Relic gravitational waves in the accelerating Universe

Zhang, Yang; Yuan, Yefei; Zhao, Wen; Ying-Tian, Chen

doi:10.1088/0264-9381/22/7/011

Cited by 92 publications

(249 citation statements)

References 28 publications

(39 reference statements)

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“…There are three types of couplings: scalar-scalar, scalar-tensor, and tensor-tensor in (23), (28), and (34). In order to deal with these equations separately, we split the 2nd-order perturbations into three parts according to the type of couplings…”

Section: The Second-order Perturbed Einstein Equationsmentioning

confidence: 99%

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

Wang¹,

Zhang²

2017

Phys. Rev. D

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We present a systematic study of the 2nd-order scalar, vector and tensor metric perturbations in the Einstein-de Sitter Universe in synchronous coordinates. For the scalar-scalar coupling between 1st-order perturbations, we decompose the 2nd-order perturbed Einstein equation into the respective field equations of 2nd-order scalar, vector, and tensor perturbations, and obtain their solutions with general initial conditions. In particular, the decaying modes of solution are included, the 2nd-order vector is generated even if the 1st-order vector is absent, and the solution of the 2nd-order tensor corrects that in literature. We perform general synchronous-to-synchronous gauge transformations up to 2nd-order generated by a 1st-order vector field ξ (1)µ and a 2nd-order ξ (2)µ . All the residual gauge modes of 2nd-order metric perturbations and density contrast are found, and their number is substantially reduced when the transformed 3-velocity of dust is set to zero. Moreover, we show that only ξ (2)µ is effective in carrying out 2nd order transformations that we consider, because ξ(1)µ has been used in obtaining the 1st-order perturbations. Holding the 1st-order perturbations fixed, the transformations by ξ (2)µ on the 2nd-order perturbations have the same structure as those by ξ(1)µ on the 1st-order perturbations.PACS numbers: 98.80.Hw, 04.25.Nx

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Section: The Second-order Perturbed Einstein Equationsmentioning

confidence: 99%

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

Wang¹,

Zhang²

2017

Phys. Rev. D

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“…By numerically solving the Friedmann equation in both models, we plot the scale factor a(t) in Fig.2, showing that the ratio of scale factors at present is a(τ H ) ΛCDM /a(τ H ) CDM ≃ 1.8. As is known [1,3], for wavelengths shorter than the horizon the modes decay as h k (τ ) ∝ 1/a(τ ), so the CDM model would predict an amplitude of RGWs higher than the ΛCDM model. This is indeed confirmed by our calculation including the QCD transition and the e + e − annihilation, and the ratio is…”

Section: Analytical Solution Of Rgwsmentioning

confidence: 99%

“…(95% CL) [37].. From the relation n s = 2β + 5 [1,3], the inflation index β = −2.02 for n s = 0.951. As Note that the constant A is directly proportional to A 0 in Eq.…”

Section: Spectrum Of Relic Gravitational Wavesmentioning

confidence: 99%

“…Watanabe and Komatsu [30] investigated these effects with more details, and gave a numerical solution of the energy density spectrum of RGWs. In these works, the important effect of the accelerating expansion of the present universe [3] has not been included, neither the effects of inflation and reheating. Moreover, to show the prospects of detecting RGWs at the laser interferometers gravity-wave detection, an explicit demonstration of the current spectrum of RGWs itself and its direct comparison with the sensitivity curve of gravity-wave detection are also needed.…”

Section: Introductionmentioning

confidence: 99%

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Modifications by the QCD transition ande+e−annihilation of the analytic spectrum of relic gravitational waves in the accelerating universe

et al. 2008

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As predicted by quantum chromodynamics(QCD), around T ∼ 190 MeV in the early universe, the QCD transition occurs during which the quarks are combined into the massive hadrons.This process reduces the effective relativistic degree of freedom, and causes a change in the expansion behavior of the universe. Similarly, the e + e − annihilation occurred around T ∼ 0.5 Mev has the same kind of effect. Besides, the dark energy also drives the present stage accelerating expansion. We study these combined effects on the relic gravitational waves (RGWs). In our treatment, the QCD transition and the e + e − annihilation, each is respectively represented by a short period of expansion inserted into the radiation era. Incorporating these effects, the equation of RGWs is analytically solved for a spatially flat universe, evolving from the inflation up to the current acceleration, and the spectrum of RGWs is obtained, covering the whole range of frequency > 10 −19 Hz. It is found that the QCD transition causes a reduction of the amplitude of RGWs by ∼ 20% in the range > 10 −9 Hz, and the e + e − annihilation causes a reduction ∼ 10% in the range > 10 −12 Hz. In the presence of the dark energy, the combination of the QCD transition and the e + e − annihilation, causes a larger reduction of the amplitude by ∼ 30% for the range > 10 −9 Hz, which covers the bands of operation of LIGO and LISA. By analysis, it is shown that RGWs will be difficult to detect by the present LIGO, but can be tested by LISA for certain inflationary models.

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“…From the consideration of physics of the Universe, we take the following specifications [30] − [32]:…”

Section: Rgw In the Accelerating Universementioning

confidence: 99%

Relic Gravitational Waves and CMB Polarization in the Accelerating Universe

Zhang

Zhao

Xia

et al. 2008

Int. J. Mod. Phys. D

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In this paper we briefly present our works on the relic gravitational waves (RGW) and the CMB polarization in the accelerating universe. The spectrum of RGW has been obtained, showing the influence of the dark energy. Compared with those from non-accelerating models, the shape of the spectrum is approximately similar, nevertheless, the amplitude of RGW now acquires a suppressing factor of the ratio of matter over dark energy ∝ Ω m /Ω Λ ∼ 0.4 over almost the whole range of frequencies. The RGW spectrum is then used as the source to calculate the spectra of CMB polarization. By a two half Gaussian function as an approximation to the visibility function during the photon decoupling, both the "electric" and "magnetic" spectra have been analytically derived, which are quite close to the numerical ones. Several physical elements that affect the spectra have been examined, such as the decoupling process, the inflation, the dark energy, the baryons, etc.

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Relic gravitational waves in the accelerating Universe

Cited by 92 publications

References 28 publications

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge

Modifications by the QCD transition ande+e−annihilation of the analytic spectrum of relic gravitational waves in the accelerating universe

Relic Gravitational Waves and CMB Polarization in the Accelerating Universe

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