Effects Of Higher-order Derivative Terms Of Gravity On The Inflationary Power Spectrum And GWs

This paper is devoted to studying the effects of the existence of higher-order derivatives in gravity theory on the inflationary perturbation spectra and gravitational waves.We mainly considered two types of higher-order derivative terms,one is the fourth-order and sixth-order spatial derivative terms introduced in the extended effective field theory of inflation models,and another one is the higher-order parity violating terms introduced in the ghost-free parity-violating gravity.The introduction of the former shows that the gravitational Lorentz symmetry is broken,and leads to the nonlinear dispersion relationship of cosmological scalar perturbation during the inflation,while the latter one contains the odd-order spatial derivative terms which lead to violation of the parity symmetry of gravity.We first studied the effect of all fourth-and sixth-order spatial derivatives in the extended effective field theory of inflation on the scalar perturbation spectrum generated during inflation.Because of the existence of higher-order derivative operators,the primordial scalar perturbation modes will undergo a period of non-adiabatic evolution before they cross the Hubble radius,resulting in that these perturbation modes are no longer in an adiabatic vacuum state but an excited state before exiting the Hubble horizon.To study the effects of the non-adiabatic evolution on the primordial scalar perturbation power spectrum,we apply the uniform asymptotic approximation to construct the approximate analytical solution of the scalar perturbation during inflation.Based on the obtained approximate solution,the primordial scalar perturbation power spectrum is calculated in detail.We find that the resulting modified power spectrum is still near-scale invariant,which means that the higher-order derivative operator terms only affect the overall amplitude of the power spectrum.Then,we considered the effect of the parity-violating terms in ghost-free parity-violating theory of gravity on the propagation of gravitational waves,and calculated in detail the corrections to the waveform of the gravitational waves generated during the inspiral stage or coalescence of compact binaries during the propagation.By comparing the two circular polarization modes of gravitational waves,we find that the parity violation of gravity leads to amplitude birefringence and velocity birefringence effects during the propagation of gravitational waves,which are clearly shown in the gravitational wave waveform by amplitude and phase correction,respectively.Combining both modes,we obtain the waveform of the gravitational wave in the Fourier domain and find that the deviation from general relativity is dominated by the velocity birefringence effect of the gravitational wave.The result of the obtained gravitational wave waveform is also written into a parameterized post-Einstein formalism,and the corresponding post-Einstein parameters are given.In addition,we investigated the polarization of the primordial gravitational wave in the ghost-free parity-violating gravity.In the general theories of parity-violating gravity,one of the fundamental results is that the primordial gravitational waves produced during the slow-roll inflation are circularly polarized.We use the uniform asymptotic approximation to construct an approximate analytical solution for the mode function of the primordial gravitational waves during slow-roll inflation,and explicitly calculate the power spectrum and the corresponding circular polarization of the primordial gravitational waves.The contribution of the parity violating terms in the ghost-free parity-violating theory of gravity to the circular polarization is at the same order of magnitude as that in the Chern-Simons(CS)gravity.The circular polarization of the primordial gravitational waves is suppressed by the energy scale of parity violation in gravity,which is difficult to detect or constrain it using only the two-point statistics of the future cosmic microwave background radiation.