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The detection of gravitational waves with Advanced LIGO and Advanced Virgo has enabled novel tests of general relativity, including direct study of the polarization of gravitational waves. While general relativity allows for only two tensor gravitational-wave polarizations, general metric theories can additionally predict two vector and two scalar polarizations. The polarization of gravitational waves is encoded in the spectral shape of the stochastic gravitational-wave background, formed by the superposition of cosmological and individually-unresolved astrophysical sources. Using data recorded by Advanced LIGO during its first observing run, we search for a stochastic background of generically-polarized gravitational waves. We find no evidence for a background of any polarization, and place the first direct bounds on the contributions of vector and scalar polarizations to the stochastic background. Under log-uniform priors for the energy in each polarization, we limit the energy-densities of tensor, vector, and scalar modes at 95% credibility to $Omega^T_0 < 5.6 times 10^{-8}$, $Omega^V_0 < 6.4times 10^{-8}$, and $Omega^S_0 < 1.1times 10^{-7}$ at a reference frequency $f_0 = 25$ Hz.
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The detection of gravitational waves by the Laser Interferometer Gravitational-Wave Observatory opens a new era to use gravitational waves to test alternative theories of gravity. We investigate the polarizations of gravitational waves in $f(R)$ gravity and Horndeski theory, both containing scalar modes. These theories predict that in addition to the familiar $+$ and $times$ polarizations, there are transverse breathing and longitudinal polarizations excited by the massive scalar mode and the new polarization is a single mixed state. It would be very difficult to detect the longitudinal polarization by interferometers, while pulsar timing array may be the better tool to detect the longitudinal polarization.
Formation of primordial black holes from inflationary fluctuations is accompanied by a scalar induced gravitational wave background. We perform a Bayesian search of such background in the data from Advanced LIGO and Virgos first, second and third observing runs, parametrizing the peak in the curvature power spectrum by a log-normal distribution. The search shows no evidence for such a background. We place 95% confidence level upper limits on the integrated power of the curvature power spectrum peak which, for a narrow width, reaches down to $0.02$ at $10^{17},{rm Mpc}^{-1}$. The resulting constraints are stronger than those arising from BBN or CMB observations. In addition, we find that LIGO and Virgo, at its design sensitivity, and the Einstein Telescope can compete with the constraints related to the abundance of the formed primordial black holes.
Among all cosmological quantum-gravity or quantum-gravity-inspired scenarios, only very few predict a blue-tilted primordial tensor spectrum. We explore five of them and check whether they can generate a stochastic gravitational-wave background detectable by present and future interferometers: non-local quantum gravity, string-gas cosmology, new ekpyrotic scenario, Brandenberger-Ho non-commutative inflation and multi-fractional spacetimes. We show that non-local quantum gravity is unobservable, while all the other models can reach the strain sensitivity of DECIGO but not that of LIGO-Virgo-KAGRA, LISA or Einstein Telescope. Other quantum-gravity models with red-tilted spectra (most loop quantum cosmologies) or with exceptionally tiny quantum corrections (Wheeler-DeWitt quantum cosmology) are found to be non-detectable.
We analyze the propagation of high-frequency gravitational waves (GW) in scalar-tensor theories of gravity, with the aim of examining properties of cosmological distances as inferred from GW measurements. By using symmetry principles, we first determine the most general structure of the GW linearized equations and of the GW energy momentum tensor, assuming that GW move with the speed of light. Modified gravity effects are encoded in a small number of parameters, and we study the conditions for ensuring graviton number conservation in our covariant set-up. We then apply our general findings to the case of GW propagating through a perturbed cosmological space-time, deriving the expressions for the GW luminosity distance $d_L^{({rm GW})}$ and the GW angular distance $d_A^{({rm GW})}$. We prove for the first time the validity of Etherington reciprocity law $d_L^{({rm GW})},=,(1+z)^2,d_A^{({rm GW})}$ for a perturbed universe within a scalar-tensor framework. We find that besides the GW luminosity distance, also the GW angular distance can be modified with respect to General Relativity. We discuss implications of this result for gravitational lensing, focussing on time-delays of lensed GW and lensed photons emitted simultaneously during a multimessenger event. We explicitly show how modified gravity effects compensate between different coefficients in the GW time-delay formula: lensed GW arrive at the same time as their lensed electromagnetic counterparts, in agreement with causality constraints.
We study the cosmology on the Friedmann-Lemaitre-Robertson-Walker background in scalar-vector-tensor theories with a broken $U(1)$ gauge symmetry. For parity-invariant interactions arising in scalar-vector-tensor theories with second-order equations of motion, we derive conditions for the absence of ghosts and Laplacian instabilities associated with tensor, vector, and scalar perturbations at linear order. This general result is applied to the computation of the primordial tensor power spectrum generated during inflation as well as to the speed of gravity relevant to dark energy. We also construct a concrete inflationary model in which a temporal vector component $A_0$ contributes to the dynamics of cosmic acceleration besides a scalar field $phi$ through their kinetic mixings. In this model, we show that all the stability conditions of perturbations can be consistently satisfied during inflation and subsequent reheating.
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