Covariant and gauge-invariant formulation of the Sachs-Wolfe effect

Russ, Heinz; Söffel, M.; Chun, Xu; Dunsby, Peter K. S.

doi:10.1103/physrevd.48.4552

Cited by 9 publications

(9 citation statements)

References 17 publications

(13 reference statements)

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“…This improves on earlier work by Russ et al [24], where a similar formula was obtained by taking first order variations of the redshift.…”

Section: A Gauge -Invariant Measure Of Cmb Temperature Anisotropiessupporting

confidence: 71%

“…In this paper we have calculated a fully covariant formula for the CMB temperature anisotropy improving on earlier work by Russ et al [24]. This formulation has a number of distinct advantages over the more standard approaches as it is independent of gauge conditions, non -local splittings of spacetime, and related Fourier decompositions of perturbations around a FRW metric.…”

Section: Resultsmentioning

confidence: 99%

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A fully covariant description of cosmic microwave background anisotropies

Dunsby

1997

Class. Quantum Grav.

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Abstract. Starting from the exact non -linear description of matter and radiation, a fully covariant and gauge -invariant formula for the observed temperature anisotropy of the cosmic microwave background (CBR) radiation, expressed in terms of the electric (E ab ) and magnetic (H ab ) parts of the Weyl tensor, is obtained by integrating photon geodesics from last scattering to the point of observation today. This improves and extends earlier work by Russ et al where a similar formula was obtained by taking first order variations of the redshift. In the case of scalar (density) perturbations, E ab is related to the harmonic components of the gravitational potential Φ k and the usual dominant Sachs -Wolfe contribution δT R /T R ∼ Φ k to the temperature anisotropy is recovered, together with contributions due to the time variation of the potential (ReesSciama effect), entropy and velocity perturbations at last scattering and a pressure suppression term important in low density universes. We also explicitly demonstrate the validity of assuming that the perturbations are adiabatic at decoupling and show that if the surface of last scattering is correctly placed and the background universe model is taken to be a flat dust dominated Friedmann -Robertson -Walker model (FRW), then the large scale temperature anisotropy can be interpreted as being due to the motion of the matter relative to the surface of constant temperature which defines the surface of last scattering on those scales.

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“…This improves on earlier work by Russ et al [24], where a similar formula was obtained by taking first order variations of the redshift.…”

Section: A Gauge -Invariant Measure Of Cmb Temperature Anisotropiessupporting

confidence: 71%

Section: Resultsmentioning

confidence: 99%

A fully covariant description of cosmic microwave background anisotropies

Dunsby

1997

Class. Quantum Grav.

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“…Since power-law inflation is known to produce one of the strongest tensor signals during slow-roll [42] the signal to noise (due to cosmic variance and instrument) ratio for the tensor component in the CMB may be significantly larger than previously hoped [43]. The CMB anisotropy from a tensor signal is [34,35]:…”

Section: Chaotic Inflation and Dualitymentioning

confidence: 99%

Preheating–gravitational-wave correspondence

Bassett

1997

Phys. Rev. D

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The gravitational wave equations form a parametric resonance system during oscillatory reheating after inflation, when cast in terms of the electric and magnetic parts of the Weyl tensor. This is in direct analogy with preheating. For chaotic inflation with a quadratic potential, this analogy is exact. The resulting amplification of the gravitational wave spectrum begins in the broad-resonance regime for chaotic inflation but quickly moves towards narrow resonance. This increases the amplitude and breaks the scale invariance of the tensor spectrum generated during inflation, an effect which may be detectable. The parametric amplification is absent, however, in first-order phase transition models and ''warm'' inflationary models with continuous entropy production.

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“…Critical to that comparison is the accurate theoretical calculation of the anisotropies. Since the pioneering work of Sachs and Wolfe [2], the theoretical anisotropies have been refined and recalculated using different formalisms many times (see, e.g., [3,4,5,6,7,8,9]). Accurate calculations are now readily available via public code packages such as camb [10,11].…”

Section: Introductionmentioning

confidence: 99%

Gauging the cosmic microwave background

2008

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We provide a new derivation of the anisotropies of the cosmic microwave background (CMB), and find an exact expression that can be readily expanded perturbatively. Close attention is paid to gauge issues, with the motivation to examine the effect of super-Hubble modes on the CMB. We calculate a transfer function that encodes the behaviour of the dipole, and examine its long-wavelength behaviour. We show that contributions to the dipole from adiabatic super-Hubble modes are strongly suppressed, even in the presence of a cosmological constant, contrary to claims in the literature. We also introduce a naturally defined CMB monopole, which exhibits closely analogous long-wavelength behaviour. We discuss the geometrical origin of this super-Hubble suppression, pointing out that it is a simple reflection of adiabaticity, and hence argue that it will occur regardless of the matter content.Comment: 17 pages, 5 figures; minor changes; version accepted to Phys. Rev.

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Covariant and gauge-invariant formulation of the Sachs-Wolfe effect

Cited by 9 publications

References 17 publications

A fully covariant description of cosmic microwave background anisotropies

A fully covariant description of cosmic microwave background anisotropies

Preheating–gravitational-wave correspondence

Gauging the cosmic microwave background

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