General slow-roll spectrum for gravitational waves

Gong, Jinn‐Ouk

doi:10.1088/0264-9381/21/23/016

Cited by 33 publications

(52 citation statements)

References 23 publications

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“…From the table one can see that both results are essentially identically within the errors allowed. (5.13) and the expression from the Green function method [32] is (5.14) In Table III, we compare the amplitude and the numerical coefficients of the above two expressions for the tensor spectrum, and find that the two results are essentially the same. Now we turn to consider the spectral index, which can be written as In Table IV, we compare the numerical coefficients for the first-order and second-order terms in the tensor spectral index, with the results obtained by using the Green function method [32].…”

Section: Scalar Spectrum and Spectral Indexmentioning

confidence: 89%

“…Now we turn to consider the spectral index, which can be written as In Table IV, we compare the numerical coefficients for the first-order and second-order terms in the tensor spectral index, with the results obtained by using the Green function method [32]. With the scalar spectrum and tensor spectrum given in the above, we find that the tensor-to-scalar ratio is expressed as Finally, we note that, although we only compared our results with those obtained by the Green function method [31,32], our results are also comparable with results obtained by the WKB approximation method [33]. In fact, in Ref.…”

Section: Scalar Spectrum and Spectral Indexmentioning

confidence: 99%

“…(1.2) in the slow-roll inflation approximation. To test the consistency of our formulas, we further restrict ourselves to the relativistic case (b 1 =b 2 = 0), in which the power spectra, spectral indices, and the corresponding runnings of spectral indices have been calculated to the second-order by using the Green function method [31,32] 2 . We compare the results obtained by these two different methods, and show that they are essentially the same within the allowed errors.…”

Section: Introductionmentioning

confidence: 99%

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Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

et al. 2014

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The uniform asymptotic approximation method provides a powerful, systematically-improved, and error-controlled approach to construct accurate analytical approximate solutions of mode functions of perturbations of the Friedmann-Robertson-Walker universe, designed especially for the cases where the relativistic linear dispersion relation is modified after gravitational quantum effects are taken into account. These include models from string/M-Theory, loop quantum cosmology and Hořava-Lifshitz quantum gravity. In this paper, we extend our previous studies of the first-order approximations to high orders for the cases where the modified dispersion relation (linear or nonlinear) has only one-turning point (or zero). We obtain the general expressions for the power spectra and spectral indices of both scalar and tensor perturbations up to the third-order, at which the error bounds are 0.15%. As an application of these formulas, we calculate the power spectra and spectral indices in the slow-roll inflation with a nonlinear power-law dispersion relation. To check the consistency of our formulas, we further restrict ourselves to the relativistic case, and calculate the corresponding power spectra, spectral indices and runnings to the second-order. Then, we compare our results with the ones obtained by the Green function method, and show explicitly that the results obtained by these two different methods are consistent within the allowed errors.

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Section: Scalar Spectrum and Spectral Indexmentioning

confidence: 89%

Section: Scalar Spectrum and Spectral Indexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

et al. 2014

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“…The scalar power spectra in the slow-roll approximation to second-order is given by the expression [13,31] 23) where b ≃ 0.7296 is the Euler constant. The spectral index in the slow-roll approximation to second-order is…”

Section: Slow-roll Approximationmentioning

confidence: 99%

Computation of the power spectrum in chaotic ¼λϕ⁴inflation

Rojas

Villalba

2012

J. Cosmol. Astropart. Phys.

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Abstract. The phase-integral approximation devised by Fröman and Fröman, is used for computing cosmological perturbations in the quartic chaotic inflationary model. The phaseintegral formulas for the scalar power spectrum are explicitly obtained up to fifth order of the phase-integral approximation. As in previous reports [1-3], we point out that the accuracy of the phase-integral approximation compares favorably with the numerical results and those obtained using the slow-roll and uniform approximation methods.

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“…More recently, studies has been made on the effects of the detailed slow-roll inflationary on the relic GW [15] [16] [17], and on the other post-inflationary physical effects on the relic GW [18]. A constraint on the the tensor-to-scalar ratio r has been derived, using the CMB-galaxy cross-correlation [19].…”

Section: Introductionmentioning

confidence: 99%

An exact analytic spectrum of relic gravitational waves in an accelerating universe

Zhang

Er²,

Xia³

et al. 2006

Class. Quantum Grav.

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An exact analytic calculation is presented for the spectrum of relic gravitational waves in the scenario of accelerating Universe Ω Λ + Ω m = 1. The spectrum formula contains explicitly the parameters of acceleration, inflation, reheating, and the (tensor/scalar) ratio, so that it can be employed for a variety of cosmological models. We find that the spectrum depends on the behavior of the present accelerating expansion. The amplitude of gravitational waves for the model Ω Λ = 0.65 is about ∼ 50% greater than that of the model Ω Λ = 0.7, an effect accessible to the designed sensitivities of LIGO and LISA. The spectrum sensitively depends on the inflationary models with a(τ ) ∝ |τ | 1+β , and a larger β yields a flatter spectrum, producing more power. The current LIGO results rule out the inflationary models of β ≥ −1.8. The LIGO with its design sensitivity and the LISA will also be able to test the model of β = −1.9. We also examine the constraints on the spectral energy density of relic gravitational waves. Both the LIGO bound and the nucleosynthesis bound point out that the model β = −1.8 is ruled out, but the model β = −2.0 is still alive. The exact analytic results also confirm the approximate spectrum and the numerical one in our previous work.PACS 98.80.Es, 04.62+v,

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General slow-roll spectrum for gravitational waves

Abstract: We derive the power spectrum P ψ (k) of the gravitational waves produced during general classes of inflation with second order corrections. Using this result, we also derive the spectrum and the spectral index in the standard slow-roll approximation with new higher order corrections.

Cited by 33 publications

References 23 publications

Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

Computation of the power spectrum in chaotic ¼λϕ⁴inflation

An exact analytic spectrum of relic gravitational waves in an accelerating universe

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General slow-roll spectrum for gravitational waves

Abstract: We derive the power spectrum P ψ (k) of the gravitational waves produced during general classes of inflation with second order corrections. Using this result, we also derive the spectrum and the spectral index in the standard slow-roll approximation with new higher order corrections.

Cited by 33 publications

References 23 publications

Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

Gravitational quantum effects on power spectra and spectral indices with higher-order corrections

Computation of the power spectrum in chaotic ¼λϕ4inflation

An exact analytic spectrum of relic gravitational waves in an accelerating universe

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Computation of the power spectrum in chaotic ¼λϕ⁴inflation