Qualitative dynamics and inflationary attractors in loop cosmology

Qualitative dynamics of three different loop quantizations of spatially flat isotropic and homogeneous models is studied using effective spacetime description of the underlying quantum geometry. These include the standard loop quantum cosmology (LQC), its recently revived modification (referred to as mLQC-I), and another related modification of LQC (mLQC-II) whose dynamics is studied in detail for the first time. Various features of LQC, including quantum bounce and pre-inflationary dynamics, are found to be shared with the mLQC-I and mLQC-II models. We study universal properties of dynamics for chaotic inflation, fractional monodromy inflation, Starobinsky potential, non-minimal Higgs inflation, and an exponential potential. We find various critical points and study their stability, which reveal 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. In the dynamical analysis, some of the fixed points turn out to be degenerate for which center manifold theory is used. For all these potentials, non-perturbative quantum gravitational effects always result in a non-singular inflationary scenario with a phase of super-inflation succeeded by the conventional inflation. We show the existence of inflationary attractors, and obtain scaling solutions in the case of the exponential potential. Since all of the models agree with general relativity at late times, our results are also of use in classical theory where qualitative dynamics of some of the potentials has not been studied earlier.Comment: 29 pages, 18 figures. Minor changes. To appear in Phys. Rev.

Towards Cosmological Dynamics from Loop Quantum Gravity

We present a systematic study of the cosmological dynamics resulting from an effective Hamiltonian, recently derived in loop quantum gravity using Thiemann's regularization and earlier obtained in loop quantum cosmology (LQC) by keeping the Lorentzian term explicit in the Hamiltonian constraint. We show that quantum geometric effects result in higher than quadratic corrections in energy density in comparison to LQC causing a non-singular bounce. Dynamics can be described by 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, similar to a quantization of the Schwarzschild interior in LQC, and the post-bounce branch yields the classical general relativity. For a quadratic potential, we find that a slow-roll inflation generically happens after the bounce, which is quite similar to what happens in LQC.Comment: Version to appear in Phys. Rev. D97, 084029 (2018

Alternative effective mass functions in the modified Mukhanov-Sasaki equation of loop quantum cosmology

Modifications to the Mukhanov-Sasaki equation in loop quantum cosmology (LQC) have been phenomenologically explored using polymerization of the connection and related variables in the classical expressions in order to capture the quantum gravity effects in cosmological perturbations which replace the classical big bang by a big bounce. Examples of this strategy include the dressed metric and the hybrid approaches whose inter-relationship at an effective level was demonstrated by the authors recently. In this manuscript, we propose a new family of the effective mass functions in the modified Mukhanov-Sasaki equation of LQC by investigating the polymerization of a particular form of the classical mass function in terms of variable $z_s$($=a\dot \phi/H$) which relates the Mukhanov-Sasaki variable with the comoving curvature perturbation. Using a generalized ansatz motivated by quantum gravity effects in the background dynamics we find alternative effective mass functions which are distinct from those used in the dressed metric and the hybrid approaches with differences originating from the non-commutativity of the evaluation of the Poisson brackets and the polymerization procedures. The new effective mass functions acquire four correction terms in the effective potential whose exact forms are closely tied up with the ansatz used for polymerizing the inverse Hubble rate. In contrast to earlier works, one of these correction terms can in principle produce sizable effects even when the bounce is kinetic dominated. Our investigation opens a new window to explore the phenomenological implications of a large family of effective mass functions in LQC which can potentially lead to significant departures from the dressed metric and the hybrid approaches in the bounce regime.Comment: 15 page

Does the Loop Quantum μo Scheme Permit Black Hole Formation?

We explore the way different loop quantization prescriptions affect the formation of trapped surfaces in the gravitational collapse of a homogeneous dust cloud, with particular emphasis on the so-called mu o scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the mu over bar scheme. While the jury is still out on the right scheme for black hole spacetimes, we show that as far as black hole formation is concerned, the mu o scheme has another, so far unknown, serious problem. We found that in the mu o scheme, no trapped surfaces would form for a nonsingular collapse of a homogeneous dust cloud in the marginally bound case unless the minimum nonzero area of the loops over which holonomies are computed or the Barbero-Immirzi parameter decreases almost four times from its standard value. It turns out that the trapped surfaces in the mu o scheme for the marginally bound case are also forbidden for an arbitrary matter content as long as the collapsing interior is isometric to a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. We found that in contrast to the situation in the mu o scheme, black holes can form in the mu over bar scheme, as well as other lattice refinements with a mass gap determined by quantum geometry

Loop quantum cosmology and its gauge-covariant avatar: a weak curvature relationship

We explore the relationship between the effective dynamics in standard loop quantum cosmology (LQC) based on holonomies and triads obtained from gauge-fixing fluxes, and a modification of LQC based on holonomies and gauge-covariant fluxes (referred to as gLQC). Both the models yield singularity resolution via a bounce because of non-perturbative quantum geometric effects resulting in a maximum for energy density. In LQC, the bounce is extremely well captured by a $\rho^2$ term in energy density with a negative sign which emerges as a non-perturbative modification to the classical Friedmann and Raychaudhuri equations. But, details of such modifications in gLQC have remained hidden due to an arduous nature of gauge-covariant flux modifications which do not allow writing above equations in a closed form. To extract these modifications we explore the large volume, weak curvature limit for matter with a fixed equation of state and obtain higher order corrections to the classical theory. We find that in the weak curvature limit of gLQC, in the post-bounce branch, the first order correction beyond classical theory fully recovers the form of modified Friedmann and Raychaudhuri equations of LQC. In contrast, due to an asymmetric bounce in gLQC, the weak curvature limit of the pre-bounce branch exhibits a novel structure with a $\rho^{3/2}$ term as a first order correction beyond classical theory while the $\rho^2$ term appears as a second order correction. Our work shows that gLQC has a far richer structure which includes the form of dynamical equations with non-perturbative modifications in LQC in its weak curvature limit. This indicates that more general loop quantizations of cosmological sectors can reveal LQC at some truncation, and possibly there exist a tower of potentially interesting higher order modifications from quantum geometry which are hidden in the setting of LQC.Comment: 14 page

Study on the mechanism of open-flavor strong decays

The open-flavor strong decays are studied based on the interaction of potential quark model. The decay process is related to the s-channel contribution of the same scalar confinment and one-gluon-exchange(OGE) interaction in the quark model. After we adopt the prescription of massive gluons in time-like region from the lattice calculation, the approximation of four-fermion interaction is applied. The numerical calculation is performed to the meson decays in $u$, $d$, $s$ light flavor sector. The analysis of the $D/S$ ratios of $b_1\rightarrow \omega \pi$ and $a_1\rightarrow \rho \pi$ show that the scalar interaction should be dominant in the open-flavor decays