Scale-dependent bias of galaxies and mu-type distortion of the cosmic microwave background spectrum from single-field inflation with a modified initial state

We investigate the phenomenological consequences of a modification of the initial state of a single inflationary field. While single-field inflation with the standard Bunch-Davies initial vacuum state does not generally produce a measurable three-point function (bispectrum) in the squeezed configuration, allowing for a non-standard initial state produces an exception. Here, we calculate the signature of an initial state modification in single-field slow-roll inflation in both the scale-dependent bias of the large-scale structure (LSS) and mu-type distortion in the black-body spectrum of the cosmic microwave background (CMB). We parametrize the initial state modifications and identify certain choices of parameters as natural, though we also note some fine-tuned choices that can yield a larger bispectrum. In both cases, we observe a distinctive k^-3 signature in LSS (as opposed to k^-2 for the local-form). As a non-zero bispectrum in the squeezed configuration correlates a long-wavelength mode with two short-wavelength modes, it induces a correlation between the CMB temperature anisotropy on large scales with the temperature-anisotropy-squared on very small scales; this correlation persists as the small-scale anisotropy-squared is processed into mu-type distortions. While the local-form mu-distortion turns out to be too small to detect in the near future, a modified initial vacuum state enhances the signal by a large factor owing to an extra factor of k_1/k. For example, a proposed absolutely-calibrated experiment, PIXIE, is expected to detect this correlation with a signal-to-noise ratio greater than 10, for an occupation number of about 0.5 in the observable modes. Relatively calibrated experiments such as Planck and LiteBIRD should also be able to measure this effect, provided that the relative calibration between different frequencies meets the required precision. (Abridged)Comment: 14 pages, 6 figures. Matches version in PRD. Improved explanation in Sec. IV; added references and corrected typo

Redshift-Independent Distances to Type Ia Supernovae

We describe a procedure for accurately determining luminosity distances to Type Ia supernovae (SNe Ia) without knowledge of redshift. This procedure, which may be used as an extension of any of the various distance determination methods currently in use, is based on marginalizing over redshift, removing the requirement of knowing $z$ a priori. We demonstrate that the Hubble diagram scatter of distances measured with this technique is approximately equal to that of distances derived from conventional redshift-specific methods for a set of 60 nearby SNe Ia. This indicates that accurate distances for cosmological SNe Ia may be determined without the requirement of spectroscopic redshifts, which are typically the limiting factor for the number of SNe that modern surveys can collect. Removing this limitation would greatly increase the number of SNe for which current and future SN surveys will be able to accurately measure distance. The method may also be able to be used for high-$z$ SNe Ia to determine cosmological density parameters without redshift information.Comment: 12 pages, 3 figures, accepted for publication in Astrophysical Journal Letter

Generalized Huygens principle with pulsed-beam wavelets

Huygens' principle has a well-known problem with back-propagation due to the spherical nature of the secondary wavelets. We solve this by analytically continuing the surface of integration. If the surface is a sphere of radius $R$, this is done by complexifying $R$ to $R+ia$. The resulting complex sphere is shown to be a real bundle of disks with radius $a$ tangent to the sphere. Huygens' "secondary source points" are thus replaced by disks, and his spherical wavelets by well-focused pulsed beams propagating outward. This solves the back-propagation problem. The extended Huygens principle is a completeness relation for pulsed beams, giving a representation of a general radiation field as a superposition of such beams. Furthermore, it naturally yields a very efficient way to compute radiation fields because all pulsed beams missing a given observer can be ignored. Increasing $a$ sharpens the focus of the pulsed beams, which in turn raises the compression of the representation.Comment: 49 pages, 14 figure

Extractability of different forms of mineral-associated phosphorus

The sequential extraction scheme introduced by Hedley et al. (1982) and modified by Tiessen and Moir (2008) has become the preeminent measure for estimating biological availability and binding forms of phosphorus in soil. However, the method’s underlying assumptions, especially on the binding forms, have never been subjected to rigorous testing under defined conditions. We reacted different forms of phosphorus (orthophosphate, phytic acid, RNA) with several potentially phosphorus-binding mineral phases (kaolinite, montmorillonite, goethite, ferrihydrite, amorphous Al hydroxide, allophane) at pH 4. Then, the phosphorus-loaded mineral phases were rinsed for removal of excess phosphorus compounds, shock-frozen in liquid N2 and freeze dried. Each 1 g of phosphorus-loaded samples was then mixed with 9 g of purified quartz (sieved to <63 µm) to mimic relations of reactive and nonreactive mineral phases in soil. All samples were then subjected to sequential extraction in line with the Hedley fractionation scheme (water‒resin extraction, extraction with 0.5 M NaHCO3, extraction with 0.1 M NaOH, extraction with 1 M HCl, extraction with concentrated HCl at 80°C). All extracts were analysed for orthophosphate and total phosphorus. The minerals retained different amounts of phosphorus compounds, with the hydrous metal oxides and allophane binding orthophosphate and most of the organic species most strongly. Clay minerals showed the weakest binding of phosphorus compounds. The water‒resin extraction mobilised surprisingly large portions of orthophosphate from all mineral phases and also some of the organic compounds. The NaHCO3 and NaOH extracts removed increasing portions of phosphorus compounds. Amorphous Al hydroxide largely dissolved in 1 M NaOH; the iron oxides and allophane, however, withstood the alkaline extraction. Treatment with 1 M HCl resulted in further release of phosphorus compounds from all minerals, especially from ferrihydrite. The assumption of the Hedley fraction that the 1 M HCl extraction represents exclusively Ca-bound phosphorus, thus, is obviously wrong. In summary, phosphorus forms bound to different minerals contribute to all extracts. Thus, the individual extraction steps of the Hedley do not represent phosphorus bound to certain compounds but phosphorus bound to various mineral phases via bonds of different strength

Chiral 3π\pi-exchange NN-potentials: Results for dominant next-to-leading order contributions

We calculate in (two-loop) chiral perturbation theory the local NN-potentials generated by the three-pion exchange diagrams with one insertion from the second order chiral effective pion-nucleon Lagrangian proportional to the low-energy constants $c_{1,2,3,4}$. The resulting isoscalar central potential vanishes identically. In most cases these $3\pi$-exchange potentials are larger than the ones generated by the diagrams involving only leading order vertices due to the large values of $c_{3,4}$ (which mainly represent virtual $\Delta$-excitation). A similar feature has been observed for the chiral $2\pi$-exchange. We also give suitable (double-integral) representations for the spin-spin and tensor potentials generated by the leading-order diagrams proportional to $g_A^6$ involving four nucleon propagators. In these cases the Cutkosky rule cannot be used to calculate the spectral-functions in the infinite nucleon mass limit since the corresponding mass-spectra start with a non-vanishing value at the $3\pi$-threshold. Altogether, one finds that chiral $3\pi$-exchange leads to small corrections in the region $r\geq 1.4$ fm where $1\pi$- and chiral $2\pi$-exchange alone provide a very good strong NN-force as shown in a recent analysis of the low-energy pp-scattering data-base.Comment: 11 pages, 7 figures, to be published in The Physical Review

J1420--0545: The radio galaxy larger than 3C236

We report the discovery of the largest giant radio galaxy, J1420-0545: a FR type II radio source with an angular size of 17.4' identified with an optical galaxy at z=0.3067. Thus, the projected linear size of the radio structure is 4.69 Mpc (if we assume that H_{0}=71 km\s\Mpc, Omega_{m}=0.27, and Omega_{\Lambda}=0.73). This makes it larger than 3C236, which is the largest double radio source known to date. New radio observations with the 100 m Effelsberg telescope and the Giant Metrewave Radio Telescope, as well as optical identification with a host galaxy and its optical spectroscopy with the William Herschel Telescope are reported. The spectrum of J1420-0545 is typical of elliptical galaxies in which continuum emission with the characteristic 4000A discontinuity and the H and K absorption lines are dominated by evolved stars. The dynamical age of the source, its jets' power, the energy density, and the equipartition magnetic field are calculated and compared with the corresponding parameters of other giant and normal-sized radio galaxies from a comparison sample. The source is characterized by the exceptionally low density of the surrounding IGM and an unexpectedly high expansion speed of the source along the jet axis. All of these may suggest a large inhomogeneity of the IGM.Comment: 20 pages, 5 figures, 3 table