Relic gravitational waves with a running spectral index and its constraints at high frequencies

Abstract

We study the impact of a running index α t on the spectrum of relic gravitational waves (RGWs) over the whole range of frequency (10 −18 ∼ 10 10 ) Hz and reveal its implications in RGWs detections and in cosmology. Analytical calculations show that, although the spectrum of RGWs on low frequencies is less affected by α t = 0, but, on high frequencies, the spectrum is modified substantially. Investigations are made toward potential detections of the α t -modified RGWs for several kinds of current and planned detectors. The Advanced LIGO will likely be able to detect RGWs with α t ≥ 0 for inflationary models with the inflation index β = −1.956 and the tensor-scalar ratio r = 0.55. The future LISA can detect RGWs for a much broader range of (α t , β, r), and will have a better chance to break a degeneracy between them. Constraints on α t are estimated from several detections and cosmological observations. Among them, the most stringent one is from the bound of the Big Bang nucleosynthesis (BBN), and requires α t < 0.008 rather conservatively for any reasonable (β, r), preferring a nearly power-law spectrum of RGWs. In light of this result, one would expect the scalar running index α s to be of the same magnitude as α t , if both RGWs and scalar perturbations are generated by the same scalar inflation.

Electromagnetic response to high-frequency gravitational waves having additional polarization states: distinguishing and probing tensor-mode, vector-mode and scalar-mode gravitons

“…On the other hand, almost all mainstream inflationary theories and universe models predicted the primordial (relic) GWs, with spectrum distributed in a very wide frequency region, which may be from extreme-low-frequency range ( ∼ 10 −16 to ∼ 10 −17 Hz) to high-frequency band ( ∼ 10 8 to ∼ 10 10 Hz or higher) [25][26][27][28][29][30][31][32]. Especially, the peak region or partial peak region of the energy densities of the relic HFGWs predicted by the pre-big-bang models [27,28], the quintessential inflationary models [29][30][31], and the shortterm anisotropic inflation model [32], are just distributed in the typical microwave band ( ν ∼ 10 8 to ∼ 10 10 Hz), in which corresponding amplitudes might reach up to h ∼ 10 −26 to h ∼ 10 −30 .…”

“…This means that either the EM response to HFGWs in the transverse background EM fields [see Eqs. 24, (25), (26), (27), (28), (29)] or in the longitudinal background EM fields [see Eqs. (34) to (37)], it is all possible to detect or observe such an effect provided these background EM fields are distributed in a very wide region.…”

Quasi-B-mode generated by high-frequency gravitational waves and corresponding perturbative photon fluxes

“…Ordinary Quintessential Pre-big-bang Brane Interaction of HFGWs inlationary [9,10] inflationary [11][12][13] [ 5,14] Oscillation [15] astrophysical plasma with intense EM radiation [7] Frequency bands ∼ 10 8 − 10 10 Hz ∼ 10 9 − 10 10 Hz ∼ 10 9 − 10 10 Hz ∼ 10 8 erty, which can be not only expressed as B-mode polarization [3,26] in the CMB for very low-frequency relic GWs, but also quasi-B-mode distribution of perturbative photon fluxes in electromagnetic response for HFGWs. However, the duality and similarity between the B-mode of the CMB experiment for the very low frequency GWs and the quasi-B-mode of electromagnetic(EM) response for the HFGWs, almost have never been studied in the past.…”

“…For the relic GWs, A ⊕ = A(k g )/a(t), A ⊗ = A(k g )/a(t), [9,10] are the stochastic values of the amplitudes of the relic GWs in the laboratory frame of reference, ⊕ and ⊗ represent the ⊕-type and ⊗-type polarizations, and k g , ω g and a(t) are wave vector, angular frequency and the cosmology scale factor in the laboratory frame of reference, respectively. For the non-stochastic coherent GWs, A ⊕ and A ⊗ are constants.…”

Relic gravitational wave in universe and gravitational radiation of binary

“…二中频段, f=(10 3~1 0 3 ) Hz, 地面激光干涉探测 器LIGO [43] , VIRGO [44] , GEO [45] , KAGRA [46] , AIGO [47] , LIGO-India [48] 等 计 划 已 在 进 行 , 还 有 低 温 共 振 棒 EXPLORER [49] 、谐振腔MAGO [50] , 空间激光干涉仪 探 测 器 LISA [51] (f ~10 3 Hz) 等 探 测 器 . 我 们 计 算 表 明 [52] , LISA比LIGO更有可能探测到RGW. 天体剧烈 爆发过程辐射出的中高频引力波也在此频段.…”