Lensing of gravitational waves: efficient wave-optics methods and validation with symmetric lenses

Gravitational wave (GW) astronomy offers the potential to probe the wave-optics regime of gravitational lensing. Wave optics (WO) effects are relevant at low frequencies, when the wavelength is comparable to the characteristic lensing time delay multiplied by the speed of light, and are thus often negligible for electromagnetic signals. Accurate predictions require computing the conditionally convergent diffraction integral, which involves highly oscillatory integrands and is numerically difficult. We develop and implement several methods to compute lensing predictions in the WO regime valid for general gravitational lenses. First, we derive approximations for high and low frequencies, obtaining explicit expressions for several analytic lens models. Next, we discuss two numerical methods suitable in the intermediate frequency range: 1) Regularized contour flow yields accurate answers in a fraction of a second for a broad range of frequencies. 2) Complex deformation is slower, but requires no knowledge of solutions to the geometric lens equation. Both methods are independent and complement each other. We verify sub-percent accuracy for several lens models, which should be sufficient for applications to GW astronomy in the near future. Apart from modelling lensed GWs, our method will also be applicable to the study of plasma lensing of radio waves and tests of gravity

Through the lens of Sgr A*: identifying strongly lensed Continuous Gravitational Waves beyond the Einstein radius

Once detected, lensed gravitational waves will afford new means to probe thematter distribution in the universe, complementary to electromagnetic signals.Sources of continuous gravitational waves (CWs) are long-lived and stable,making their lensing signatures synergic to short mergers of compact binaries.CWs emitted by isolated neutron stars and lensed by Sgr A$^*$, thesuper-massive black hole at the center of our galaxy, might be observable bythe next generation of gravitational wave detectors. However, it is unknownunder which circumstances these sources can be identified as lensed. Here weshow that future detectors can distinguish lensed CWs and measure allparameters with precision $\sim 1-10\%$ for sources within $2-4$ Einstein radiiof Sgr A$^*$, depending on the source's distance. Such a detection, whichrelies on the relative motion of the observer-lens-source system, can beobserved for transverse velocities above 3 km/s. Therefore, the chances ofobserving strongly lensed neutron stars increase by one order of magnitude withrespect to previous estimates. Observing strongly lensed CWs will enable novelprobes of the galactic center and fundamental physics.<br

Probing lens-induced gravitational-wave birefringence as a test of general relativity

Theories beyond general relativity (GR) modify the propagation ofgravitational waves (GWs). In some, inhomogeneities (aka. gravitational lenses)allow interactions between the metric and additional fields to causelens-induced birefringence (LIB): a different speed of the two linear GWpolarisations ($+$ and $\times$). Inhomogeneities then act as non-isotropiccrystals, splitting the GW signal into two components whose relative time delaydepends on the theory and lens parameters. Here we study the observationalprospects for GW scrambling, i.e when the time delay between both GWpolarisations is smaller than the signal's duration and the waveform recordedby a detector is distorted. We analyze the latest LIGO-Virgo-KAGRA catalog,GWTC-3, and find no conclusive evidence for LIB. The highest log Bayes factorthat we find in favour of LIB is $3.21$ for GW$190521$, a particularly loud butshort event. However, when accounting for false alarms due to (Gaussian) noisefluctuations, this evidence is below 1-$\sigma$. The tightest constraint on thetime delay is $non-observation of GW scrambling, we constrain the optical depth for LIB,accounting for the chance of randomly distributed lenses (eg. galaxies) alongthe line of sight. Our LIB constraints on a (quartic) scalar-tensor Horndeskitheory are more stringent than solar system tests for a wide parameter rangeand comparable to GW170817 in some limits. Interpreting GW190521 as an AGNbinary (i.e. taking an AGN flare as a counterpart) allows even more stringentconstraints. Our results demonstrate the potential and high sensitivityachievable by tests of GR, based on GW lensing.<br

Fully relativistic predictions in Horndeski gravity from standard Newtonian N-body simulations

The N-body gauge allows the introduction of relativistic effects in Newtonian cosmological simulations. Here we extend this framework to general Horndeski gravity theories, and investigate the relativistic effects that the scalar field introduces in the matter power spectrum at intermediate and large scales. In particular, we show that the kineticity function at these scales enhances the amplitude of the signal of contributions coming from the extra degree of freedom. Using the Quasi-Static Approximation (QSA), we separate modified gravity effects into two parts: one that only affects small-scale physics, and one that is due to relativistic effects. This allows our formalism to be readily implemented in modified gravity N-body codes in a straightforward manner, e.g., relativistic effects can be included as an additional linear density field in simulations. We identify the emergence of gravity acoustic oscillations (GAOs) in the matter power spectrum at large scales, $k \sim 10^{-3}-10^{-2}$ Mpc$^{-1}$. GAO features have a purely relativistic origin, coming from the dynamical nature of the scalar field. GAOs may be enhanced to detectable levels by the rapid evolution of the dark energy sound horizon in certain modified gravity models and can be seen as a new test of gravity at scales probed by future galaxy and intensity-mapping surveys

Galaxy correlations and the BAO in a void universe: structure formation as a test of the Copernican Principle

A suggested solution to the dark energy problem is the void model, where accelerated expansion is replaced by Hubble-scale inhomogeneity. In these models, density perturbations grow on a radially inhomogeneous background. This large scale inhomogeneity distorts the spherical Baryon Acoustic Oscillation feature into an ellipsoid which implies that the bump in the galaxy correlation function occurs at different scales in the radial and transverse correlation functions. We compute these for the first time, under the approximation that curvature gradients do not couple the scalar modes to vector and tensor modes. The radial and transverse correlation functions are very different from those of the concordance model, even when the models have the same average BAO scale. This implies that if void models are fine-tuned to satisfy average BAO data, there is enough extra information in the correlation functions to distinguish a void model from the concordance model. We expect these new features to remain when the full perturbation equations are solved, which means that the radial and transverse galaxy correlation functions can be used as a powerful test of the Copernican Principle.Comment: 12 pages, 8 figures, matches published versio

Searching for a Cosmological Preferred Axis: Union2 Data Analysis and Comparison with Other Probes

We review, compare and extend recent studies searching for evidence for a preferred cosmological axis. We start from the Union2 SnIa dataset and use the hemisphere comparison method to search for a preferred axis in the data. We find that the hemisphere of maximum accelerating expansion rate is in the direction $(l,b)=({309^\circ}^{+23^\circ}_{-3^\circ}, {18^\circ}^{+11^\circ}_{-10^\circ})$ (\omm=0.19) while the hemisphere of minimum acceleration is in the opposite direction $(l,b)=({129^\circ}^{+23^\circ}_{-3^\circ},{-18^\circ}^{+10^\circ}_{-11^\circ})$ (\omm=0.30). The level of anisotropy is described by the normalized difference of the best fit values of \omm between the two hemispheres in the context of \lcdm fits. We find a maximum anisotropy level in the Union2 data of \frac{\Delta \ommax}{\bomm}=0.43\pm 0.06. Such a level does not necessarily correspond to statistically significant anisotropy because it is reproduced by about $30$ of simulated isotropic data mimicking the best fit Union2 dataset. However, when combined with the axes directions of other cosmological observations (bulk velocity flow axis, three axes of CMB low multipole moments and quasar optical polarization alignment axis), the statistical evidence for a cosmological anisotropy increases dramatically. We estimate the probability that the above independent six axes directions would be so close in the sky to be less than $1$. Thus either the relative coincidence of these six axes is a very large statistical fluctuation or there is an underlying physical or systematic reason that leads to their correlation.Comment: 10 pages, 7 figures. Accepted in JCAP (to appear). Extended analysis with redshift tomography of SnIa, included errorbars and increased number of axes. The Mathematica 7 files with the data used for the production of the figures along with a Powerpoint file with additional figures may be downloaded from http://leandros.physics.uoi.gr/anisotrop

Filtering out the cosmological constant in the Palatini formalism of modified gravity

According to theoretical physics the cosmological constant (CC) is expected to be much larger in magnitude than other energy densities in the universe, which is in stark contrast to the observed Big Bang evolution. We address this old CC problem not by introducing an extremely fine-tuned counterterm, but in the context of modified gravity in the Palatini formalism. In our model the large CC term is filtered out, and it does not prevent a standard cosmological evolution. We discuss the filter effect in the epochs of radiation and matter domination as well as in the asymptotic de Sitter future. The final expansion rate can be much lower than inferred from the large CC without using a fine-tuned counterterm. Finally, we show that the CC filter works also in the Kottler (Schwarzschild-de Sitter) metric describing a black hole environment with a CC compatible to the future de Sitter cosmos.Comment: 22 pages, 1 figure, discussion extended, references added, accepted by Gen.Rel.Gra

Extended LCDM: generalized non-minimal coupling for dark matter fluids

In this paper we discuss a class of models that address the issue of explaining the gravitational dynamics at the galactic scale starting from a geometric point of view. Instead of claiming the existence of some hidden coupling between dark matter and baryons, or abandoning the existence of dark matter itself, we consider the possibility that dark matter and gravity have some non trivial interaction able to modify the dynamics at astrophysical scales. This interaction is implemented assuming that dark matter gets non--minimally coupled with gravity at suitably small scales and late times. After showing the predictions of the model in the Newtonian limit we also discuss the possible origin of it non-minimal coupling. This investigation seems to suggest that phenomenological mechanisms envisaged for the dark matter dynamics, such as the Bose--Einstein condensation of dark matter halos, could be connected to this class of models.Comment: 15 pages, more references added, minor changes, accepted for publication on JCA

Conserved quantities in Lemaitre-Tolman-Bondi cosmology

We study linear perturbations to a Lema{\^\i}tre-Tolman-Bondi (LTB) background spacetime. Studying the transformation behaviour of the perturbations under gauge transformations, we construct gauge invariant quantities. We show, using the perturbed energy conservation equation, that there are conserved quantities in LTB, in particular a spatial metric trace perturbation, \zeta_{SMTP}, which is conserved on all scales. We then briefly extend our discussion to the Lema{\^\i}tre spacetime, and construct gauge-invariant perturbations in this extension of LTB spacetime.Comment: 16 pages, 0 figures, revtex4; v5: minor changes, additional 2+2 formalism appendix added, references added, version accepted by CQ