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Register a new userOn the waveform of the scalar induced gravitational waves
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The scalar induced gravitational waves (SIGWs) is a useful tool to probe the physics in the early universe. To study inflationary models with this tool, we need to know how the waveform of SIGWs is related to the shape of the scalar power spectrum. We propose two parameterizations to approximate the scalar power spectrum with either a sharp or a broad spike at small scales, and then use these two parameterizations to study the relation between the shapes of $Omega_{GW}$ and the scalar power spectrum. We find that the waveform of SIGWs has a similar shape to the power spectrum. Away from the peak of the spike, the frequency relation $Omega_{GW}(k)sim mathcal{P}_zeta^2(k)$ holds independent of the functional form of the scalar power spectrum. We also give a physical explanation for this general relationship. The general relation is useful for determining the scalar power spectrum and probing inflationary physics with the waveform of SIGWs.
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The gauge dependence of the scalar induced gravitational waves (SIGWs) generated at the second order imposes a challenge to the discussion of the secondary gravitational waves generated by scalar perturbations. We provide a general formula that is valid in any gauge for the calculation of SIGWs and the relationship for SIGWs calculated in various gauges under the coordinate transformation. The formula relating SIGWs in the Newtonian gauge to other gauges is used to calculate SIGWs in six different gauges. We find that the Newtonian gauge, the uniform curvature gauge, the synchronous gauge and the uniform expansion gauge yield the same result for the energy density of SIGWs. We also identify and eliminate the pure gauge modes that exist in the synchronous gauge. In the total matter gauge and the comoving orthogonal gauge, the energy density of SIGWs increases as $eta^2$. While in the uniform density gauge, the energy density of SIGWs increases as $eta^6$.
In this talk I review recent progresses in the detection of scalar gravitational waves. Furthermore, in the framework of the Jordan-Brans-Dicke theory, I compute the signal to noise ratio for a resonant mass detector of spherical shape and for binary sources and collapsing stars. Finally I compare these results with those obtained from laser interferometers and from Einsteinian gravity.
The speed of gravitational waves provides us a new tool to test alternative theories of gravity. The constraint on the speed of gravitational waves from GW170817 and GRB170817A is used to test some classes of Horndeski theory. In particular, we consider the coupling of a scalar field to Einstein tensor and the coupling of the Gauss-Bonnet term to a scalar field. The coupling strength of the Gauss-Bonnet coupling is constrained to be in the order of $10^{-15}$. In the Horndeski theory we show that in order for this theory to satisfy the stringent constraint on the speed of GWs the mass scale $M$ introduced in the non-minimally derivative coupling is constrained to be in the range $10^{15}text{GeV}gg M gtrsim 2times 10^{-35}$GeV taking also under consideration the early times upper bound for the mass scale $M$. The large mass ranges require no fine-tuning because the effect of non-minimally derivative coupling is negligible at late times.
We discuss the scalar mode of gravitational waves emerging in the context of $F(R)$ gravity by taking into account the chameleon mechanism. Assuming a toy model with a specific matter distribution to reproduce the environment of detection experiment by a ground-based gravitational wave observatory, we find that chameleon mechanism remarkably suppresses the scalar wave in the atmosphere of Earth, compared with the tensor modes of the gravitational waves. We also discuss the possibility to detect and constrain scalar waves by the current gravitational observatories and advocate a necessity of the future space-based observations.
The direct detection of gravitational waves (GWs) is an invaluable new tool to probe gravity and the nature of cosmic acceleration. A large class of scalar-tensor theories predict that GWs propagate with velocity different than the speed of light, a difference that can be $mathcal{O}(1)$ for many models of dark energy. We determine the conditions behind the anomalous GW speed, namely that the scalar field spontaneously breaks Lorentz invariance and couples to the metric perturbations via the Weyl tensor. If these conditions are realized in nature, the delay between GW and electromagnetic (EM) signals from distant events will run beyond human timescales, making it impossible to measure the speed of GWs using neutron star mergers or other violent events. We present a robust strategy to exclude or confirm an anomalous speed of GWs using eclipsing binary systems, whose EM phase can be exquisitely determined. he white dwarf binary J0651+2844 is a known example of such system that can be used to probe deviations in the GW speed as small as $c_g/c-1gtrsim 2cdot 10^{-12}$ when LISA comes online. This test will either eliminate many contender models for cosmic acceleration or wreck a fundamental pillar of general relativity.
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