We use the effective field theory for gravitational bound states, proposed by Goldberger and Rothstein, to compute the interaction Lagrangian of a binary system at the second post-Newtonian order. Throughout the calculation, we use a metric parametrization based on a temporal Kaluza-Klein decomposition and test the claim by Kol and Smolkin that this parametrization provides important calculational advantages. We demonstrate how to use the effective field theory method efficiently in precision calculations, and we reproduce known results for the second post-Newtonian order equations of motion in harmonic gauge in a straightforward manner. I. INTRODUCTIONIn the last two decades, significant progress has been made towards the detection of gravitational waves (GWs) via laser interferometry. Currently, the ground-based experiments LIGO [1], VIRGO [2], GEO [3], and TAMA [4] are actively searching for GWs [5]. Moreover, the proposed LISA experiment [6], due to be the first space-based GW detector, will search for GWs in a complementary frequency band to the ground-based experiments and is expected to achieve high event rates at an unprecedented signal-to-noise ratio [7].A particularly interesting source of GWs, which is expected to be detected, is the compact binary system undergoing coalescence, with neutron star (NS) and/or black hole (BH) constituents. Current experiments have yet to detect the binary inspiral signal. However, Advanced LIGO [8], an upgrade of LIGO scheduled to come online in 2014, may allow for routine detection of such events. This is due to a ∼ 10-fold increase in sensitivity over LIGO, which will in turn result in an increase of the accessible event rate by a factor ∼ 1000. Current estimates for the number of expected NS/NS, BH/BH, and BH/NS events in Advanced LIGO are roughly 10 − 100, 1 − 500, and 1 − 30 per year, respectively [9,10].All three stages of the binary coalescence, inspiral, merger, and ringdown, are potentially detectable. The inspiral phase, where the characteristic orbital velocity is v 2 ≪ 1 (in units where c = 1), can be computed analytically using an expansion in v 2 ∼ Gm/r. The merger is computed numerically [11], and there has been significant recent progress in this area [12]. The ringdown can be treated analytically using quasinormal modes [13].The perturbative calculation of the inspiral phase has been performed with a variety of methods [14,15]. Because of the phase evolution of the inspiral signal and the ability to measure the total orbital phase to ∼ 10 −3 over the LIGO bandwidth [16], these perturbation expansions must be calculated to high order. If we consider a circular orbit in the adiabatic approximation, the signal phase Φ(ω) is related to the orbital energy E(ω) and the radiated power P (ω) through the relation d 2 Φ/dω 2 ∼ (dE/dω)/P . An accuracy of ∼ 10 −3 in the cumulative orbital phase, over the LIGO bandwidth, can be achieved if the perturbation expansion is calculated to O(v 6 ) beyond Newtonian dynamics i.e., at third post-Newtonian order (3PN) [9,17]....

We analyze the evolution of the perturbations in the inflaton field and metric following the end of inflation. We present accurate analytic approximations for the perturbations, showing that the coherent oscillations of the post-inflationary condensate necessarily break down long before any current phenomenological constraints require the universe to become radiation dominated. Further, the breakdown occurs on length-scales equivalent to the comoving postinflationary horizon size. This work has implications for both the inflationary "matching" problem, and the possible generation of a stochastic gravitational wave background in the post-inflationary universe.We can understand our results heuristically by noting that in a universe dominated by pressureless dust, sub-horizon perturbations grow linearly with a(t). Given the apparent red tilt of the primordial perturbation spectrum, perturbations on scales near the postinflationary horizon volume have a lower initial amplitude than those at longer scales, but they also spend more time inside the horizon during this effective matter dominated era. The growth of these modes during this period more than compensates for the diminished initial amplitude, and shorter modes become nonlinear before longer modes. However, modes whose frequency is higher than the oscillation frequency of the coherent field "resolve" the oscillations. At this point our the analogy with a simple p = 0 fluid breaks down, and modes with higher frequencies will be suppressed.Given the age and the simplicity of this model, these issues have been touched upon a number of times in the past. Nambu and Sasaki consider a related problem in the context of the invisible axion [6], while Nambu and Taruya [7] write down the equations of motion for the inflaton perturbations and scalar metric fluctuations, showing that they are described by a Mathieu-like equation. Leach and Liddle [8] compute the spectrum of perturbations for modes that leave the horizon near the end of inflation, while Assadullahi and Wands [9,10] show that nonlinearities formed during a generic matter dominated phase likely leads to gravitational wave production, and a high-frequency, stochastic background of gravitational waves in the present-day universe. Recently, Jedamzik, Lemoine and Martin [11] (see also [12]) discussed the gravitational growth of perturbations in this system, highlighting the parametric resonance "hidden" in the scalar field perturbations (see also [7]).The purpose of this analysis is to understand and clarify the connection between the detailed evolution of inflaton and metric perturbations. In particular, we carefully explore the basis of the simple analogy between the post-inflationary coherent oscillations and a dust-dominated universe. We show that the universe necessarily becomes inhomogeneous (and the perturbations nonlinear) if reheating is delayed long enough, and thus compute the maximum duration of a phase of coherent oscillations. We are careful to perform our postinflationary analysis using quantities t...

Land‐use change is one of the biggest threats to biodiversity globally. The effects of land use on biodiversity manifest primarily at local scales which are not captured by the coarse spatial grain of current global land‐use mapping. Assessments of land‐use impacts on biodiversity across large spatial extents require data at a similar spatial grain to the ecological processes they are assessing. Here, we develop a method for statistically downscaling mapped land‐use data that combines generalized additive modeling and constrained optimization. This method was applied to the 0.5° Land‐use Harmonization data for the year 2005 to produce global 30″ (approx. 1 km2) estimates of five land‐use classes: primary habitat, secondary habitat, cropland, pasture, and urban. The original dataset was partitioned into 61 bio‐realms (unique combinations of biome and biogeographical realm) and downscaled using relationships with fine‐grained climate, land cover, landform, and anthropogenic influence layers. The downscaled land‐use data were validated using the PREDICTS database and the geoWiki global cropland dataset. Application of the new method to all 61 bio‐realms produced global fine‐grained layers from the 2005 time step of the Land‐use Harmonization dataset. Coarse‐scaled proportions of land use estimated from these data compared well with those estimated in the original datasets (mean R 2: 0.68 ± 0.19). Validation with the PREDICTS database showed the new downscaled land‐use layers improved discrimination of all five classes at PREDICTS sites (P < 0.0001 in all cases). Additional validation of the downscaled cropping layer with the geoWiki layer showed an R 2 improvement of 0.12 compared with the Land‐use Harmonization data. The downscaling method presented here produced the first global land‐use dataset at a spatial grain relevant to ecological processes that drive changes in biodiversity over space and time. Integrating these data with biodiversity measures will enable the reporting of land‐use impacts on biodiversity at a finer resolution than previously possible. Furthermore, the general method presented here could be useful to others wishing to downscale similarly constrained coarse‐resolution data for other environmental variables.

By stacking an ensemble of strong lensing clusters, we demonstrate the feasibility of placing constraints on the dark energy equation of state. This is achieved by using multiple images of sources at two or more distinct redshift planes. The sample of smooth clusters in our simulations is based on observations of massive clusters and the distribution of background galaxies is constructed using the Hubble Deep Field. Our source distribution reproduces the observed redshift distribution of multiply imaged sources in Abell 1689. The cosmology recovery depends on the number of image families with known spectroscopic redshifts and the number of stacked clusters. Our simulations suggest that constraints comparable to those derived from other competing established techniques on a constant dark energy equation of state can be obtained using 10 to 40 clusters with 5 or more families of multiple images. We have also studied the observational errors in the image redshifts and positions. We find that spectroscopic redshifts and high resolution {\it Hubble Space Telescope} images are required to eliminate confidence contour relaxation relative to the ideal case in our simulations. This suggests that the dark energy equation of state, and other cosmological parameters, can be constrained with existing {\it Hubble Space Telescope} images of lensing clusters coupled with dedicated ground-based arc spectroscopy.Comment: MNRAS in press, 13 pages, 5 figure

We present calculations of the stochastic gravitational wave (GW) background resulting from neutron star birth throughout the Universe. We update previous calculations by employing three GW waveforms from Dimmelmeier, Font & Müller, based on three models incorporating general relativistic effects for the axisymmetric core collapse of rotating massive stars. Source‐rate evolution is accounted for by using a simulated star formation rate model based on a ‘flat‐Λ’ cosmology given by Hernquist & Springel. We show that the GW background is only weakly dependent on the source‐rate evolution model. Prominent features in the single‐source GW spectral strain can be related to the calculated background spectra, even though the features are broadened and redshifted because of contributions from high‐redshift sources. The background spectral closure density is reduced by 1–2 orders of magnitude compared with previous calculations, a consequence of using relativistic single‐source GW waveforms and a more slowly evolving source‐rate density. Duty cycle estimates for this background imply a non‐continuous signal, assuming that it consists predominantly of ‘regular’ and ‘rapid’ core‐collapse models. We note that the background may be considerably enhanced by the inclusion of dynamic post‐collapse instabilities (bar modes), which are not included in this work, so our estimates for this background may be lower limits.