Einstein-Yang-Mills Isolated Horizons: Phase Space, Mechanics, Hair and Conjectures

The concept of "Isolated Horizon" has been recently used to provide a full Hamiltonian treatment of black holes. It has been applied successfully to the cases of {\it non-rotating}, {\it non-distorted} black holes in Einstein Vacuum, Einstein-Maxwell and Einstein-Maxwell-Dilaton Theories. In this note, it is investigated the extent to which the framework can be generalized to the case of non-Abelian gauge theories where `hairy black holes' are known to exist. It is found that this extension is indeed possible, despite the fact that in general, there is no `canonical normalization' yielding a preferred Horizon Mass. In particular the zeroth and first laws are established for all normalizations. Colored static spherically symmetric black hole solutions to the Einstein-Yang-Mills equations are considered from this perspective. A canonical formula for the Horizon Mass of such black holes is found. This analysis is used to obtain nontrivial relations between the masses of the colored black holes and the regular solitonic solutions in Einstein-Yang-Mills theory. A general testing bed for the instability of hairy black holes in general non-linear theories is suggested. As an example, the embedded Abelian magnetic solutions are considered. It is shown that, within this framework, the total energy is also positive and thus, the solutions are potentially unstable. Finally, it is discussed which elements would be needed to place the Isolated Horizons framework for Einstein-Yang-Mills theory in the same footing as the previously analyzed cases. Motivated by these considerations and using the fact that the Isolated Horizons framework seems to be the appropriate language to state uniqueness and completeness conjectures for the EYM equations --in terms of the horizon charges--, two such conjectures are put forward.Comment: 24 pages, 3 figures, Revtex fil

Selection rules for the Wheeler-DeWitt equation in quantum cosmology

Selection of physically meaningful solutions of the Wheeler-DeWitt equation for the wavefunction in quantum cosmology, can be attained by a reduction of the theory to the sector of true physical degrees of freedom and their canonical quantization. The resulting physical wavefunction unitarily evolving in the time variable introduced within this reduction can then be raised to the level of the cosmological wavefunction in superspace of 3-metrics. We apply this technique in several simple minisuperspace models and discuss both at classical and quantum level physical reduction in {\em extrinsic} time -- the time variable determined in terms of extrinsic curvature. Only this extrinsic time gauge can be consistently used in vicinity of turning points and bounces where the scale factor reaches extremum. Since the 3-metric scale factor is canonically dual to extrinsic time variable, the transition from the physical wavefunction to the wavefunction in superspace represents a kind of the generalized Fourier transform. This transformation selects square integrable solutions of the Wheeler-DeWitt equation, which guarantee Hermiticity of canonical operators of the Dirac quantization scheme. Semiclassically this means that wavefunctions are represented by oscillating waves in classically allowed domains of superspace and exponentially fall off in classically forbidden (underbarrier) regions. This is explicitly demonstrated in flat FRW model with a scalar field having a constant negative potential and for the case of phantom scalar field with a positive potential. The FRW model of a scalar field with a vanishing potential does not lead to selection rules for solutions of the Wheeler-DeWitt equation, but this does not violate Hermiticity properties, because all these solutions are anyway of plane wave type and describe cosmological dynamics without turning points and bounces.Comment: final version, to appear in Physical Review

Planck scale operators, inflation and fine tuning

Ultraviolet completion of the standard model plus gravity at and beyond the Planck scale is a daunting problem to which no generally accepted solution exists. Principal obstacles include (a) lack of data at the Planck scale (b) nonrenormalizability of gravity and (c) unitarity problem. Here we make a simple observation that, if one treats all Planck scale operators of equal canonical dimension democratically, one can tame some of the undesirable features of these models. With a reasonable amount of fine tuning one can satisfy slow roll conditions required in viable inflationary models. That remains true even when the number of such operators becomes very large.Comment: 9 pages, 0 figure

On the Assumption of Initial Factorization in the Master Equation for Weakly Coupled Systems I: General Framework

We analyze the dynamics of a quantum mechanical system in interaction with a reservoir when the initial state is not factorized. In the weak-coupling (van Hove) limit, the dynamics can be properly described in terms of a master equation, but a consistent application of Nakajima-Zwanzig's projection method requires that the reference (not necessarily equilibrium) state of the reservoir be endowed with the mixing property.Comment: 33 page

Dark energy, α\alpha-attractors, and large-scale structure surveys

Over the last few years, a large family of cosmological attractor models has been discovered, which can successfully match the latest inflation-related observational data. Many of these models can also describe a small cosmological constant $\Lambda$, which provides the most natural description of the present stage of the cosmological acceleration. In this paper, we study $\alpha$-attractor models with dynamical dark energy, including the cosmological constant $\Lambda$ as a free parameter. Predominantly, the models with $\Lambda > 0$ converge to the asymptotic regime with the equation of state $w=-1$. However, there are some models with $w\neq -1$, which are compatible with the current observations. In the simplest models with $\Lambda = 0$, one has the tensor to scalar ratio $r=\frac{12\alpha}{N^2}$ and the asymptotic equation of state $w=-1+\frac{2}{9\alpha}$ (which in general differs from its present value). For example, in the seven disk M-theory related model with $\alpha = 7/3$ one finds $r \sim 10^{-2}$ and the asymptotic equation of state is $w \sim -0.9$. Future observations, including large-scale structure surveys as well as B-mode detectors will test these, as well as more general models presented here. We also discuss gravitational reheating in models of quintessential inflation and argue that its investigation may be interesting from the point of view of inflationary cosmology. Such models require a much greater number of $e$-folds, and therefore predict a spectral index $n_{s}$ that can exceed the value in more conventional models by about $0.006$. This suggests a way to distinguish the conventional inflationary models from the models of quintessential inflation, even if they predict $w = -1$.Comment: 61 pages, 27 figures. v3: Improved version in response to referee's comments; added references, expanded discussion, moved some results to an appendix; conclusions unchange

Inflation as a Probe of Short Distance Physics

We show that a string-inspired Planck scale modification of general relativity can have observable cosmological effects. Specifically, we present a complete analysis of the inflationary perturbation spectrum produced by a phenomenological Lagrangian that has a standard form on large scales but incorporates a string-inspired short distance cutoff, and find a deviation from the standard result. We use the de Sitter calculation as the basis of a qualitative analysis of other inflationary backgrounds, arguing that in these cases the cutoff could have a more pronounced effect, changing the shape of the spectrum. Moreover, the computational approach developed here can be used to provide unambiguous calculations of the perturbation spectrum in other heuristic models that modify trans-Planckian physics and thereby determine their impact on the inflationary perturbation spectrum. Finally, we argue that this model may provide an exception to constraints, recently proposed by Tanaka and Starobinsky, on the ability of Planck-scale physics to modify the cosmological spectrum.Comment: revtex, 8 pages, eps figures included, references adde

The density matrix renormalization group for ab initio quantum chemistry

During the past 15 years, the density matrix renormalization group (DMRG) has become increasingly important for ab initio quantum chemistry. Its underlying wavefunction ansatz, the matrix product state (MPS), is a low-rank decomposition of the full configuration interaction tensor. The virtual dimension of the MPS, the rank of the decomposition, controls the size of the corner of the many-body Hilbert space that can be reached with the ansatz. This parameter can be systematically increased until numerical convergence is reached. The MPS ansatz naturally captures exponentially decaying correlation functions. Therefore DMRG works extremely well for noncritical one-dimensional systems. The active orbital spaces in quantum chemistry are however often far from one-dimensional, and relatively large virtual dimensions are required to use DMRG for ab initio quantum chemistry (QC-DMRG). The QC-DMRG algorithm, its computational cost, and its properties are discussed. Two important aspects to reduce the computational cost are given special attention: the orbital choice and ordering, and the exploitation of the symmetry group of the Hamiltonian. With these considerations, the QC-DMRG algorithm allows to find numerically exact solutions in active spaces of up to 40 electrons in 40 orbitals.Comment: 24 pages; 10 figures; based on arXiv:1405.1225; invited review for European Physical Journal