Optical Clocks and Relativity
C. W. Chou, D. B. Hume, T. Rosenband, D. J. Wineland
Science 329, 1630 – 1633 (2010)
Rapid Separable Analysis of Higher Order Correlators in Large Scale Structure
J.R. Fergusson, D.M. Regan, E.P.S. Shellard
arXiv:1008.1730
Resonant Trispectrum and a Dozen More Primordial N-point functions
L. Leblond and E. Pajer
arXiv:1010.4565
Full Details of This Week's Papers:
Optical Clocks and Relativity
C. W. Chou, D. B. Hume, T. Rosenband, D. J. Wineland
C. W. Chou, D. B. Hume, T. Rosenband, D. J. Wineland
Observers in relative motion or at different gravitational potentials measure disparate clock rates. These predictions of relativity have previously been observed with atomic clocks at high velocities and with large changes in elevation. We observed time dilation from relative speeds of less than 10 meters per second by comparing two optical atomic clocks connected by a 75-meter length of optical fiber. We can now also detect time dilation due to a change in height near Earth’s surface of less than 1 meter. This technique may be extended to the field of geodesy, with applications in geophysics and hydrology as well as in space-based tests of fundamental physics.
Rapid Separable Analysis of Higher Order Correlators in Large Scale Structure
J.R. Fergusson, D.M. Regan, E.P.S. Shellard
We present an efficient separable approach to the estimation and reconstruction of the bispectrum and the trispectrum from observational (or simulated) large scale structure data. This is developed from general CMB (poly-)spectra methods which exploit the fact that the bispectrum and trispectrum in the literature can be represented by a separable mode expansion which converges rapidly (with $n_\textrm{max}={\cal{O}}(30)$ terms). With an effective grid resolution $l_\textrm{max}$ (number of particles/grid points $N=l_\textrm{max}^3$), we present a bispectrum estimator which requires only ${\cal O}(n_\textrm{max} \times l_\textrm{max}^3)$ operations, along with a corresponding method for direct bispectrum reconstruction. This method is extended to the trispectrum revealing an estimator which requires only ${\cal O}(n_\textrm{max}^{4/3} \times l_\textrm{max}^3)$ operations. The complexity in calculating the trispectrum in this method is now involved in the original decomposition and orthogonalisation process which need only be performed once for each model. However, for non-diagonal trispectra these processes present little extra difficulty and may be performed in ${\cal O}(l_\textrm{max}^4)$ operations. A discussion of how the methodology may be applied to the quadspectrum is also given. An efficient algorithm for the generation of arbitrary nonGaussian initial conditions for use in N-body codes using this separable approach is described. This prescription allows for the production of nonGaussian initial conditions for arbitrary bispectra and trispectra. A brief outline of the key issues involved in parameter estimation, particularly in the non-linear regime, is also given.
Resonant Trispectrum and a Dozen More Primordial N-point functions
L. Leblond and E. Pajer
We compute all N-point primordial curvature correlation functions from inflation at tree-level up to N of order ten or more depending on the choice of parameters. This is achieved for resonant inflationary models in which the inflaton potential has a periodic modulation on top of a slow-roll flat term. These models find a natural UV completion in string theory implementation of axion monodromy. Key to the success of our computation is the observation that gravitational interactions among the perturbations can be neglected, which we argue is justified for any model of inflation with parametrically large non-Gaussianity. We provide a comprehensive review and detailed derivations of known consistency relations for squeezed and collinear limits, and generalize them to any N-point function.
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