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To date, the most precise measurement of the observer's peculiar velocity comes from the dipole in the Cosmic Microwave Background (CMB). This velocity also generates a dipole in the source number counts, whose amplitude is governed not only by the observer velocity, but also by specific properties of the sources, that are difficult to determine precisely. Quantitative studies of the source number counts currently give dipoles which are reasonably well aligned with the CMB dipole, but with a significantly larger amplitude than that of the CMB dipole. In this work, we explore an alternative way of measuring the observer velocity from the source number counts, using correlations between neighboring spherical harmonic coefficients, induced by the velocity. We show that these correlations contain both a term sensitive to the source properties and another one directly given by the observer velocity. We explore the potential of a Euclid-like survey to directly measure this second contribution, independently of the characteristics of the population of sources. We find that the method can reach a precision of 4%, corresponding to a detection significance of 24 sigma, on the observer velocity. This will settle with precision the present "dipole tension"., Comment: 20 pages main, 12 pages appendix, 6 figures

Dark sirens are a powerful way to infer cosmological and astrophysical parameters from the combination of gravitational wave sirens and galaxy catalogues. Importantly, the method relies on the completeness of the galaxy catalogues being well modelled. A magnitude-limited catalogue will always be incomplete to some extent, requiring a completion scheme to avoid biasing the parameter inference. Standard methods include homogeneous and multiplicative completion, which have the advantage of simplicity but underestimate or overestimate the amplitude of structure at low completeness, respectively. In this work, we propose a new method to complete galaxy catalogues which uses clustering information to incorporate knowledge of the large scale structure into the dark sirens method. We find that if the structure of the true number of galaxies is sufficiently well preserved in the catalogue, our estimator can perform drastically better than both homogeneous and multiplicative completion. We lay the foundations for a maximally informative dark sirens analysis and discuss its limitations., Comment: 29 pages, 11 figures, adapted to match published version in JCAP

Two major challenges of contemporary cosmology are the Hubble tension and the cosmic dipole tension. At the crossroad of these, we investigate the impact of peculiar velocities on estimations of the Hubble constant from time-delay cosmography. We quantify the bias on the inference of the Hubble constant due to peculiar velocities of the lens, the source and of the observer. The former two, which may cancel from one system to another, affect the determination of the angular diameter distances in the time-delay formula, and reconstructed quantities like the angle to the source, via a lens model. On the other hand, the peculiar velocity of the observer, which is a debated quantity in the context of the cosmic dipole tension, systematically affects observed angles through aberration, redshifts, angular diameter distance and reconstructed quantities. We compute in detail the effect of these peculiar velocities on the inference of the Hubble constant to linear order in the peculiar velocities for the seven lenses of the H0LiCOW/TDCOSMO collaboration. The bias generated by the observer's peculiar velocity alone can reach $1.15\%$ for the lenses which are well aligned with it. This results in a $0.25 \%$ bias for the seven combined lenses. Assuming a typical peculiar velocity of $300$ km s$^{-1}$ for the lens and the source galaxies, these add an additional random uncertainty, which can reach $1\%$ for an individual lens, but reduces to $0.24\%$ for the full TDCOSMO sample. The picture may change if peculiar velocities turn out to be larger than expected. Any time-delay cosmography program which aims for percent precision on the Hubble constant may need to take this source of systematic bias into account. This is especially so for future ground-based surveys which cover a fraction of the celestial sphere that is well aligned with the observer's peculiar velocity., Comment: 19 pages, 8 figures, 2 tables, online version adapted to make it consistent with published version

The velocity of the Sun with respect to the cosmic microwave background (CMB) can be extracted from the CMB dipole, provided its intrinsic dipole is assumed to be small in comparison. This interpretation is consistent, within fairly large error bars, with the measurement of the correlations between neighboring CMB multipoles induced by the velocity of the observer, which effectively breaks isotropy. In contrast, the source number count dipole was reported to privilege a velocity of the observer with an amplitude which is about twice as large as the one extracted from the entirely kinematic interpretation of the CMB dipole, with error bars which indicate a more and more significant tension. In this work, we study the effect of the peculiar velocity of the observer on correlations of nearby multipoles in the source number counts. We provide an unbiased estimator for the kinetic dipole amplitude, which is proportional to the peculiar velocity of the observer and we compute the expected signal to noise ratio. Near future experiments can achieve better than 5$\%$ constraints on the velocity of the Sun with our estimator., Comment: 12 pages, 1 figure, matches published version

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

Our motion through the Universe generates a dipole in the temperature anisotropies of the Cosmic Microwave Background (CMB) and also in the angular distribution of sources. If the cosmological principle is valid, these two dipoles are directly linked, such that the amplitude of one determines that of the other. However, it is a longstanding problem that number counts of radio sources and of quasars at low and intermediate redshifts exhibit a dipole that is well aligned with that of the CMB but with about twice the expected amplitude, leading to a tension reaching up to $4.9 \sigma$. In this paper, we revisit the theoretical derivation of the dipole in the sources number counts, explicitly accounting for the redshift evolution of the population of sources. We argue that if the spectral index and magnification bias of the sources vary with redshift, the standard theoretical description of the dipole may be inaccurate. We provide an alternative expression which does not depend on the spectral index, but instead on the time evolution of the population of sources. We then determine the values that this evolution rate should have in order to remove the tension with the CMB dipole., Comment: 11 pages, 8 figures, typo corrected in Eq. (28), (43). Subsequent Eqs. (54), (56), (59), Fig. 7 and 8 adapted with respect to v1

As first noted by Robert Wagoner in the 1970s, if a scalar field is nonminimally coupled to the Ricci scalar and propagates at subluminal speeds, then there exists the possibility of scalar $\check{\hbox{C}}$erenkov radiation from a moving particle. The mere observation of high-energy cosmic rays could in principle rule out the existence of such scalar fields since any particle moving faster than scalar perturbations would lose energy in the form of scalar waves until it moves slower than those. We compute in detail the energy loss to scalar waves and find that it scales with the square of the ultra-violet (UV) cutoff frequency of the effective field theory (EFT) of gravity. For dark-energy-motivated EFTs, the UV cutoff can be low, in which case that energy loss could always be negligible. In contrast, if viewed as a covariant theory valid at all scales or as an EFT valid at higher energies, perhaps even all the way up to the Planck scale, as may be the case if motivated by quantum-gravity perspectives, then the energy loss to scalar waves may diverge or become dramatically large. In this case, high-energy cosmic rays of extragalactic origin stringently constrain any conformally coupled scalar fields with non-canonical kinetic terms, although a minimum scalar phase velocity is required to trust the EFT., Comment: 8 pages, 3 figues, matches published version

Scalar-tensor theories leaving significant modifications of gravity at cosmological scales rely on screening mechanisms to recover General Relativity (GR) in high-density regions and pass stringent tests with astrophysical objects. Much focus has been placed on the signatures of such modifications of gravity on the propagation of gravitational waves (GWs) through cosmological distances while typically assuming their emission from fully screened regions with the wave generation strictly abiding by GR. Here, we closely analyse the impact of screening mechanisms on the inspiral GW waveforms from compact sources by employing a scaling method that enables a post-Newtonian (PN) expansion in screened regimes. Particularly, we derive the leading-order corrections to a fully screened emission to first PN order in the near zone and we also compute the modifications in the unscreened radiation zone to second PN order. For a concrete example, we apply our results to a cubic Galileon model. The resulting GW amplitude from a binary black hole inspiral deviate from its GR counterpart at most by one part in $10^{2}$ for the modifications in the radiation zone and at most one part in $10^{11}$ due to next-order corrections to the fully screened near zone. We expect such modifications to be undetectable by the current generation of GW detectors, but the deviation is not so small as to remain undetectable in future experiments., Comment: 26 pages, 1 figure

In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross polarization modes which are the signature of a massless spin-2 field. However, diffraction of GWs caused by intervening objects along the line of sight can cause the apparent rise of additional polarizations due to GW-curvature interactions. In this paper, we continue the analysis by two of the authors of the present article, on lensing of gravitational waves beyond geometric optics. In particular, we calculate the lensing effect caused by a point-like lens, in the regime where its Schwarzschild radius $R_s$ is much smaller than the wavelength $\lambda$ of the signal, itself smaller than the impact parameter $b$. In this case, the curvature of spacetime induces distortions in the polarization of the wave such that effective scalar and vector polarizations may appear. We find that the amplitude of these apparent non-GR polarizations is suppressed by a factor $R_s\lambda/b^2$ with respect to the amplitude of the GR-like tensor modes. We estimate the probability to develop these extra polarization modes for a nearly monochromatic GW in the Pulsar Timing Arrays band traveling through a distribution of galaxies., Comment: 18 pages, 5 figures, added Appendix C

In dark-energy models where a scalar field is nonminimally coupled to the spacetime geometry, gravitational waves are expected to be supplemented with a scalar mode. Such scalar waves may interact with the standard tensor waves, thereby affecting their observed amplitude and polarization. Understanding the role of scalar waves is thus essential in order to design reliable gravitational-wave probes of dark energy and gravity beyond general relativity. In this article, we thoroughly investigate the propagation of scalar and tensor waves in the subset of Horndeski theories in which tensor waves propagate at the speed of light. We work at linear order in scalar and metric perturbations, in the eikonal regime, and for arbitrary scalar and spacetime backgrounds. We diagonalize the system of equations of motion and identify the physical tensor mode, which differs from the metric perturbation. We find that interactions between scalar and tensor waves generally depend on the scalar propagation speed. If the scalar waves are luminal or quasiluminal, then interactions are negligible. In the subluminal case, scalar-tensor interactions are effectively suppressed due to the incoherence of the wave's phases., Comment: 12+6 pages, 1 figure. v2: extended results for subluminal scalar waves, matches published version in PRD up to minor typos corrected here in Eq. (102), (103), (110), (A.68), (A.28)

The Einstein-Hilbert action with a cosmological constant is the most general local four-dimensional action leading to second-order derivative equations of motion that are symmetric and divergence free. In higher dimensions, additional terms can appear. We investigate a generalised metric decomposition involving a scalar degree of freedom to express the higher-dimensional action as an effective four-dimensional scalar-tensor theory. From the higher-dimensional Ricci scalar alone and a subclass of our metric ansatz, we recover the subset of Horndeski theories with luminal speed of gravitational waves. More generally, beyond-Horndeski terms appear. When including a Gauss-Bonnet scalar in the higher-dimensional action, we generate contributions to all cubic-order second-derivative terms present in the degenerate higher-order scalar-tensor theory as well as higher-derivative terms beyond that. We discuss this technique as a way to generate healthy four-dimensional gravity theories with an extra scalar degree of freedom and outline further generalisations of our method., Comment: 29 pages, published version

Standard sirens have been proposed as probes of alternative theories of gravity, such as Horndeski models. Hitherto, all studies have been conducted on a homogeneous-isotropic cosmological background, which is unable to consistently account for realistic distributions of matter, and for inhomogeneities in the Horndeski scalar field. Yet, the latter are essential for screening mechanisms. In this article, we comprehensively analyze the propagation of Horndeski gravitational waves in an arbitrary background spacetime and scalar field. We restrict to the class of theories in which gravitational waves propagate at light speed, and work in the geometric-optics regime. We find that kinetic braiding only produces a nonphysical longitudinal mode, whereas conformal coupling affects the amplitude of the standard transverse modes but not their polarization. We confirm that any observable deviation from general relativity depends on the local value of the effective Planck mass at emission and reception of the wave. This result is interpreted as the conservation of the number of gravitons., Comment: 17 pages, 1 figure. v2: title changed upon PRD request; improved discussion on scalar waves in Sec. II.D; extended discussion on polarization in Sec. III.C; detailed comparison with another recent work in Appendix E; version accepted for publication in PRD

Modified gravity theories with an effective Newton constant that varies over cosmological timescales generally predict a different gravitational wave luminosity distance than General Relativity. While this holds for a uniform variation, we show that if locally screened at the source and at the observer as required to pass stringent astrophysical tests of gravity, the General Relativistic distance is restored. In the absence of such a screening, the same effect must modify electromagnetic luminosity distances inferred from supernovae Type Ia, to the extent that the effects can cancel in the comparison. Hence, either the modifications considered employ screening, which leaves no signature in Standard Sirens of a cosmological modification of gravity, or screening does not operate, in which case there can be a signal that is however well below the forseeable sensitivity of the probe when astrophysical bounds are employed. We recover these results both in the Jordan and Einstein frames, paying acute attention to pecularities of each frame such as the notion of redshift or geodesic motions. We emphasise that despite these limitations, Standard Sirens provide valuable independent tests of gravity that differ fundamentally from other probes, a circumstance that is generally important for the wider scope of gravitational modifications and related scenarios. Finally, we use our results to show that the gravitational wave propagation is not affected by dark sector interactions, which restores a dark degeneracy between conformal and disformal couplings that enables observationally viable cosmic self-acceleration to emenate from those., Comment: 41 pages, 2 figures

The growing wealth of cosmological observations places increasingly more stringent constraints on dark energy and alternative gravity models. Particularly successful in efficiently probing the vast model space has been the effective field theory of dark energy and modified gravity, providing a unified framework for generalised cosmological predictions. However, the optimal parametrisation of the free time-dependent functions inherent to the formalism is still unresolved. It should respect a multitude of requirements, ranging from simplicity, generality, and representativity of known theories to computational efficiency. But in particular, for theoretical soundness, the parameter space should adhere to strict stability requirements. We have recently proposed an inherently stable effective field theory with physical basis of Planck mass evolution, sound speed of the scalar field fluctuation, kinetic coefficient, and background expansion, which covers Horndeski models with luminal speed of gravity. Here we devise a parametrisation of these basis functions that can straightforwardly be configured to evade theoretical pathologies such as ghost or gradient instabilities or to accommodate further theoretical priors such as (sub)luminal scalar sound speed. The parametrisation is simple yet general, conveniently represents a broad range of known dark energy and gravitational theories, and with a simple additional approximation can be rendered numerically highly efficient. Finally, by operating in our new basis, we show that there are no general limitations from stability requirements on the current values that can be assumed by the phenomenological modification of the Poisson equation and the gravitational slip besides the exclusion of anti-gravity. The inherently stable effective field theory is ready for implementation in parameter estimation analyses employing linear cosmological observations., Comment: 31 pages, 4 figures, 2 tables; comments welcome