Transverse Perturbative Photon Flux Research Articles

Identifying extra high frequency gravitational waves generated from oscillons with cuspy potentials using deep neural networks

During oscillations of cosmology inflation around the minimum of a cuspy potential after inflation, the existence of extra high frequency gravitational waves (HFGWs) (∼GHz) has been proven effectively recently. Based on the electromagnetic resonance system for detecting such extra HFGWs, we adopt a new data processing scheme to identify the corresponding GW signal, which is the transverse perturbative photon fluxes (PPF). In order to overcome the problems of low efficiency and high interference in traditional data processing methods, we adopt deep learning to extract PPF and make some source parameters estimation. Deep learning is able to provide an effective method to realize classification and prediction tasks. Meanwhile, we also adopt anti-overfitting technique and make adjustment of some hyperparameters in the course of study, which improve the performance of classifier and predictor to a certain extent. Here the convolutional neural network (CNN) is used to implement deep learning process concretely. In this case, we investigate the classification accuracy varying with the ratio between the number of positive and negative samples. When such ratio exceeds to 0.11, the accuracy could reach up to 100%. Besides, we also investigate the classification accuracy with different amplitude of extra HFGWs. As a predictor, the mean relative error of parameters estimation decreases when the amplitude of extra HFGWs increases. Especially, when amplitude h(t) is in 10−31–10−30 the mean relative error reaches around 0.014. On the contrary, the mean relative error increases with frequency increasing in 108–1011 Hz. At the optimal resonance frequency 5 × 109 Hz, the mean relative error is 0.12. Then we also study the mean relative error varying with waist radius W0 of Gaussian beam, its optimal value is 0.138 when W0 is in (0.05 m, 0.1 m) approximately. Compared with classifiers and predictors using other machine learning algorithms, deep CNN for our datasets has higher accuracy and lower error.

The Effect of Inhomogeneous Background Magnetic Field on the Electromagnetic Response to High-Frequency Gravitational Waves

Transverse perturbative photon fluxes (PPFs) generated by an electromagnetic (EM) response system for high-frequency gravitational waves (HFGWs) detection, is a special physical effect related to some properties of HFGWs. Meanwhile, it is also influenced by the background static magnetic field. In this paper, based on the relationship between PPFs and the distribution of a Gaussian Beam with a homogeneous background static magnetic field, we study the distribution of PPFs and the width of positive signal photon fluxes with an inhomogeneous background static magnetic field. Under this condition, the strength of PPFs is enhanced significantly. Furthermore, by adjusting some parameters and an embedded non-coaxial coil in the background magnetic coil, the width of positive-signal photon fluxes would be enlarged greatly.

Electromagnetic Resonance of Astigmatic Gaussian Beam to the High Frequency Gravitational Waves**Supported by the National Natural Science Foundation of China under Grant Nos 11205254 and 61501069, and the Fundamental Research Funds for the Central Universities under Grant No 106112016CDJXY300002.

The high frequency gravitational waves (around 108−1012 Hz) could interact with a specially designed electromagnetic resonance system. It is found that the power of transverse perturbative photon flux (PPF) of an electromagnetic resonance system can be improved significantly by virtue of an astigmatic Gaussian beam. Correspondingly the signal-to-noise ratio (SNR) would also be improved. When the eccentric ratio of waist satisfying w0x: w0y > 1, the peak value of signal photon flux could be raised by 2–4 times with typical systematic parameters, while the background photon flux would be depressed. Therefore, the ratio of transverse PPF to background photon flux (i.e., SNR) can be further improved 3–8 times with dimensionless amplitude of relic gravitational wave ht = 10−36.

Signal photon flux generated by high-frequency relic gravitational waves**Supported by National Natural Science Foundation of China (11305181,11322545,11335012) and Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Y5KF181CJ1)

The power spectrum of primordial tensor perturbations increases rapidly in the high frequency region if the spectral index nt > 0. It is shown that the amplitude of relic gravitational waves ht(5 × 109 Hz) varies from 10−36 to 10−25 while nt 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 (5 × 109 Hz) varies from 1.40 × 10−4 s−1 to 2.85 × 107 s−1 while nt varies from −6.25 × 10−3 to 0.87. Correspondingly, the ratio of the transverse perturbative photon flux to the background photon flux varies from 10−28 to 10−16.

Resonance of Gaussian Electromagnetic Field to the High Frequency Gravitational Waves

We consider a Gaussian Beam (GB) resonant system for high frequency gravitational waves (HFGWs) detection. At present, we find the optimal signal strength in theory through setting the magnetic component of GB in a standard gaussian form. Under the synchro-resonance condition, we study the signal strength (i.e., transverse perturbative photon fluxes) from the relic HFGWs (predicted by ordinary inflationary model) and the braneworld HFGWs (from braneworld scenarios). Both of them would generate potentially detectable transverse perturbative photon fluxes (PPFs). Furthermore we find optimal system parameters and the relationship between frequency and effective width of energy fluxes accumulation.

Optimization of the Electromagnetic (EM) Perturbative Effects Produced by High-Frequency Gravitational Waves

For the relic gravitational waves in high frequency band, we survey the electromagnetic resonance effect generated from the high frequency gravitational waves, which can be described in the transverse perturbative photon fluxes. Under the fixed tensor-scalar ratio r = 0.2, spectral index nt = 0 and running index αt = 0.01, we discuss several properties and quantity changes of the transverse perturbative photon fluxes, which can be improved significantly through setting the longitudinal magnetic component of background EM field in the standard gaussian form, and wave impedance analysis on the transverse direction. Through the theoretical calculation, the transverse perturbative photon fluxes can reach up to 103s−1 with some optimal parameters such as waist of EM field W0 = 0.05m, initial stochastic phase of gravitational waves δ = (0.21 + n)π(n = 0,1,2...). Furthermore the interference of the background transverse photon fluxes can be removed completely through establishing a suitable wave impedance function.

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 νg = 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.

Perturbative photon fluxes generated by high-frequency gravitational waves and their physical effects

We consider the electromagnetic (EM) perturbative effects produced by high-frequency gravitational waves (HFGWs) in the GHz band in a special EM resonance system, which consists of fractal membranes, a Gaussian beam (GB) passing through a static magnetic field. Under the synchro-resonance condition, coherence modulation of the HFGWs to the preexisting transverse components of the GB is predicted to produce the transverse perturbative photon flux (PPF), which has three novel and important properties. (1) The PPF has a maximum at a longitudinal symmetrical surface of the GB where the transverse background photon flux (BPF) vanishes; (2) the resonant effect will be high sensitive to the propagating directions of the HFGWs; (3) the PPF reflected or transmitted by the fractal membrane exhibits a very small decay to be compared with a very large decay of the much stronger BPF. Such properties might provide a new way to distinguish and display the perturbative effects produced by the HFGWs. We also discuss the high-frequency asymptotic behavior of the relic GWs in the microwave band and the positive definite issues of their energy-momentum pseudo-tensor.