Higher-derivative Quantum Cosmology

The quantum cosmology of a higher-derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler–DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques for solving the Wheeler–DeWitt equation with appropriate boundary conditions shall be described, and implications for semiclassical theories of inflationary cosmology will be outlined.     

Double Self-Dual and Anti-Self-Dual Structure of N=1 Supergravity

Using the Dirac matrices the double self-dual and anti-self-dual structure of N=1 supergravity is discussed. It is shown that the (anti-)self-dual part of the curvature does not consist of the (anti-)self-dual part of the connection alone, and the (anti-)self-dual part of the Lagrangian quadratic in the curvature consists of the (anti-)self-dual part of the curvature alone only when the Lagrangian does not include torsion terms if the torsion of the spacetime does not vanish. Such a new Lagrangian is constructed. It includes no Einstein-Hilbert term but its self-dual part contains an Ashtekar term.     

D = 5, N = 2 Geometric Higher Curvature Supergravity in the Second-Order Canonical Theory

The supersymmetric extension of the five-dimensional Chern–Simons gravity is studied from the Hamiltonian point of view. This model containing the Gauss–Bonnet term quadratic in the Riemann curvature is the gauge theory of the supergroup SU(2,2/1). In the first order, the theory has a polynomial structure, but the second-order leads to a nonpolynomial structure for both the Hamiltonian and the supersymmetry transformation rules of the fields. The second-order theory has the advantage that the apparent gauge degrees of freedom are unambiguously removed leaving only the physical ones. This important feature is analyzed by constructing the second-order Hamiltonian theory. The gauge invariances of the model and the generator of time evolution are found.     

3维N=1超引力理论和超Higgs效应

本文利用超Poincare张量运算,构造了一个3维N=1超引力理论,给出了一般的拉氏密度,详细讨论了超对称自发破缺机制及超Higgs效应.     

4＋2D维Einstein－Maxwell量子宇宙

利用推广的Ｈａｒｔｌｅ－Ｈａｗｋｉｎｇ假设，研究了４＋２Ｄ维Ｅｉｎｓｔｅｉｎ－Ｍａｘｗｅｌｌ量子宇宙，计算了微超空间波函数的近似解．发现当Ｄ≤２时存在与观测宇宙相符合的暴胀解．     

Quantum Hamilton-Jacobi Cosmology and Classical-Quantum Correlation

How the time evolution which is typical for classical cosmology emerges from quantum cosmology? The answer is not trivial because the Wheeler-DeWitt equation is time independent. A framework associating the quantum Hamilton-Jacobi to the minisuperspace cosmological models has been introduced in Fathi et al. (Eur. Phys. J. C 76, 527 2016). In this paper we show that time dependence and quantum-classical correspondence both arise naturally in the quantum Hamilton-Jacobi formalism of quantum mechanics, applied to quantum cosmology. We study the quantum Hamilton-Jacobi cosmology of spatially flat homogeneous and isotropic early universe whose matter content is a perfect fluid. The classical cosmology emerge around one Planck time where its linear size is around a few millimeter, without needing any classical inflationary phase afterwards to make it grow to its present size.     

Iso-Spectral Potentials and Inflationary Quantum Cosmology

Using the factorization approach of quantum mechanics, we obtain a family of isospectral scalar potentials for power law inflationary cosmology. The construction is based on a scattering Wheeler-DeWitt solution. These iso-potentials have new features, they give a mechanism to end inflation, as well as the possibility to have new inflationary epochs. The procedure can be extended to other cosmological models. PACS numbers: 02.30.Jr; 04.60.Ds; 04.60.Kz; 98.80.Cq.     

Dynamical Vacuum in Quantum Cosmology

By regarding the vacuum as a perfect fluid with equation of state p = -, de Sitter's cosmological model is quantized. Our treatment differs from previous ones in that it endows the vacuum with dynamical degrees of freedom, following modern ideas that the cosmological term is a manifestation of the vacuum energy. Instead of being postulated from the start, the cosmological constant arises from the degrees of freedom of the vacuum regarded as a dynamical entity, and a time variable can be naturally introduced. Taking the scale factor as the sole degree of freedom of the gravitational field, stationary and wave-packet solutions to the Wheeler-DeWitt equation are found, whose properties are studied. It is found that states of the Universe with a definite value of the cosmological constant do not exist. For the wave packets investigated, quantum effects are noticeable only for small values of the scale factor, a classical regime being attained at asymptotically large times.     

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the universe is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes suggests that a “quantum bounce” is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a “quantum bounce” is thus not possible in these models.     

Relativistie Cosmology With Quantum Corrections

Homogeneous isotropic, anisotropic, and inhomogeneous cosmological models are studied using Einstein's general relativity with quntum corrections in field theoretical approximation. In particular we discuss coherent scalar fields and curvature squared terms in the gravitational Lagrangian. The conformal equivalence of the field equations of fourth order to general relativity with a scalar field as source is an example of the geometrization of a matter field. The aemiclassical quantum eorrections of the scalar fields can avoid the initial cosmological singularity and they lead to an inflationary evolution stage as transient attrator. The review provides new points of view on questions like the probability of the inflationary stage and the question of mechanisms for multiple inflation.     

Quantum Cosmology with Hyperbolic Potential

For an FRW model with a minimally coupled scalar field having hyperbolic(exponential) potential we evaluate the wave function both by solving theWheeler-Dewitt (WD) equation and by evaluating the path integral. The WDequation is solved in configuration as well as in momentum space, while thepath integral is evaluated by dividing the lapse integral into a number of pieces.     

Quantum Cosmology in CGBD Theory

We apply the theory developed in quantum cosmology to a model of charged generalized Brans–Dicke gravity. This is a quantum model of gravitation interacting with a charged Brans–Dicke type scalar field which is considered in the Pauli frame. The Wheeler–DeWitt equation describing the evolution of the quantum Universe is solved in the semiclassical approximation by applying the WKB approximation. The wave function of the Universe is also obtained by applying both the Vilenkin-like and the Hartle–Hawking-like boundary conditions. We then make predictions from the wave functions and infer that the Vilenkin's boundary condition is more reasonable in the Brans–Dicke gravity models leading a large vacuum energy density at the beginning of the inflation.     

The Weak Energy Condition and Singularities in Classical Free N = 1 Supergravity

With the use of the modification of the weak energy condition for theories with torsion developed by Hehl, we analyse classical free N = 1 supergravity in the hope that spin-spin contact interactions may avert singularities, as happens in the neutrinic case. We find that this does not happen, since the appearence of singularities is conditioned by the cosmological model of the gravitino field in consideration. We present a very simple singularity free model for a spatially homogeneous Rarita-Schwinger field in a Robertson-Walker spacetime.     

Quantum Cosmology with Scalar-Vector and Scalar-Spinor Interactions

The problem of matter creation in the early Universe is considered in terms of quantum cosmology, introducing interactions of the scalar field with the spinor and vector fields of matter.     

Noncommutative Bianchi Type II Quantum Cosmology

In this paper we present the noncommutative Bianchi Class A cosmological models coupled to barotropic perfect fluid. The commutative and noncommutative quantum solution to the Wheeler–DeWitt equation for any factor ordering, to the anisotropic Bianchi type II cosmological model are found, using a stiff fluid (γ=1). In our toy model, we introduce noncommutative scale factors, is say, we consider that all minisuperspace variables q ⁱ does not commute, so the simplectic structure was modified.     

The Bohm Interpretation of Quantum Cosmology

I make a review on the aplications of the Bohm-de Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohms view can avoid the initial singularity, and isotropize the Universe. In the general case, I enumerate the possible structures of quantum space and time.     

LETTER: A Simple Quantum Cosmology

A simple and surprisingly realistic model of the origin of the universe can be developed using the Friedmann equation from general relativity, elementary quantum mechanics, and the experimental values of , c, G and the proton mass m _p. The model assumes there are N space dimensions (with N > 6), and the potential constraining the radius r of the invisible N – 3 compact dimensions varies as r ⁴. In this model, the universe has zero total energy and is created from nothing. There is no initial singularity. If space-time is eleven dimensional, as required by M theory, the scalar field corresponding to the size of the compact dimensions inflates the universe by about 26 orders of magnitude (60 e-folds). If H ₀ = 65 km sec^–1 Mpc^–1, the energy density of the scalar field after inflation results in = 0.68, in agreement with recent COBE and Type SNe Ia supernova data.