This review on "wave optics in gravitational lensing" includes a derivation of the diffraction integral formula for the lensed wave amplitude using the path integral ( §2), reduction of this formula to the geometric optics approximation in the short wavelength limit along with discussion on the condition that the wave effects become important ( §3), examples of wave effects for a point-mass lens and the fold caustic ( §4), and a numerical method of evaluating the diffraction integral ( §5). * ) To our knowledge this approach is new to the gravitational lens theory. at University of British Columbia on June 24, 2015 http://ptps.oxfordjournals.org/ Downloaded from

Gravitational lensing of gravitational waves from inspiraling binaries is discussed in the context of advanced laser-interferometer detectors, taking correct account of the diffraction effect. Convolving the spectrum of the lensed waveform with that of the detector noise, we calculate how much the signal-to-noise ratio is magnified by gravitational lensing as a function of the mass and position of the lens. When the lens is much lighter than ϳ10 2 M Ø , the diffraction is so effective that the wave flux is not magnified appreciably. We predict that lensed waveforms are distinguishable from unlensed ones in that the signal-to-noise ratio shows an oscillatory behavior as the frequency sweeps up.[S0031-9007(97)05167-3] PACS numbers: 04.30.Nk, 04.80.Nn, 95.30.Sf, 97.80.Fk The gravitational waves emitted during the inspiral stage before the final coalescence of two neutron stars (NS-NS binary) is the most promising source for the laser-interferometer detectors under construction such as the LIGO [1]. To this end, much effort has been made to calculate accurately the waveform template [2] which is matched filtered with the observed signal, and also to estimate the event rate [3]. Thus it is important to consider every possible source of noise that alters the results of these theoretical calculations. One such kind of noise may be the gravitational focusing of gravitational waves [4], the subject we shall investigate in this paper.Previously, Wang et al.[5] considered the microlensing of gravitational waves from inspiraling binaries by (hypothetical) stellar mass lenses distributed over the Universe (since the probability of lensing by galaxies is negligible), and concluded that, due to the lensing magnification, there may be a significant number of those inspiral events which would be too distant to be detected had it not been for the lensing. They simply calculated the lensing magnification using geometric optics limit in the same way as for the optical light, and took the maximum magnification to be infinite on the caustics. As shown by several authors [6], however, if the wavelength l is longer than the Schwarzschild radius of the lens mass M, then the wave effect (diffraction) becomes important so the maximum magnification should be small. Since the wavelength is typically ϳ10 2 10 4 km in the observable frequency range of the planned detectors, the wave flux cannot be magnified significantly for lens masses lighter than ϳ10 2 M Ø , as is the case for the microlensing considered in Ref. [5].This paper provides the first proper treatment of gravitational lensing of gravitational waves from inspiraling binaries in the context of advanced laser-interferometer detectors, taking correct account of the diffraction effect. We show that the lensed events should be much rarer than estimated in Ref.[5] for the LIGO type detectors, but that it is possible to distinguish lensed waveforms from unlensed ones once the former are actually detected. We assume the V 1 and L 0 cosmology and use the units c G 1.To give a rough acco...

We derive general analytic formulae for the power spectrum and spectral index of the curvature perturbation produced during inflation driven by a multi-component inflaton field, up to the second order in the slow-roll approximation. We do not assume any specific properties of the potential or the metric on the scalar field space, except for the slow-roll condition, Einstein gravity, and the absence of any permanent isocurvature modes.

Constraints on cosmological models from strong gravitational lensing statistics are investigated. We pay particular attention to the role of the velocity function in the calculation of the lensing probability. The velocity function derived from the observed galaxy luminosity function, which is used in most previous work, is unable to predict the large separation lensing events. In this paper, we also use the Press-Schechter theory to construct a velocity function theoretically. Model predictions are compared with the observed velocity function and the HST snapshot survey. Comparison with the latter observation shows that the predictions based on the theoretical velocity function are consistent with the observed large separation events in COBE normalized low-density models, especially with a non-vanishing cosmological constant. Adopting the COBE normalization, however, we have not been able to find a model which simultaneously satisfies both the observed velocity function and the HST snapshot survey. We systematically investigate various uncertainties in the gravitationallensing statistics including finite core radius, the distance formula, magnification bias, and dust obscuration. The results are very sensitive to these effects as well as theoretical models for the velocity function, implying that current limits on the cosmological parameters should be interpreted with caution. Predictions for future surveys are also presented. at University of Manchester on April 11, 2015 http://ptp.oxfordjournals.org/ Downloaded from H := -= Ho noa + 1no -Ao a + Ao , a (1·1) (1·2) where p = po/a 3 = Po(1 + z)3 is the mean density of the universe at redshift z and the subscripts 0 mean the present epoch z = o.This paper is largely based on a master thesis 36 ) (unpublished) of one of the authors which contains further detailed discussion.

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