Motivated by recent studies of the one-bubble inflationary universe scenario that predicts a low density, negative curvature universe, we investigate the Euclidean vacuum mode functions of a scalar field in a spatially open chart of de Sitter space which is foliated by hyperbolic time slices. When we consider the possibility of an open inflationary universe, we are faced with the problem of the initial condition for the quantum fluctuations of the inflaton field, because the inflationary era should not last too long to lose every information of the initial condition. In the one-bubble scenario in which an open universe is created in an exponentially expanding false vacuum universe triggered by quantum decay of false vacuum, it seems natural that the initial state is the de Sitter-invariant Euclidean vacuum. Here we present explicit expressions for the Euclidean vacuum mode functions in the open chart for a scalar field with arbitrary mass and curvature coupling.03.65.Sq, 03.70.+k and 98.80.Cq.

We report a measurement of the quadrupole power spectrum in the two degree field (2dF) QSO redshift (2QZ) survey. The analysis uses an algorithm parallel to that for the estimation of the standard monopole power spectrum without first requiring computation of the correlation function or the anisotropic power spectrum. The error on the quadrupole spectrum is rather large but the best fit value of the bias parameter from the quadrupole spectrum is consistent with that from previous investigations of the 2dF data.

Abstract. We propose a novel method to test the gravitational interactions in the outskirts of galaxy clusters. When gravity is modified, this is typically accompanied by the introduction of an additional scalar degree of freedom, which mediates an attractive fifth force. The presence of an extra gravitational coupling, however, is tightly constrained by local measurements. In chameleon modifications of gravity, local tests can be evaded by employing a screening mechanism that suppresses the fifth force in dense environments. While the chameleon field may be screened in the interior of the cluster, its outer region can still be affected by the extra force, introducing a deviation between the hydrostatic and lensing mass of the cluster. Thus, the chameleon modification can be tested by combining the gas and lensing measurements of the cluster. We demonstrate the operability of our method with the Coma cluster, for which both a lensing measurement and gas observations from the X-ray surface brightness, the X-ray temperature, and the Sunyaev-Zel'dovich effect are available. Using the joint observational data set, we perform a Markov chain Monte Carlo analysis of the parameter space describing the different profiles in both the Newtonian and chameleon scenarios. We report competitive constraints on the chameleon field amplitude and its coupling strength to matter. In the case of f (R) gravity, corresponding to a specific choice of the coupling, we find an upper bound on the background field amplitude of |f R0 | < 6 × 10 −5 , which is currently the tightest constraint on cosmological scales.

A generic second-order scalar-tensor theory contains a nonlinear derivative self-interaction of the scalar degree of freedom à la Galileon models, which allows for the Vainshtein screening mechanism. We investigate this effect on subhorizon scales in a cosmological background, based on the most general second-order scalar-tensor theory. Our analysis takes into account all the relevant nonlinear terms and the effect of metric perturbations consistently. We derive an explicit form of Newton's constant, which in general is time-dependent and hence is constrained from observations, as suggested earlier. It is argued that in the most general case the inverse-square law cannot be reproduced on the smallest scales. Some applications of our results are also presented. 1 In the course of the preparation of this manuscript, we became aware of the very recent paper by De Felice, Kase, and Tsujikawa [11], in which the metric under the influence of the Vainshtein mechanism is obtained for a static and spherically symmetric configuration in a subclass of the most general theory.

We first develop a method to calculate a complete set of mode functions which describe the quantum fluctuations generated in one-bubble open inflation models. We consider two classes of models. One is a single scalar field model proposed by Bucher, Goldhaber and Turok and by us as an example of the open inflation scinario, and the other is a two-field model such as the "supernatural" inflation proposed by Linde and Mezhlumian. In both cases we assume the difference in the vacuum energy density between inside and outside the bubble is negligible. There are two kinds of mode functions. One kind has usual continuous spectrum and the other has discrete spectrum with characteristic wavelengths exceeding the spatial curvature scale. The latter can be further devided into two classes in terms of its origin. One is called the de Sitter super-curvature mode, which arises due to the global spacetime structure of de Sitter space, and the other is due to fluctuations of the bubble wall. We calculate the spectrum of quantum fluctuations in these models and evaluate the resulting large angular scale CMB anisotropies. We find there are ranges of model parameters that are consistent with observed CMB anisotropies.