Scalar induced gravitational waves review

Gravitational waves (GWs) induced by scalar curvature fluctuations are an important source of the cosmological GW background and a crucial counterpart of the primordial black hole scenario. However, doubts have been cast on the theoretically predicted induced GW spectrum due to its seeming gauge dependence. In this paper, we shed light on the gauge dependence issue of the induced GW spectrum in general cosmological backgrounds. First, inspired by the Hamiltonian formalism we provide very simple formulas for the tensor modes at second order in cosmological perturbation theory. We also emphasize the difference between observable and gauge invariant variables. Second, we argue that the Newton (or shear-free) gauge is suitable for both the calculation of induced GWs and the physical interpretation.

Abstract A tensor-type cosmological perturbation, defined as a transverse and traceless spatial fluctuation, is often interpreted as gravitational waves. While decoupled from the scalar-type perturbations in linear order, the tensor perturbations can be sourced from the scalar-type in nonlinear order. The tensor perturbations generated by the quadratic combination of a linear scalar-type cosmological perturbation are widely studied in the literature, but all previous studies are based on a zero-shear gauge without proper justification. Here, we show that, being second order in perturbation, such an induced tensor perturbation is generically gauge dependent. In particular, the gravitational wave power spectrum depends on the hypersurface (temporal gauge) condition taken for the linear scalar perturbation. We further show that, during the matter-dominated era, the induced tensor modes dominate over the linearly evolved primordial gravitational wave amplitude for even for the gauge that g …

We consider a novel contribution to the polarization of the cosmic microwave background induced by vector and tensor modes generated by the nonlinear evolution of primordial scalar perturbations. Our calculation is based on relativistic second-order perturbation theory and allows us to estimate the effects of these secondary modes on the polarization angular power spectra. We show that a nonvanishing B-mode polarization unavoidably arises from pure scalar initial perturbations, thus limiting our ability to detect the signature of primordial gravitational waves generated during inflation. This secondary effect dominates over that of primordial tensors for an inflationary tensor-to-scalar ratio $r<{10}^{\ensuremath{-}6}.$ The magnitude of the effect is smaller than the contamination produced by the conversion of polarization of type E into type B, by weak gravitational lensing. However, the lensing signal can be cleaned, making the secondary modes discussed here the actual background lim …

In a very recent paper [1], we have proposed a novel $4$-dimensional gravitational theory with two dynamical degrees of freedom, which serves as a consistent realization of $D\to4$ Einstein-Gauss-Bonnet gravity with the rescaled Gauss-Bonnet coupling constant $\tildeα$. This has been made possible by breaking a part of diffeomorphism invariance, and thus is consistent with the Lovelock theorem. In the present paper, we study cosmological implications of the theory in the presence of a perfect fluid and clarify the similarities and differences between the results obtained from the consistent $4$-dimensional theory and those from the previously considered, naive (and inconsistent) $D\rightarrow 4$ limit. Studying the linear perturbations, we explicitly show that the theory only has tensorial gravitational degrees of freedom (besides the matter degree) and that for $\tildeα>0$ and $\dot{H}<0$, perturbations are free of any pathologies so that we can implement the setup to construct early …

This paper investigates the propagation of cosmological gravitational waves interacting with free-streaming neutrinos within the context of Horndeski theories of gravity constrained by the detection of GW170817. We apply the theory of cosmological perturbations to explicitly derive the Einstein-Boltzmann equation for the damped propagation of first-order transverse traceless gravitational waves. In contrast to general relativity, we argue that modified gravity can give rise to non-vanishing free-streaming damping effects during the cosmological matter dominated era. We also provide an analytic formula for the main multipole order with which modified gravity and free-streaming neutrinos damp the variety of tensor correlation functions of the cosmic microwave background.