Modeling Quantum Gravity Effects in Inflation

Cosmological models in 1+1 dimensions are an ideal setting for investigating the quantum structure of inflationary dynamics -- gravity is renormalizable, while there is room for spatial structure not present in the minisuperspace approximation. We use this fortuitous convergence to investigate the mechanism of slow-roll eternal inflation. A variant of 1+1 Liouville gravity coupled to matter is shown to model precisely the scalar sector of cosmological perturbations in 3+1 dimensions. A particular example of quintessence in 1+1d is argued on the one hand to exhibit slow-roll eternal inflation according to standard criteria; on the other hand, a field redefinition relates the model to pure de Sitter gravity coupled to a free scalar matter field with no potential. This and other examples show that the standard logic leading to slow-roll eternal inflation is not invariant under field redefinitions, thus raising concerns regarding its validity. Aspects of the quantization of Liouville gravity as a model of quantum de Sitter space are also discussed.Comment: 43 pages, no figure

The Snowmelt-Runoff Model (SRM) user's manual

A manual to provide a means by which a user may apply the snowmelt runoff model (SRM) unaided is presented. Model structure, conditions of application, and data requirements, including remote sensing, are described. Guidance is given for determining various model variables and parameters. Possible sources of error are discussed and conversion of snowmelt runoff model (SRM) from the simulation mode to the operational forecasting mode is explained. A computer program is presented for running SRM is easily adaptable to most systems used by water resources agencies

Matrix Black Holes

Four and five dimensional extremal black holes with nonzero entropy have simple presentations in M-theory as gravitational waves bound to configurations of intersecting M-branes. We discuss realizations of these objects in matrix models of M-theory, investigate the properties of zero-brane probes, and propose a measure of their internal density. A scenario for black hole dynamics is presented.Comment: 26 pages, harvmac; a few more references and additional comment

Scattered Results in 2D String Theory

The nonperturbative $1\to N$ tachyon scattering amplitude in 2D type 0A string theory is computed. The probability that $N$ particles are produced is a monotonically decreasing function of $N$ whenever $N$ is large enough that statistical methods apply. The results are compared with expectations from black hole thermodynamics.Comment: 22 pages, 5 figures, harvmac. v2: minor comments added, typos correcte

Vacuum Energy Cancellation in a Non-supersymmetric String

We present a nonsupersymmetric orbifold of type II string theory and show that it has vanishing cosmological constant at the one and two loop level. We argue heuristically that the cancellation persists at higher loops.Comment: 31 pages harvmac big, 6 figures. New version includes the 2-loop analysis of hep-th/9810129 and elimination of one of the two heuristic arguments for higher loop cancellatio

Critical and Topological Properties of Cluster Boundaries in the 3d3d Ising Model

We analyze the behavior of the ensemble of surface boundaries of the critical clusters at $T=T_c$ in the $3d$ Ising model. We find that $N_g(A)$, the number of surfaces of given genus $g$ and fixed area $A$, behaves as $A^{-x(g)}$ $e^{-\mu A}$. We show that $\mu$ is a constant independent of $g$ and $x(g)$ is approximately a linear function of $g$. The sum of $N_g(A)$ over genus scales as a power of $A$. We also observe that the volume of the clusters is proportional to its surface area. We argue that this behavior is typical of a branching instability for the surfaces, similar to the ones found for non-critical string theories with $c > 1$. We discuss similar results for the ordinary spin clusters of the $3d$ Ising model at the minority percolation point and for $3d$ bond percolation. Finally we check the universality of these critical properties on the simple cubic lattice and the body centered cubic lattice

M-branes and N=2 Strings

The string field theory of N=(2,1) heterotic strings describes a set of self-dual Yang-Mills fields coupled to self-dual gravity in 2+2 dimensions. We show that the exact classical action for this field theory is a certain complexification of the Green-Schwarz/Dirac-Born-Infeld string action, closely related to the four dimensional Wess-Zumino action describing self-dual gauge fields. This action describes the world-volume of a 2+2d ``M-brane'', which gives rise upon different null reductions to critical strings and membranes. We discuss a number of further properties of N=2 heterotic strings, such as the geometry of null reduction, general features of a covariant formulation, and possible relations to BPS and GKM algebras.Comment: 49 pages, harvmac; 1 figure (uses epsf.tex). References adde

Rolling Tachyons from Liouville theory

In this work we propose an exact solution of the c=1 Liouville model, i.e. of the world-sheet theory that describes the homogeneous decay of a closed string tachyon. Our expressions are obtained through careful extrapolation from the correlators of Liouville theory with c > 25. In the c=1 limit, we find two different theories which differ by the signature of Liouville field. The Euclidean limit coincides with the interacting c=1 theory that was constructed by Runkel and Watts as a limit of unitary minimal models. The couplings for the Lorentzian limit are new. In contrast to the behavior at c > 1, amplitudes in both c=1 models are non-analytic in the momenta and consequently they are not related by Wick rotation.Comment: 22 page

Partition Function for (2+1)-Dimensional Einstein Gravity

Taking (2+1)-dimensional pure Einstein gravity for arbitrary genus $g$ as a model, we investigate the relation between the partition function formally defined on the entire phase space and the one written in terms of the reduced phase space. In particular the case of $g=1$ is analyzed in detail. By a suitable gauge-fixing, the partition function $Z$ basically reduces to the partition function defined for the reduced system, whose dynamical variables are $(\tau^A, p_A)$. [The $\tau^A$'s are the Teichm\"uller parameters, and the $p_A$'s are their conjugate momenta.] As for the case of $g=1$, we find out that $Z$ is also related with another reduced form, whose dynamical variables are $(\tau^A, p_A)$ and $(V, \sigma)$. [Here $\sigma$ is a conjugate momentum to 2-volume $V$.] A nontrivial factor appears in the measure in terms of this type of reduced form. The factor turns out to be a Faddeev-Popov determinant coming from the time-reparameterization invariance inherent in this type of formulation. Thus the relation between two reduced forms becomes transparent even in the context of quantum theory. Furthermore for $g=1$, a factor coming from the zero-modes of a differential operator $P_1$ can appear in the path-integral measure in the reduced representation of $Z$. It depends on the path-integral domain for the shift vector in $Z$: If it is defined to include $\ker P_1$, the nontrivial factor does not appear. On the other hand, if the integral domain is defined to exclude $\ker P_1$, the factor appears in the measure. This factor can depend on the dynamical variables, typically as a function of $V$, and can influence the semiclassical dynamics of the (2+1)-dimensional spacetime. These results shall be significant from the viewpoint of quantum gravity.Comment: 21 pages. To appear in Physical Review D. The discussion on the path-integral domain for the shift vector has been adde