between the two descriptions is not one-to-one. A careful analysis resolves the tension on symmetric versus asymmetric bounce in this model, showing that the bounce must be asymmetric and symmetric bounce is physically inconsistent, in contrast to the standard LQC. In addition, the current observations only allow a scenario where the pre-bounce branch is asymptotically de Sitter and the post-bounce branch yields the classical general relativity.

LIEGENER, Klaus

New Loop Quantum Cosmology Modifications from Symplectic Structures

Loop Quantum Cosmology (LQC) is a loop inspired quantization of cosmological spacetimes. In recent years, attempts are being made to incorporate more features of the full theory into this framework. Most recent improvements are based on the fact that the effective Hamiltonian of LQC can also be obtained as the expectation value of suitable coherent states in the full theory.

In this talk we notice challenges which arise on using conventional flux variables with respect to gauge transformations in approaches so far. We show that these problems can be successfully circumvented using  gauge covariant fluxes proposed by Thiemann.  Computing the expectation value of quantum operators on the new corresponding semi-classical states, leads to so-far unseen modifications.

A subsequent talk will demonstrate that this important and novel modification results in non-trivial changes in Planck-scale physics.

MUENCH, Johannes

Holographic Signatures of Resolved Cosmological Singularities

A common strategy to investigate the fate of gravitational singularities in asymptotically AdS spacetimes is to translate the question from the gravitational side to a dual field theory using the gauge/gravity correspondence and to do a field theory computation. Given recent progress in singularity resolution via non-perturbative quantum gravity, it is natural to now turn the question around and to ask about field theory signatures of resolved singularities. In the framework of classical Kasner-AdS spacetime it has been shown that the two-point correlator of a scalar-massive operator exhibits a finite-distance pole. This pole can be interpreted as a holographic signature of the cosmological bulk singularity. In this talk we discuss how resolving the singularity using techniques inspired by loop quantum cosmology results in a resolution of the finite-distance pole in the two-point correlator that we interpret as a holographic signature of the resolved singularity.

MA, Yongge

Conformally invariant loop quantum Brans-Dicke cosmology

The loop quantization of the conformally invariant Brans-Dicke Bianchi I cosmology is carried out. In this model the conformal gauge symmetry can be consistently implemented by the standard polymer-like quantization along with the other constraints, leading to a well-defined physical Hilbert space. The approach of quantum reference frames is applied to extract the  Schrodinger evolutions for the model. It turns our that, in certain reference frames the familiar GR Bianchi I loop quantum cosmological models could be reproduced from the Brans-Dicke model, and hence the important results of familiar LQC such as singularity resolutions are reproduced. Further, these apparently distinct Bianchi I loop quantum cosmological models with distinct gravitational "constants" are unified by the conformal symmetry.

MARTIN-BENITO, Mercedes

On the relation at the physical level between sLQC and the original v-representation of LQC: Domain of the volume in sLQC

The flat Friedmann-Lemaitre-Robertson-Walker model minimally coupled to a massless scalar field admits an appropriate solvable representation in the context of Loop Quantum Cosmology, named sLQC. The form of the domain of the volume, the main observable to track the quantum evolution, is not straightforward in this solvable representation. In this talk I will explain how to derive the explicit form of physical states belonging to the domain of the volume in sLQC. Specifically, given a physical state in the v-representation where the volume acts diagonally, I will write its form in the representation employed in sLQC, making explicit the connection between both representations at the physical level. To this end, we resort to the Wheeler-De Witt (WDW) approach, which shares the physical Hilbert space with sLQC when cast in an analog solvable representation, while being analytically solvable as well in the v-representation. Then the domain of the volume for the WDW approach provides that for sLQC.

MENA MARUGAN, Guillermo

The MMO prescription for the Dapor-Liegener model

(Authors: Alejandro Garcia-Quismondo, Guillermo A. Mena Marugan.)

Recently, an alternative Hamiltonian constraint for Loop Quantum Cosmology has been put forward by Dapor and Liegener. Here, we quantize this Hamiltonian following a prescription proposed by Martín-Benito, Mena Marugán, and Olmedo. We compute the action of this Hamiltonian operator in the volume eigenbasis and show that it takes the form of a fourth-order difference equation. We investigate the superselection sectors, proving that they are semilattices supported only on either the positive or the negative semiaxis, depending on the triad orientation. The decoupling between semiaxes allows us to write a closed expression for the generalized eigenfunctions of the geometric part of the constraint. This expression is totally determined by the values at the two points of smallest eigenvolume. This result indicates that the degeneracy of the new geometric Hamiltonian operator is equal to two, doubling the possible number of solutions with respect to the conventional quantization considered until now.

POLACZEK, Axel

Generalized effective cosmology from group field theory

We extend various recent results regarding the derivation of effective cosmological dynamics from suitable states in group field theory (GFT). In particular we focus on deriving effective equations for expectation values of cosmological observables that do not require a mean-field approximation. We show how GFT coherent states can have very small relative uncertainties at late times. We also compare the effect of adding interactions in the classical and quantum effective GFT description. We also include the effect of interactions in the GFT Hamiltonian into the resulting cosmology. The quantum states considered generally excite a single field mode (i.e. a single spin as viewed from loop quantum gravity). Our results clarify precise conditions under which effective cosmological equations derived from GFT provide reliable approximations to the full quantum dynamics.

SCHANDER, Susanne

On the Treatment of Backreactions in Quantum Cosmology

In (loop) quantum cosmology there are several proposals for how to take into account the quantum back reaction between the homogeneous background degrees of freedom and the inhomogeneous perturbation degrees of freedom respectively. In this talk we review these proposals and suggest an alternative approach which rests on the Born-Oppenheimer approximation idea.

SINGH, Parampreet

Physical implications of gauge covariant fluxes in loop quantum cosmology

We incorporate gauge covariant fluxes in loop quantum cosmological models and understand various implications for different regularizations of the Hamiltonian constraint. These include treating Euclidean and Lorentzian terms independently as well as together as in standard loop quantum cosmology. We find that gauge covariant fluxes result in a far richer and complex structure of modified dynamics in the Planck regime which has so far not been seen in loop quantum cosmology or its modified versions. A key prediction of using gauge covariant fluxes is the generic asymmetric nature of bounce even for simplest models irresepective of the choice of regularization. Various novel results in the Planck scale physics and the infra-red behavior will be discussed.

SINGH, Parampreet - second abstract

Numerical simulations in loop quantum cosmology for a cyclic potential

Abstract: One of the open questions in loop quantum cosmology is how good are the effective equations in presence of potentials. Here we discuss the case of a negative potential which leads to cyclic non-singular cosmology due to quantum geometric effects. We perform  numerical simulations for the sharply peaked states using the quantum Hamiltonian constraint and show that effective dynamics approximates the quantum dynamics to an excellent accuracy including for the regions where bounce is potential dominated. Our results extend the known domain of validity of effective dynamics and demonstrate its reliableness in cases more general than considered so far.

VILENSKY, Ilya

Uniqueness of minimal loop quantum cosmology dynamics

(Authors: J. Engle, I. Vilensky)

We show that the standard improved dynamics Hamiltonian constraint of isotropic loop quantum quantum cosmology is rigidly selected by physical criteria plus one extra assumption: that it have a minimal number of terms, naturally defined. One of the physical criteria used is that of covariance under dilations, the one-parameter family of diffeomorphisms remaining in the homogeneous isotropic context. This family of diffeomorphisms acts on the homogeneous isotropic phase space via transformations which are not canonical but rather conformally canonical. The present work thus also includes a proposal for the implementation of conformally canonical transformations in quantum theory. The fact that the infrared regulator -- the fiducial cell -- must be removed to have physically meaningful results ensures independence of ordering ambiguities. We also show the exact freedom allowed when the one freely chosen assumption, minimality, is relaxed and find that even in this case the energy density is bounded.

WANG, Anzhong

Qualitative dynamics of  quantum cosmology from loop quantum gravity

(Collaborators: Bao-Fei Li, Parampreet Singh)

In this talk, we shall present our recent studies on qualitative dynamics of three different quantizations of the flat FLRW universe in loop quantum gravity (LQG) from an effective description of the quantum spacetime derived by using the geometric quantum mechanics of coherent states.  These include the standard loop quantum cosmology (LQC) and its two recently-revived modifications, referred to as mLQC-I and mLQC-II, respectively.  Various features of LQC, including quantum bounce and pre-inflationary dynamics, are found to be shared with the mLQC-I and mLQC-II models. I shall present universal properties of the evolution of the FLRW universe with, respectively, the chaotic, fractional monodromy, Starobinsky, non-minimal Higgs, and exponential potentials, and show various qualitative similarities in the post-bounce phase for all these models. The pre-bounce qualitative dynamics of LQC and mLQC-II turns out to be very similar, but is strikingly different from that of mLQC-I. For all these potentials, non-perturbative quantum gravitational effects always result generically in a slow-roll inflationary phase. Between it and the quantum bounce a phase of super-inflation always exists.

WILSON-EWING, Edward

A quantum gravity extension to the Mixmaster dynamics

In the loop quantum cosmology effective dynamics for the vacuum Bianchi type I and type IX space-times, a non-singular bounce replaces the classical singularity. The bounce can be approximated as an instantaneous transition between two classical vacuum Bianchi I solutions, with simple transition rules relating the solutions before and after the bounce: the evolution of the mean logarithmic scale factor is reversed, while the shape parameters are unaffected. As a result, the loop quantum cosmology effective dynamics for the vacuum Bianchi IX space-time can be approximated by a sequence of classical vacuum Bianchi I solutions, following the usual Mixmaster transition maps in the classical regime, and undergoing a bounce with this new transition rule in the Planck regime.

WUHRER, Dennis

SU(1,1) coherent states for loop quantum cosmology

We discuss ongoing work in using coherent states based on an SU(1,1) structure in loop quantum cosmology and comment on the coarse graining properties of these states. In particular, they allow to define a certain notion of fiducial cell independence that holds exactly at the quantum level.