We study the propagation of a massless scalar wave in de Sitter spacetime perturbed by an arbitrary central mass. By focusing on the late time limit, this probes the portion of the scalar signal traveling inside the null cone. Unlike in asymptotically flat spacetimes, the amplitude of the scalar field detected by an observer at timelike infinity does not decay back to zero but develops a spacetime constant shift—both at zeroth and at first order in the central mass $M$. This indicates that massless scalar field propagation in asymptotically de Sitter spacetimes exhibits both linear and nonlinear tail-induced memories. On the other hand, for sufficiently late retarded times, the monopole portion of the scalar signal measured at null infinity is found to be amplified relative to its timelike infinity counterpart, by its nonlinear interactions with the gravitation field at first order in $M$.

We show, through an explicit calculation of the relevant Green’s functions, that the transverse-traceless (TT) portion of the gravitational perturbations of Minkowski spacetime and of spatially flat cosmologies with a constant equation-of-state w receive contributions from their isolated matter source(s) outside the past null cone of the observer. This implies the TT gravitational wave (GW) cannot be a standalone observable—despite widespread (apparent) claims in the gravitational wave literature to the contrary. About a Minkowski background, all 4 of the gauge-invariant variables—the two scalars, one vector and tensor—play crucial roles to ensure the spatial tidal forces encoded within the gauge-invariant linearized Riemann tensor are causal. These gravitational tidal forces do not depend solely on the TT graviton but rather on the causal portion of its acceleration. However, in the far zone radiative limit, the flat spacetime ‘TT’ graviton Green’s function does reduce to the causal ‘tt’ ones, which are the ones commonly used to compute gravitational waveforms. Similar remarks apply to the spin-1 photon; for instance, the electric field does not depend solely on the photon, but is the causal part of its velocity. As is known within the quantum theory of photons and linearized gravitons, there are obstacles to the construction of simultaneously gauge-invariant and Lorentz-covariant descriptions of these massless spin-1 and spin-2 states. Our results transparently demonstrate that the quantum operators associated with the helicity-1 photon and helicity-2 linear graviton both violate micro-causality: namely, they do not commute outside the light cone in flat and cosmological spacetimes.

We provide evidence that gravitational radiation in a 4D radiation dominated universe, with equation of state $w=1/3$, consists of two components: helicity-2 gravitons and massless scalar acoustic waves. On physical grounds, we would expect the homogeneous solution of the Weyl tensor components to be a good approximation to its inhomogeneous counterparts, whenever the observer is located well in the far zone of an isolated astrophysical source of cosmological gravitational radiation. We show explicitly that these homogeneous and inhomogeneous solutions both receive contributions from the gauge-invariant tensor and the two Bardeen (acoustic) scalars. Comparison of these Weyl tensor computations thus allows us to not only identify, in the high frequency limit, the corresponding gravitational tensor and scalar radiation; but also their oscillatory polarization patterns.

Cherenkov radiation may occur whenever the source is moving faster than the waves it generates. In a radiation dominated universe, with equation-of-state $w=1/3$, we have recently shown that the Bardeen scalar-metric perturbations contribute to the linearized Weyl tensor in such a manner that its wavefront propagates at acoustic speed $\sqrt{w}=1/\sqrt{3}$. In this work, we explicitly compute the shape of the Bardeen Cherenkov cone and wedge generated respectively by a supersonic point mass (approximating a primordial black hole) and a straight Nambu-Goto wire (approximating a cosmic string) moving perpendicular to its length. When the black hole or cosmic string is moving at ultra-relativistic speeds, we also calculate explicitly the sudden surge of scalar-metric induced tidal forces on a pair of test particles due to the passing Cherenkov shock wave. These forces can stretch or compress, depending on the orientation of the masses relative to the shock front’s normal.

We study the propagation of a massless scalar wave in de Sitter spacetime perturbed by an arbitrary central mass. By focusing on the late time limit, this probes the portion of the scalar signal traveling inside the null cone. Unlike in asymptotically flat spacetimes, the amplitude of the scalar field detected by an observer at timelike infinity does not decay back to zero but develops a spacetime constant shift - both at zeroth and first order in the central mass M. This indicates that massless scalar field propagation in asymptotically de Sitter spacetimes exhibits both linear and nonlinear tail-induced memories. On the other hand, for sufficiently late retarded times, the monopole portion of the scalar signal measured at null infinity is found to be amplified relative to its timelike infinity counterpart, by its nonlinear interactions with the gravitation field at first order in M.

We point out, the scalar sector of gravitational perturbations may be excited by an isolated astrophysical system immersed in a universe whose accelerated expansion is not due to the cosmological constant, but due to extra field degrees of freedom. This is true even if the source of gravitational radiation did not couple directly to these additional fields. We illustrate this by considering a universe driven by a single canonical scalar field. By working within the gauge-invariant formalism, we solve for the electric components of the linearised Weyl tensor to demonstrate that both the gravitational massless spin-2 (transverse-traceless) tensor and the (Bardeen) scalar modes are generated by a generic astrophysical source. For concreteness, the Dark Energy scalar field is either released from rest, or allowed to asymptote toward the minimum in a certain class of potentials; and we compute the traceless tidal forces induced by gravitational radiation from a hypothetical compact binary system residing in such a universe. Though their magnitudes are very small compared to the tensors', spin zero gravitational waves in such a canonical scalar driven universe are directly sensitive to both the Dark Energy equation of state and the eccentricity of the binary's orbit.