Power spectrum and correlation function errors: Poisson vs. Gaussian shot noise

Poisson distributed shot noise is normally considered in the Gaussian limit in cosmology. However, if the shot noise is large enough and the correlation function/power spectrum conspires, the Gaussian approximation mis-estimates the errors and their covariance significantly. The power spectrum, even for initially Gaussian densities,acquires cross correlations which can be large, while the change in the correlation function error matrix is diagonal except at zero separation. Two and three dimensional power law correlation function and power spectrum examples are given. These corrections appear to have a large effect when applied to galaxy clusters, e.g. for SZ selected galaxy clusters in 2 dimensions. This can increase the error estimates for cosmological parameter estimation and consequently affect survey strategies, as the corrections are minimized for surveys which are deep and narrow rather than wide and shallow. In addition, a rewriting of the error matrix for the power spectrum/correlation function is given which eliminates most of the Bessel function dependence (in two dimensions) and all of it (in three dimensions), which makes the calculation of the error matrix more tractable. This applies even when the shot noise is in the (usual) Gaussian limit.Comment: 22 pages, 4 figures, 3 equations corrected/figures updated, results unchange

Conditions for Successful Extended Inflation

We investigate, in a model-independent way, the conditions required to obtain a satisfactory model of extended inflation in which inflation is brought to an end by a first-order phase transition. The constraints are that the correct present strength of the gravitational coupling is obtained, that the present theory of gravity is satisfactorily close to general relativity, that the perturbation spectra from inflation are compatible with large scale structure observations and that the bubble spectrum produced at the phase transition doesn't conflict with the observed level of microwave background anisotropies. We demonstrate that these constraints can be summarized in terms of the behaviour in the conformally related Einstein frame, and can be compactly illustrated graphically. We confirm the failure of existing models including the original extended inflation model, and construct models, albeit rather contrived ones, which satisfy all existing constraints.Comment: 8 pages RevTeX file with one figure incorporated (uses RevTeX and epsf). Also available by e-mailing ARL, or by WWW at http://star-www.maps.susx.ac.uk/papers/infcos_papers.html; Revised to include extra references, results unchanged, to appear Phys Rev

General Relativity as an Attractor in Scalar-Tensor Stochastic Inflation

Quantum fluctuations of scalar fields during inflation could determine the very large-scale structure of the universe. In the case of general scalar-tensor gravity theories these fluctuations lead to the diffusion of fundamental constants like the Planck mass and the effective Brans--Dicke parameter, $\omega$. In the particular case of Brans--Dicke gravity, where $\omega$ is constant, this leads to runaway solutions with infinitely large values of the Planck mass. However, in a theory with variable $\omega$ we find stationary probability distributions with a finite value of the Planck mass peaked at exponentially large values of $\omega$ after inflation. We conclude that general relativity is an attractor during the quantum diffusion of the fields.Comment: LaTeX (with RevTex) 11 pages, 2 uuencoded figures appended, also available on WWW via http://star.maps.susx.ac.uk/index.htm

Late-time cosmology in (phantom) scalar-tensor theory: dark energy and the cosmic speed-up

We consider late-time cosmology in a (phantom) scalar-tensor theory with an exponential potential, as a dark energy model with equation of state parameter close to -1 (a bit above or below this value). Scalar (and also other kinds of) matter can be easily taken into account. An exact spatially-flat FRW cosmology is constructed for such theory, which admits (eternal or transient) acceleration phases for the current universe, in correspondence with observational results. Some remarks on the possible origin of the phantom, starting from a more fundamental theory, are also made. It is shown that quantum gravity effects may prevent (or, at least, delay or soften) the cosmic doomsday catastrophe associated with the phantom, i.e. the otherwise unavoidable finite-time future singularity (Big Rip). A novel dark energy model (higher-derivative scalar-tensor theory) is introduced and it is shown to admit an effective phantom/quintessence description with a transient acceleration phase. In this case, gravity favors that an initially insignificant portion of dark energy becomes dominant over the standard matter/radiation components in the evolution process.Comment: LaTeX file, 48 pages, discussion of Big Rip is enlarged, a reference is adde

Dynamics of liquid He-4 in confined geometries from Time-Dependent Density Functional calculations

We present numerical results obtained from Time-Dependent Density Functional calculations of the dynamics of liquid He-4 in different environments characterized by geometrical confinement. The time-dependent density profile and velocity field of He-4 are obtained by means of direct numerical integration of the non-linear Schrodinger equation associated with a phenomenological energy functional which describes accurately both the static and dynamic properties of bulk liquid He-4. Our implementation allows for a general solution in 3-D (i.e. no symmetries are assumed in order to simplify the calculations). We apply our method to study the real-time dynamics of pure and alkali-doped clusters, of a monolayer film on a weakly attractive surface and a nano-droplet spreading on a solid surface.Comment: q 1 tex file + 9 Ps figure

On Physical Equivalence between Nonlinear Gravity Theories

We argue that in a nonlinear gravity theory, which according to well-known results is dynamically equivalent to a self-gravitating scalar field in General Relativity, the true physical variables are exactly those which describe the equivalent general-relativistic model (these variables are known as Einstein frame). Whenever such variables cannot be defined, there are strong indications that the original theory is unphysical. We explicitly show how to map, in the presence of matter, the Jordan frame to the Einstein one and backwards. We study energetics for asymptotically flat solutions. This is based on the second-order dynamics obtained, without changing the metric, by the use of a Helmholtz Lagrangian. We prove for a large class of these Lagrangians that the ADM energy is positive for solutions close to flat space. The proof of this Positive Energy Theorem relies on the existence of the Einstein frame, since in the (Helmholtz--)Jordan frame the Dominant Energy Condition does not hold and the field variables are unrelated to the total energy of the system.Comment: 37 pp., TO-JLL-P 3/93 Dec 199

STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY

In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the probability of finding a certain value of the inflaton and dilaton fields in a physical volume of the Universe. For a typical chaotic inflation potential, the solutions for the probability distribution never become stationary but grow forever towards larger values of the fields. We show here that a non-minimal conformal coupling of the inflaton to the curvature scalar, as well as radiative corrections to the effective potential, may provide a dynamical cutoff and generate stationary solutions. We also analyze the possibility of large nonperturbative jumps of the fluctuating inflaton scalar field, which was recently revealed in the context of the Einstein theory. We find that in the Brans--Dicke theory the amplitude of such jumps is strongly suppressed.Comment: 19 pages, LaTe

String Universality

If there is a single underlying "theory of everything" which in some limits of its "moduli space" reduces to the five weakly coupled string theories in 10D, and 11D SUGRA, then it is possible that all six of them have some common domain of validity and that they are in the same universality class, in the sense that the 4D low energy physics of the different theories is the same. We call this notion String Universality. This suggests that the true vacuum of string theory is in a region of moduli space equally far (in some sense) from all perturbative theories, most likely around the self-dual point with respect to duality symmetries connecting them. We estimate stringy non-perturbative effects from wrapped brane instantons in each perturbative theory, show how they are related by dualities, and argue that they are likely to lead to moduli stabilization only around the self-dual point. We argue that moduli stabilization should occur near the string scale, and SUSY breaking should occur at a much lower intermediate scale, and that it originates from different sources. We discuss the problems of moduli stabilization and SUSY breaking in currently popular scenarios, explain why these problems are generic, and discuss how our scenario can evade them. We show that String Universality is not inconsistent with phenomenology but that it is in conflict with some popular versions of brane world scenarios.Comment: 48 pages, 1 figure; one reference adde

Suppression of Coulomb-nuclear interference in the near-barrier elastic scattering of 17 Ne from 208 Pb

The proton drip-line nucleus 17Ne is considered a good candidate for a Borromean two-proton halo with a 15O + p+ pstructure. Angular distributions of the elastic scattering and inclusive 15O production for a 136 MeV 17Ne beam incident on a 208Pb target were measured for the first time at the SPIRAL1 facility, GANIL. Use of the GLORIA detector array allowed high-resolution data over a wide angular range from 20◦up to 95◦in the laboratory frame to be obtained. The elastic scattering angular distribution shows similarities with those for both 6He and 20Ne at equivalent collision energies with respect to the corresponding Coulomb barriers, exhibiting the suppression of the Coulomb rainbow peak characteristic of strong coupling. Optical model and coupled channel fits suggest that this is due to a combination of coupling to low-lying quadrupole resonances and Coulomb dipole coupling to the low-lying continuum, although their relative importance depends on the relevant B(E2)values which remain to be firmly determined

Constraints from Inflation on Scalar-Tensor Gravity Theories

We show how observations of the perturbation spectra produced during inflation may be used to constrain the parameters of general scalar-tensor theories of gravity, which include both an inflaton and dilaton field. An interesting feature of these models is the possibility that the curvature perturbations on super-horizon scales may not be constant due to non-adiabatic perturbations of the two fields. Within a given model, the tilt and relative amplitude of the scalar and tensor perturbation spectra gives constraints on the parameters of the gravity theory, which may be comparable with those from primordial nucleosynthesis and post-Newtonian experiments.Comment: LaTeX (with RevTex) 19 pages, 8 uuencoded figures appended, also available on WWW via http://star.maps.susx.ac.uk/index.htm