Loop quantum modified gravity and its cosmological application

A general nonperturvative loop quantization procedure for metric modified gravity is reviewed. As an example, this procedure is applied to scalar-tensor theories of gravity. The quantum kinematical framework of these theories is rigorously constructed. Both the Hamiltonian and master constraint operators are well defined and proposed to represent quantum dynamics of scalar-tensor theories. As an application to models, we set up the basic structure of loop quantum Brans-Dicke cosmology. The effective dynamical equations of loop quantum Brans-Dicke cosmology are also obtained, which lay a foundation for the phenomenological investigation to possible quantum gravity effects in cosmology.     

Vacuum structure in gauge theories. The problem of strong CP violation and cosmology

An interplay between vacuum structure in gauge theories and cosmology is discussed and a possible solution of the strong CP violation problem in gauge theories is suggested.     

Hamiltonian interpretation of anomalies

A family of quantum systems parametrized by the points of a compact space can realize its classical symmetries via a new kind of nontrivial ray representation. We show that this phenomenon in fact occurs for the quantum mechanics of fermions in the presence of background gauge fields, and is responsible for both the nonabelian anomaly and Witten's SU(2) anomaly. This provides a hamiltonian interpretation of anomalies: in the affected theories Gauss' law cannot be implemented. The analysis clearly shows why there are no further obstructions corresponding to higher spheres in configuration space, in agreement with a recent result of Atiyah and Singer.     

A new inflationary universe scenario: A possible solution of the horizon,flatness, homogeneity,isotropy and primordial monopole problems

A new inflationary universe scenario is suggested, which is free of the shortcomings of the previous one and provides a possible solution of the horizon, flatness, homogeneity and isotropy problems in cosmology, and also a solution of the primordial monopole problem in grand unified theories.     

Scale invariance and spontaneous symmetry breaking

Spontaneous breaking of gauge symmetries is studied in theories with nonlinearly realized scale invariance. The classically sliding vacuum expectation values are fixed through quantum corrections. The anomaly of the dilatation current determines the vacuum energy density as well as the dilaton mass. The coupling of gravity to matter is modified in such a way that the cosmological constant vanishes.     

Exact vacuum solutions of 4-dimensional metric-affine gauge theories of gravitation

We presenttwo exact spherically symmetric vacuum solutions of gauge theories of gravity on a spacetime with non metric-compatible connection. One of them is defined on a Weyl-Cartan spacetime and the other on a general metric-affine space. We consider Lagrangians which include terms quadratic in the irreducible parts of the curvature, the torsion, and the nonmetricity. The metric part of both solutions is of the Reissner-Nordström type and includes a contribution of an effectivedilatation charge. A nontrivial Weyl 1-form is also common to both solutions. It resembles a Coulomb potential originating from thedilatation charge. The torsion is closely related to the nonmetricity.Supported by the Consejo Superior de Investigaciones Científicas, Serrano 123, E-28006 Madrid, Spain     

Fast invisible neutrino decays

Any value for the lifetime of neutrinos decaying into invisible modes (another neutrino and a Goldstone boson) is possible in theories in which the lepton number is a spontaneously broken global symmetry with different charges for every family. There are two types of models. Only in one of them neutrinos could, in a natural way, be relevant for cosmology.     

CP-violating CFT and trace anomaly

It is logically possible that the trace anomaly in four dimensions includes the Hirzebruch–Pontryagin density in CP-violating theories. Although the term vanishes at free conformal fixed points, we realize such a possibility in the holographic renormalization group and show that it is indeed possible. The Hirzebruch–Pontryagin term in the trace anomaly may serve as a barometer to understand how much CP is violated in conformal field theories.     

Superfluid analogies of cosmological phenomena

In a modern viewpoint relativistic quantum field theory is an emergent phenomenon arising in the low-energy corner of the physical fermionic vacuum – the medium, whose nature remains unknown. The same phenomenon occurs in condensed matter systems: In the extreme limit of low-energy condensed matter systems of special universality class acquire all the symmetries, which we know today in high-energy physics: Lorentz invariance, gauge invariance, general covariance, etc. The chiral fermions as well as gauge bosons and gravity field arise as fermionic and bosonic collective modes of the system. Inhomogeneous states of the condensed matter ground state – vacuum – induce nontrivial effective metrics of the space, where the free quasiparticles move along geodesics. This conceptual similarity between condensed matter and the quantum vacuum allows us to simulate many phenomena in high-energy physics and cosmology, including the axial anomaly, baryoproduction and magnetogenesis, event horizon and Hawking radiation, cosmological constant and rotating vacuum, etc., probing these phenomena in ultra-low-temperature superfluid helium, atomic Bose condensates and superconductors. Some of the experiments have been already conducted.     

Two-Dilaton Theories in Two Dimensions from Dimensional Reduction

Dimensional reduction of generalized gravity theories or string theories generically yields dilaton fields in the lower-dimensional effective theory. Thus at the level of D=4 theories and cosmology, many models contain more than just one scalar field (e.g., inflaton, Higgs, quintessence). Our present work is restricted to two-dimensional gravity theories with only two dilatons which nevertheless allow a large class of physical applications. The notions of factorizability, simplicity and conformal simplicity, Einstein form, and Jordan form are the basis of an adequate classification. We show that practically all physically motivated models belong either to the class of factorizable simple theories (e.g., dimensionally reduced gravity, bosonic string) or to factorizable conformally simple theories (e.g., spherically reduced scalar-tensor theories). For these theories a first order formulation is constructed straightforwardly. As a consequence an absolute conservation law can be established.     

Anomalous inequivalence of phenomenological theories

When the transformation between bases in a phenomenological theory is anomalous, the theories are not equivalent, but can be made so by the addition of an appropriate anomaly functional. This functional can be given a simple form which allows the derivation of a sufficient condition for the impossibility of anomaly cancellation.     

Time-dependent supergravity solutions in null dilaton background

A class of time dependent pp-waves with NS–NS flux in type IIA string theory is considered. The background preserves 1/4 supersymmetry and may provide a toy model of Big Bang cosmology with nontrivial flux. At the Big Bang singularity in early past, the string theory is strongly coupled and matrix string model can be used to describe the dynamics. We also construct some time dependent supergravity solutions for D-branes and analyze their supersymmetry properties.     

On the Gribov Problem for Generalized Connections

 The bundle structure of the space of Ashtekar's generalized connections is investigated in the compact case. It is proven that every stratum is a locally trivial fibre bundle. The only stratum being a principal fibre bundle is the generic stratum. Its structure group equals the space of all generalized gauge transforms modulo the constant center-valued gauge transforms. For abelian gauge theories the generic stratum is globally trivial and equals the total space . However, for a certain class of non-abelian gauge theories – e.g., all SU(N) theories – the generic stratum is nontrivial. This means, there are no global gauge fixings – the so-called Gribov problem. Nevertheless, for many physical measures there is a covering of the generic stratum by trivializations each having total measure 1. Finally, possible physical consequences and the relation between fundamental modular domains and Gribov horizons are discussed. Received: 4 March 2002 / Accepted: 20 August 2002 Published online: 30 January 2003 Communicated by H. Nicolai     

Global gravitational anomalies

A general formula for global gauge and gravitational anomalies is derived. It is used to show that the anomaly free supergravity and superstring theories in ten dimensions are all free of global anomalies that might have ruined their consistency. However, it is shown that global anomalies lead to some restrictions on allowed compactifications of these theories. For example, in the case of O(32) superstring theory, it is shown that a global anomaly related to ₇(O(32)) leads to a Dirac-like quantization condition for the field strength of the antisymmetric tensor field.Related to global anomalies is the question of the number of fermion zero modes in an instanton field. It is argued that the relevant gravitational instantons are exotic spheres. It is shown that the number of fermion zero modes in an instanton field is always even in ten dimensional supergravity.Supported in part by NSF Grant No. PHY80-19754     

Variable <Emphasis Type="Italic">G</Emphasis> and <Emphasis Type="Italic">Λ</Emphasis>: scalar-tensor versus RG-improved cosmology

We study the consequences due to time varying G and in scalar-tensor theories of gravity for cosmology, inspired by the modifications introduced by the Renormalization Group (RG) equations in the Quantum Einstein Gravity. We assume a power-law scale factor in presence contemporarily of both the scalar field and the matter components of the cosmic fluid, and analyze a special case and its generalization, also showing the possibility of a phantom cosmology. In both such situations we find a negative kinetic term for the scalar field Q and, possibly, an equation-of-state parameter w _Q < –1. A violation of dominant energy condition (DEC) for Q is also possible in both of them; but, while in the first special case the Q-energy density then remains positive, in the second one we find it negative.This revised version was published online in April 2005. The publishing date was inserted.     

Modifying the bosonic string vacuum

A nontrivial string vacuum can induce effects in open bosonic string theories which can be interpreted in terms of nonlocality of the mapping of the string world sheet into spacetime. This is achieved by modifying the sum over Riemann surfaces to include boundaries on which the bosonic fields satisfy a Dirichlet condition, as well as holes with the usual Neumann condition and crosscaps. Such effects profoundly alter the large-angle behaviour of string amplitudes. With suitable normalization, they also lead to a cancellation of the one-loop divergence associated with the vacuum emission of a soft dilaton.     

Gravitational coupling,dynamical changes of units and the cosmological constant problem

A spacetime interval connecting two neighbouring points can be measured in different unit systems.For instance,it can be measured in atomic unit defined in terms of fundamental constants existing in quantum theories.It is also possible to use a gravitational unit which is defined by the use of properties of macroscopic objects.These two unit systems are usually regarded as indistinguishable up to a constant conversion factor.Here we consider the possibility that these two units are related by an epoch-dependent conversion factor.This is a dynamical changes of units.Regarding a conformal transformation as a local unit transformation,we use a gravitational model in which the gravitational and the matter sectors are given in different conformal frames(or unit systems).It is relevant to the cosmological constant problem,namely the huge discrepancy between the estimated and the observational values of the cosmological constant in particle physics and cosmology,respectively.We argue that the problem arises when one ignores evolution of the conversion factor relating the two units during expansion of the Universe.Connection of the model with violation of equivalence principle and possible variation of fundamental constants are also discussed.     

Lattice gauge-higgs theories with local x global symmetry groups including exact solutions

We discuss a class of lattice gauge-Higgs models with local x global symmetry groups. These may also be viewed as a new class of disordered spin models. We give general properties of these theories and present exact solutions for certain (infinite) classes of discrete 2D models. Given the strong gauge coupling limit involved, the latter constitute the first nontrivial exactly solved gauge-Higgs theories. Our results provide the first existence proof of theories which satisfy a necessary condition of realistic gauge-Higgs models, namely that the mass gaps for the Higgs and gauge sectors must both vanish and their ratio must approach a finite constant, in the continuum limit.     

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.     

Relativistic Jets from Active Galactic Nuclei,edited by M. Boetttcher,D.E. Harris,and H. Krawczynski

Current theories of particle physics lead to the unavoidable conclusion that there must have been several phase transitions in the early Universe. Further, in the context of these theories, it is possible that cosmological phase transitions would have produced topological defects that may be roaming our heavens today. A finding of these fossils from the early Universe would provide a direct confirmation of the thermal history of the cosmos, insight into astrophysical phenomena, and vital information about particle physics. The elimination of unobserved topological defects provides important constraints on particle physics and may also suggest novel cosmology. I describe some of the research on cosmic topological defects and recent efforts to address cosmological issues in condensed matter systems.