Scalar-tensor cosmology at the general relativity limit: Jordan vs Einstein frame

We consider the correspondence between the Jordan frame and the Einstein frame descriptions of scalar-tensor theory of gravitation. We argue that since the redefinition of the scalar field is not differentiable at the limit of general relativity the correspondence between the two frames is lost at this limit. To clarify the situation we analyse the dynamics of the scalar field in different frames for two distinct scalar-tensor cosmologies with specific coupling functions and demonstrate that the corresponding scalar field phase portraits are not equivalent for regions containing the general relativity limit. Therefore the answer to the question whether general relativity is an attractor for the theory depends on the choice of the frame.Comment: 16 pages, 8 figures, version appeared in PR

Estimating Economies of Scale and Scope with Flexible Technology

Economies of scale and scope are typically modelled and estimated using cost functions that are common to all firms in an industry irrespective of whether they specialize in a single output or produce multiple outputs. We suggest an alternative flexible technology model that does not make this assumption and show how it can be estimated using standard parametric functions including the translog. The assumption of common technology is a special case of our model and is testable econometrically. Our application is for publicly owned US electric utilities. In our sample, we find evidence of economies of scale and vertical economies of scope. But the results do not support a common technology for integrated and specialized firms. In particular, our empirical results suggest that restricting the technology might result in biased estimates of economies ofscale and scope

Scalar-tensor cosmologies: fixed points of the Jordan frame scalar field

We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe the details of the phase space geometry. Using the methods of dynamical systems for the decoupled equation of the Jordan frame scalar field we find the fixed points of flows in two cases: potential domination and matter domination. We present the conditions on the mathematical form of the coupling function and potential which determine the nature of the fixed points (attractor or other). There are two types of fixed points, both are characterized by cosmological evolution mimicking general relativity, but only one of the types is compatible with the Solar System PPN constraints. The phase space structure should also carry over to the Einstein frame as long as the transformation between the frames is regular which however is not the case for the latter (PPN compatible) fixed point.Comment: 21 pages, 4 figures, some comments and references adde

Estimating economies of scale and scope with flexible technology

Economies of scope are typically modelled and estimated using a cost function that is common to all firms in an industry irrespective of their type, e.g. whether they specialize in a single output or produce multiple outputs. Instead, we estimate a flexible technology model that allows for type-specific technologies and show how it can be estimated using linear parametric forms including the translog. A common technology remains a special case of our model and is testable econometrically. Our sample, of publicly owned US electric utilities, does not support a common technology for integrated and specialized firms. Our empirical results therefore suggest that assuming a common technology might bias estimates of economies of scale and scope. Thus, how we model the production technology clearly influences the policy conclusions we draw from its characteristics

Microstructural and geochemical constraints on the evolution of deep arc lithosphere

Mantle xenoliths from the Sierra Nevada, California, USA, sampled a vertical column (60–120 km) of lithosphere that formed during Mesozoic continental arc magmatism. This lithosphere experienced an anticlockwise P-T-t path resulting in rapid cooling that effectively “quenched in” features inherited from earlier high-temperature conditions. Here we combine new mineral chemistry data (water, trace element, and major element concentrations) with mineral crystallographic preferred orientations (CPOs) to investigate the relationship between melt infiltration and deformation. The peridotites record a refertilization trend with increasing depth, starting from shallow, coarse-protogranular, less-melt-infiltrated spinel peridotite with strong, orthorhombic olivine CPO to deep, fine-porphyroclastic, highly melt-infiltrated garnet peridotite with weak, axial-[010] olivine CPO. In contrast to the observed axial-[010] CPOs, subgrain boundary orientations and misorientation axes suggest the dominant activation of the (001)[100] slip system, suggesting deformation under moderately hydrous conditions. After accounting for effects of subsolidus cooling, we see coherent trends between mineral trace element abundance and water content, indicating that melt infiltration led to an increase in water content of the peridotites. However, measured olivine and pyroxene water contents in all peridotites (5–10 and 30–500 wt ppm, respectively) are lower than that required to promote dominant (001)[100] slip system observed in both natural and experimental samples. These results suggest that deformation occurred earlier along the P-T path, probably during or shortly after hydrous melt infiltration. Subsequent rapid cooling at 90 Ma led to water loss from olivine (owing to decreased solubility at low temperature), leaving behind a deep arc lithosphere that remained viscously coupled to the Farallon slab until the opening of the slab window in the late Cenozoic