Improved calculation of relic gravitational waves

In this paper, we have improved the calculation of the relic gravitational waves (RGW) in two aspects. First, we investigate the transfer function by taking into consideration the redshift-suppression effect, the accelerating expansion effect, the damping effect of free-streaming relativistic particles, and the damping effect of cosmic phase transition, and give a simple approximate analytic expression, which clearly illustrates the dependence on the cosmological parameters. Second, we develop a numerical method to calculate the primordial power spectrum of RGW in a very wide frequency range, where the observed constraints on $n_{\rm s}$ (the scalar spectral index) and $P_{\rm S}(k_0)$ (the amplitude of primordial scalar spectrum) and the Hamilton--Jacobi equation are used. This method is applied to two kinds of inflationary models, which satisfy the current constraints on $n_{\rm s}$, $\alpha$ (the running of $n_{\rm s}$) and $r$ (the tensor--scalar ratio). We plot them in the $r-{\it\Omega}_{\rm g}$ diagram, where ${\it\Omega}_{\rm g}$ is the strength of RGW, and study their measurements from the cosmic microwave background (CMB) experiments and laser interferometers.     

Signal photon flux generated by high-frequency relic gravitational waves

The power spectrum of primordial tensor perturbations Vt increases rapidly in the high frequency region if the spectral index n_t 0.It is shown that the amplitude of relic gravitational waves ht(5×10~9 Hz) varies from 10~(-36)to 10~(-25) while n_t varies from-6.25×10~(-3) to 0.87.A high frequency gravitational wave detector proposed by F.-Y.Li detects gravitational waves through observing the perturbed photon flux that is generated by interaction between relic gravitational waves and electromagnetic field.It is shown that the perturbative photon flux N_x~1(5×10~9 Hz)varies from 1.40×10~(-4) s~(-1) to 2.85×10~7 s~(-1) while n_t varies from-6.25×10~(-3) to 0.87.Correspondingly,the ratio of the transverse perturbative photon flux N_x~1 to the background photon flux varies from 10~(-28) to 10~(-16).     

Information on the inflaton field from the spectrum of relic gravitational waves

After a review of a traditional analysis, it is shown a variation of a more recent treatment on the spectrum of relic gravitational waves (GWs). Then, a connection between the two different treatments will be analysed. Such a connection permits to obtain an interesting equation for the inflaton field. This equation gives a value that agrees with the slow roll condition on inflation.     

Erratum to: Information on the inflaton field from the spectrum of relic gravitational waves

After a review of a traditional analysis, it is shown a variation of a more recent treatment on the spectrum of relic gravitational waves (GWs). Then, a connection between the two different treatments will be analysed. Such a connection permits to obtain an interesting equation for the inflaton field. This equation gives a value that agrees with the slow roll condition on inflation.     

Detecting warm dark matter by the stochastic gravitational waves

正NANOGrav has recently reported the detection of a common-spectrum process via the time-of-arrival data of47 millisecond pulsars [1],which could be interpreted by a stochastic gravitational wave background (SGWB) in the nanohertz frequency band (f~10~(-9) Hz) with energy density parameter Q_(GW)~10~(-9).Despite the vague quadrupole correlation that obstructs the identification of gravitational waves,this report hints the possibility of some new physics at around or below 100 MeV that can generate nanohertz gravitational waves by,for instance,the first order phase transition(FOPT).     

Weak gravitational lensing of the CMB

Weak gravitational lensing has several important effects on the cosmic microwave background (CMB): it changes the CMB power spectra, induces non-Gaussianities, and generates a B-mode polarization signal that is an important source of confusion for the signal from primordial gravitational waves. The lensing signal can also be used to help constrain cosmological parameters and lensing mass distributions. We review the origin and calculation of these effects. Topics include: lensing in General Relativity, the lensing potential, lensed temperature and polarization power spectra, implications for constraining inflation, non-Gaussian structure, reconstruction of the lensing potential, delensing, sky curvature corrections, simulations, cosmological parameter estimation, cluster mass reconstruction, and moving lenses/dipole lensing.     

遗迹引力波对宇宙微波背景辐射极化的影响

根据宇宙大爆炸理论的预言,宇宙经历了由暴涨阶段到辐射阶段到物质阶段再到如今的加速膨胀阶段.在辐射阶段所残留的退耦的自由光子便形成了现在人们所观测到的宇宙微波背景辐射.如果没有扰动,微波背景辐射将是各向同性的,但是在宇宙形成的初期存在各种各样的扰动,因此宇宙微波背景辐射呈现各向异性.针对由遗迹引力波对微波背景辐射极化所产生的各向异性的影响,重点讨论电场型极化和磁场型极化. 关键词： 遗迹引力波 微波背景辐射 极化各向异性     

Testing metric-affine f(R)-gravity by relic scalar gravitational waves

We discuss the emergence of scalar gravitational waves in metric-affine f(R)-gravity. Such a component allows to discriminate between metric and metric-affine theories The intrinsic meaning of this result is that the geodesic structure of the theory can be discriminated. We extend the formalism of cross-correlation analysis, including the additional polarization mode, and calculate the detectable energy density of the spectrum for cosmological relic gravitons. The possible detection of the signal is discussed against the sensitivities of the VIRGO, LIGO and LISA interferometers.     

Probing the origin of our universe through primordial gravitational waves by Ali CMB project

正Gravitational waves(GW),which were predicted by Einstein in 1916 based on the classical theory of General Relativity(GR),were recently detected by LIGO[1].This breakthrough is expected to initiate a novel probe of cosmology,the nature of gravity as well as fundamental physics.In general,signals of GWs can be classified into two categories,which     

Detecting super-Nyquist-frequency gravitational waves using a pulsar timing array

The maximum frequency of gravitational waves(GWs) detectable with traditional pulsar timing methods is set by the Nyquist frequency( fNy) of the observation. Beyond this frequency, GWs leave no temporal-correlated signals; instead, they appear as white noise in the timing residuals. The variance of the GW-induced white noise is a function of the position of the pulsars relative to the GW source. By observing this unique functional form in the timing data, we propose that we can detect GWs of frequency f_(Ny)(super-Nyquist frequency GWs; SNFGWs). We demonstrate the feasibility of the proposed method with simulated timing data.Using a selected dataset from the Parkes Pulsar Timing Array data release 1 and the North American Nanohertz Observatory for Gravitational Waves publicly available datasets, we try to detect the signals from single SNFGW sources. The result is consistent with no GW detection with 65.5% probability. An all-sky map of the sensitivity of the selected pulsar timing array to single SNFGW sources is generated, and the position of the GW source where the selected pulsar timing array is most sensitive to is λ_s =.0.82,β_s =-1.03(rad); the corresponding minimum GW strain is h = 6.31 × 10~(-11) at f = 1 × 10~(-5) Hz.     

Massive relic gravitational waves from f(R) theories of gravity: production and potential detection

The production of a stochastic background of relic gravitational waves is well known in various works in the literature, where, by using the so called adiabatically-amplified zero-point fluctuations process, it has been shown how the standard inflationary scenario for the early universe can in principle provide a distinctive spectrum of relic gravitational waves. In this paper, it is shown that, in general, f(R) theories of gravity produce a third massive polarization of gravitational waves and the primordial production of this polarization is analyzed adapting the adiabatically-amplified zero-point fluctuations process at this case. In this way, previous results, where only particular cases of f(R) theories have been analyzed, will be generalized. The presence of the mass could also have important applications in cosmology, because the fact that gravitational waves can have mass could give a contribution to the dark matter of the Universe. An upper bound for these relic gravitational waves, which arises from the WMAP constrains, is also mentioned. At the end of the paper, the potential detection of such massive gravitational waves using interferometers like Virgo and LIGO is discussed.     

Detection of relic gravitational waves in thermal case by using Adv.LIGO data of GW150914

The thermal spectrum of relic gravitational waves enhances the usual spectrum. Our analysis shows that there exist some chances for detection of the thermal spectrum in addition to the usual spectrum by comparison with sensitivity of Adv.LIGO of GW150914 and detector based on the maser light. The behavior of the inflation and reheating stages are often known as power law expansion like \(S(\eta )\propto \eta ^{1+\beta }\), \(S(\eta )\propto \eta ^{1+\beta _s}\), respectively, with constraints \(1+\beta <0, 1+\beta _{s}>0\). The \(\beta \) and \(\beta _s\) have an unique effect on the shape of the spectrum. We find some values of the \(\beta \) and \(\beta _s\) by considering the mentioned comparison. As obtained, the results give us more information as regards the evolution of inflation and reheating stages.     

The signal photon flux,background photons and shot noise in electromagnetic response of high-frequency relic gravitational waves

On the basis of the electromagnetic response of high frequency relic gravitational waves (HFRGWs), we research on more accurate calculation of signal (i.e. transverse perturbative photon flux (PPF)) and background photons flux (BPF) in the sycro-resonance electromagnetic system, which consists of Gaussian beam (GB), a static magnetic field and fractal membranes. According to the relationship between frequency of gravitational waves and its dimensionless amplitude, we focus on the HFRGWs with ν _g  = 2.9 GHz, h ~ 10^?30 in the pre-big bang and quintessential inflationary models. The results show the peak value of the transverse BPF (~ 10²⁰ s^?1) is around |x| = 0.08 m, where |x| is the transverse distance to the longitudinal symmetrical surface of the GB, while the maximum transverse PPF always appears at x = 0 (\({N^{(1)}_{x} \sim 2.60\times10^{2}\,{\rm s}^{-1}}\) with the optimal phase difference between the GB and the resonant component of the HFRGWs δ = (n + 0.9)π, n = 0, 1, 2 . . .). However, the observable PPF should be ~ 1.19 × 10² s^?1 because of the stochastic nature of the HFRGWs’ phase. Since the decay speed of BPF is much quicker than PPF, it is hopeful to figure out the signal in some optimal regions. Moreover, we compare the decay speed of BPF and PPF in nature mode, and find the threshold value of x where PPF exceeds to BPF. It demonstrates that the limitation of our detection sensitivity comes from the strength of PPF rather than swamping by BPF. On the other hand, with the fractal membrane, the comparison between BPF and PPF provides the optimal detection area \({x\in[0.28,1]}\) m. In addition, through the calculation of shot noise and conservative estimation, we find that our sensitivity is h = 10^?26 in 4 months signal accumulate time.     

A subquantum origin of gravitational waves

The structure of the Dirac equation wavefunction reveals subquantum opposite rotations as the basis of the equation itself as well as of its predictions. We also consider briefly an experimental check of mass-energy density dependent phenomena, based on gravitational waves.     

Nonlinear gravitational waves in plasma

An exact solution is obtained for the relativistic collisionless kinetic equations describing a test plasma in the field of a strong plane gravitational wave. The gravitational wave induces in the plasma a longitudinal electric current whose amplitude is maximum at temperatures Te ip m_ec². The interaction of gravitational waves with a system consisting of Boltzmann ions and degenerate electrons is also considered.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 20–24, July 1981.The authors thank G. G. Ivanov for a number of valuable comments.     

Conformally invariant gravitational waves in a modified gravitational theory

International Journal of Theoretical Physics - An attempt is made to obtain a conformally invariant gravitational wave equation in an isotropic background universe by modifying the Einstein field...     

Toward the detection of gravitational waves

Detection of the gravitational waves predicted by the theory of general relativity is still an open experimental venture. Several detectors designed for the frequency range between 10 Hz and 10 kHz are being built. Their expected sensitivity is near the required level for the detection of realistic astrophysical events. The expected signals and the main sources of noise are discussed together with perspectives in detector improvement.     

Wide-band measurement of gravitational waves: the VIRGO project

Summary To detect gravitational waves (GW) in a frequency range between 10 Hz and few kHz a ground-based antenna was designed by the French-Italian collaboration VIRGO. The antenna is a 3 km long interferometer with special suspensions for the optical components, planned to reduce the seismic noise in order to reach the low-frequency region. Results on the seismic isolation devices are given together with some preliminary results on the use of permanent magnets on the VIRGO suspensions. Paper presented at the V Cosmic Physics National Conference, S. Miniato, November 27–30, 1990.     

On the pressure of gravitational waves

A system of coupled point masses under the influence of gravitational waves is considered. By means of the geodesic deviation equation as the equation of motion it is shown, taking into account the second order small terms, that there exist forces which cause the acceleration of the system in the longitudinal direction. The longitudinal force is due to the fact that simultaneously with energy momentum is also absorbed from waves. It is proved directly on the basis of the equations of motion of the point masses that the energy and momentum absorbed by the test system obey the special relativistic relationship of a zero rest mass particle. The case when the Weber oscillator moves at a relativistic speed with respect to the source of gravitational waves is also examined. In this case, the absorption of energy and momentum by the Weber oscillator is much larger or smaller compared to the stationary situation.     

On the dispersion of gravitational waves

The propagation of gravitational waves in cold matter has been analyzed in the geometrical-optics approximation showing no difference from the propagationin vacuum. In a cosmological background a plasmalike dispersion relation has been shown to appear in the postgeometrical optics approximation only. A qualitative discussion of the physical meaning of the present result is given and compared with previous works.