Quantum Cosmology for a Quadratic Theory of Gravity

For pure fourth order (${\cal{L}} \propto R^2$) quantum cosmology the Wheeler-DeWitt equation is solved exactly for the closed homogeneous and isotropic model. It is shown that by imposing as boundary condition that $\Psi = 0$ at the origin of the universe the wave functions behave as suggested by Vilenkin.Comment: 13 pages, latex,no figure

Extended Gravity Theories and the Einstein-Hilbert Action

I discuss the relation between arbitrarily high-order theories of gravity and scalar-tensor gravity at the level of the field equations and the action. I show that $(2n+4)$-order gravity is dynamically equivalent to Brans-Dicke gravity with an interaction potential for the Brans-Dicke field and $n$ further scalar fields. This scalar-tensor action is then conformally equivalent to the Einstein-Hilbert action with $n+1$ scalar fields. This clarifies the nature and extent of the conformal equivalence between extended gravity theories and general relativity with many scalar fields.Comment: 12 pages, Plain Latex, SUSSEX-AST-93/7-

A reduced complexity model with graph partitioning for rapid hydraulic assessment of sewer networks

Existing, high-fidelity models for sewer network modelling are accurate but too slow and inflexible for modern applications such as optimisation or scenario analysis. Reduced complexity surrogate modelling has been applied in response to this, however, current approaches are expensive to set up and still require high-fidelity simulations to derive parameters. In this study, we compare and develop graph partitioning algorithms to automatically group sections of sewer networks into semi-distributed compartments. These compartments can then be simulated using sewer network information only in the integrated modelling framework, CityWat-SemiDistributed (CWSD), which has been developed for application to sewer network modelling in this study. We find that combining graph partitioning with CWSD can produce accurate simulations 100-1,000x faster than existing high-fidelity modelling. Because we anticipate that many CWSD users will not have high-fidelity models available, we demonstrate that the approach provides reasonable simulations even under significant parametric uncertainty through a sensitivity analysis. We compare multiple graph partitioning techniques enabling users to specify the spatial aggregation of the partitioned network, also enabling them to preserve key locations for simulation. We test the impact of temporal resolution, finding that accurate simulations can be produced with timesteps up to one hour. Our experiments show a log-log relationship between temporal/spatial resolution and simulation time, enabling users to pre-specify the efficiency and accuracy needed for their applications. We expect that the efficiency and flexibility of our approach may facilitate novel applications of sewer network models ranging from continuous simulations for long-term planning to spatially optimising the placement of network sensors

Accelerated Cosmological Models in Ricci squared Gravity

Alternative gravitational theories described by Lagrangians depending on general functions of the Ricci scalar have been proven to give coherent theoretical models to describe the experimental evidence of the acceleration of universe at present time. In this paper we proceed further in this analysis of cosmological applications of alternative gravitational theories depending on (other) curvature invariants. We introduce Ricci squared Lagrangians in minimal interaction with matter (perfect fluid); we find modified Einstein equations and consequently modified Friedmann equations in the Palatini formalism. It is striking that both Ricci scalar and Ricci squared theories are described in the same mathematical framework and both the generalized Einstein equations and generalized Friedmann equations have the same structure. In the framework of the cosmological principle, without the introduction of exotic forms of dark energy, we thus obtain modified equations providing values of w_{eff}<-1 in accordance with the experimental data. The spacetime bi-metric structure plays a fundamental role in the physical interpretation of results and gives them a clear and very rich geometrical interpretation.Comment: New version: 26 pages, 1 figure (now included), Revtex

Spontaneous decompactification

Positive vacuum energy together with extra dimensions of space imply that our four-dimensional Universe is unstable, generically to decompactification of the extra dimensions. Either quantum tunneling or thermal fluctuations carry one past a barrier into the decompactifying regime. We give an overview of this process, and examine the subsequent expansion into the higher- dimensional geometry. This is governed by certain fixed-point solutions of the evolution equations, which are studied for both positive and negative spatial curvature. In the case where there is a higher-dimensional cosmological constant, we also outline a possible mechanism for compactification to a four-dimensional de Sitter cosmology.Comment: 27 pages, 5 figures, harvmac. v2: refs added, minor notation change

Classical and Quantum Solutions and the Problem of Time in R2R^2 Cosmology

We have studied various classical solutions in $R^2$ cosmology. Especially we have obtained general classical solutions in pure $R^2$\ cosmology. Even in the quantum theory, we can solve the Wheeler-DeWitt equation in pure $R^2$\ cosmology exactly. Comparing these classical and quantum solutions in $R^2$\ cosmology, we have studied the problem of time in general relativity.Comment: 17 pages, latex, no figure, one reference is correcte

R+R2R + R^2 Gravity as R+R + Backreaction

Quadratic theory of gravity is a complicated constraint system. We investigate some consequences of treating quadratic terms perturbatively (higher derivative version of backreaction effects). This approach is shown to overcome some well known problems associated with higher derivative theories, i.e., the physical gravitational degree of freedom remains unchanged from those of Einstein gravity. Using such an interpretation of $R + \beta R^2$ gravity, we investigate a classical and Wheeler DeWitt evolution of $R + \beta R^2$ gravity for a particular sign of $\beta$, corresponding to non- tachyon case. Matter is described by a phenomenological $\rho \propto a(t)^{-n}$. It is concluded that both the Friedmann potential $U(a)$ (${\dot a}^2 + 2U(a) = 0$) and the Wheeler DeWitt potential $W(a)$ ($\left[-{\partial^2\over \partial a^2} + 2W(a)\right]\psi (a) =0$) develop repulsive barriers near $a\approx 0$ for $n>4$ (i.e., $p > {1\over 3}\rho$). The interpretations is clear. Repulsive barrier in $U(a)$ implies that a contracting FRW universe ($k>0, k=0, k<0$) will bounce to an expansion phase without a total gravitational collapse. Repulsive barrier in $W(a)$ means that $a \approx 0$ is a classically forbidden region. Therefore, probability of finding a universe with the big bang singularity ($a=0$ ) is exponentially suppressed.Comment: Accepted for publication in Phy. Rev. D.,18 pages, 6 figures, Latex fil

Quantum Cosmology and Higher-Order Lagrangian Theories

In this paper the quantum cosmological consequences of introducing a term cubic in the Ricci curvature scalar $R$ into the Einstein--Hilbert action are investigated. It is argued that this term represents a more generic perturbation to the action than the quadratic correction usually considered. A qualitative argument suggests that there exists a region of parameter space in which neither the tunneling nor the no-boundary boundary conditions predict an epoch of inflation that can solve the horizon and flatness problems of the big bang model. This is in contrast to the $R^2$--theory.Comment: 13 pages, LaTeX, preprint FERMILAB-Pub-94/XXX-A, March 199

Charged black holes in quadratic gravity

Iterative solutions to fourth-order gravity describing static and electrically charged black holes are constructed. Obtained solutions are parametrized by two integration constants which are related to the electric charge and the exact location of the event horizon. Special emphasis is put on the extremal black holes. It is explicitly demonstrated that in the extremal limit, the exact location of the (degenerate) event horizon is given by \rp = |e|. Similarly to the classical Reissner-Nordstr\"om solution, the near-horizon geometry of the charged black holes in quadratic gravity, when expanded into the whole manifold, is simply that of Bertotti and Robinson. Similar considerations have been carried out for the boundary conditions of second type which employ the electric charge and the mass of the system as seen by a distant observer. The relations between results obtained within the framework of each method are briefly discussed