Covariant Analysis of Dynamics and of CBR Anisotropy

Ellis, George; Dunsby, Peter K. S.

doi:10.1007/978-94-011-5046-0_1

Cited by 5 publications

(16 citation statements)

References 17 publications

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“…2), and the approximate stationarity of the potential Φ k in the matter dominated era of a K = 0 universe. This effect was noted recently by Ellis and Dunsby [6], and was also discussed by Hu and Sugiyama [14]. Ellis and Dunsby suggested that this zero in the "monopole" contribution should be observable as a zero in the CMB power spectrum on angular scales ≃ 50 ′ .…”

Section: Cmb Anisotropy In a Universe Dominated By Baryons At Recombisupporting

confidence: 56%

“…The second "monopole" term, −Φ k Q (k) /3, is the usual Sachs-Wolfe contribution to the temperature anisotropy [1], whose effect is modified on small scales by the third and fourth "monopole" terms. As noted by Ellis and Dunsby [6], the third term is rarely seen in analytic calculations of the Sachs-Wolfe effect, although it is present in Panek's result [10]. The omission arises from subtle gauge effects at the last scattering surface which we discuss in Section 5.…”

Section: Cmb Anisotropy In a Universe Dominated By Baryons At Recombimentioning

confidence: 73%

“…The scalar S is a local scale factor satisfyinġ 6) which removes the effects of the expansion from the spatial gradients defined above.…”

Section: Covariant Cosmological Perturbationsmentioning

confidence: 99%

“…However, gauge issues still arise in connection with the definition of the temperature perturbation and the placement of the last scattering surface [2,6]. The latter gauge issues do not arise at first-order in numerical calculations which integrate the Boltzmann equation in a perturbed universe, since the visibility function (which determines the position of the last scattering surface) multiplies first-order variables giving only a second-order error from the use of a zero-order approximation to the visibility [7].…”

Section: Introductionmentioning

confidence: 99%

“…This contribution is often missed in Sachs-Wolfe type calculations through an incorrect treatment of gauge effects at the last scattering surface [6]. (Equivalently, the term is often missed through a failure to recognise the direction-dependence of the "expected temperature" used to define the temperature perturbation in many calculations.)…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations

Challinor

Lasenby

1998

Phys. Rev. D

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We present a new, fully covariant and manifestly gauge-invariant expression for the temperature anisotropy in the cosmic microwave background radiation resulting from scalar perturbations. We pay particular attention to gauge issues such as the definition of the temperature perturbation and the placing of the last scattering surface. In the instantaneous recombination approximation, the expression may be integrated up to a Rees-Sciama term for arbitrary matter descriptions in flat, open and closed universes. We discuss the interpretation of our result in the baryon-dominated limit using numerical solutions for conditions on the last scattering surface, and confirm that for adiabatic perturbations the dominant contribution to the anisotropy on intermediate scales (the location of the Doppler peaks) may be understood in terms of the spatial inhomogeneity of the radiation temperature in the baryon rest frame. Finally, we show how this term enters the usual Sachs-Wolfe type calculations (it is rarely seen in such analyses) when subtle gauge effects at the last scattering surface are treated correctly.

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Section: Cmb Anisotropy In a Universe Dominated By Baryons At Recombisupporting

confidence: 56%

Section: Cmb Anisotropy In a Universe Dominated By Baryons At Recombimentioning

confidence: 73%

“…The scalar S is a local scale factor satisfyinġ 6) which removes the effects of the expansion from the spatial gradients defined above.…”

Section: Covariant Cosmological Perturbationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations

Challinor

Lasenby

1998

Phys. Rev. D

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Recent Developments in the Calculation of CMB Anisotropies

Challinor

Lasenby

1998

Current Topics in Astrofundamental Physics: Primordial Cosmology

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We discuss three recent developments in the calculation of Cosmic Microwave Background (CMB) anisotropies. We begin with a discussion of the relativistic corrections to the Sunyaev-Zel'dovich effect. By extending the Kompaneets equation to include relativistic effects, we are able to to derive simple analytic forms for the spectral changes due to the thermal Sunyaev-Zel'dovich effect. Relativistic corrections result in a small reduction in the amplitude of the effect over the Rayleigh-Jeans region, which for a typical cluster temperature of 8 keV, amounts to a correction downwards to the value of the Hubble constant derived from combined X-ray and Sunyaev-Zel'dovich information by about 5 percent. Our second topic is a discussion of covariant kinetic theory methods for the gauge-invariant calculation of primordial CMB anisotropies. We present a covariant version of the Boltzmann equation, which we use to derive a set of covariant equations for the gauge-invariant variables in a Cold Dark Matter (CDM) model, which are independent of the background curvature and type of perturbation. Equations describing a particular type of perturbation are obtained readily from this set, as we demonstrate for scalar perturbations in a K = 0 universe. By integrating the covariant Boltzmann equations along the line of sight, and using the instantaneous recombination approximation, we obtain an expression for the large scale anisotropy which agrees with an expression derived recently by Dunsby. Finally, we discuss some recent accurate calculations of the CMB anisotropy in global defect models. In such models, the effect of vorticity generation by the causal sources proves to be significant, leading to a suppression of acoustic peaks. The result is that global defect models of structure formation may already be at variance with the growing volume of CMB (and large scale structure) data.

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Cosmic Microwave Background Anisotropies in the Cold Dark Matter Model: A Covariant and Gauge‐invariant Approach

Challinor¹,

Lasenby²

1999

ApJ

114

151

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We present a fully covariant and gauge-invariant calculation of the evolution of anisotropies in the Cosmic Microwave Background (CMB) radiation. We use the physically appealing covariant approach to cosmological perturbations, which ensures that all variables are gauge-invariant and have a clear physical interpretation. We derive the complete set of frame-independent linearised equations describing the (Boltzmann) evolution of anisotropy and inhomogeneity in an almost Friedmann-Robertson-Walker (FRW) Cold Dark Matter (CDM) universe. These equations include the contributions of scalar, vector and tensor modes in a unified manner. Frame-independent equations for scalar and tensor perturbations, which are valid for any value of the background curvature, are obtained straightforwardly from the complete set of equations. We discuss the scalar equations in detail, including the integral solution and relation with the line of sight approach, analytic solutions in the early radiation dominated era, and the numerical solution in the standard CDM model. Our results confirm those obtained by other groups, who have worked carefully with non-covariant methods in specific gauges, but are derived here in a completely transparent fashion.

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Covariant Analysis of Dynamics and of CBR Anisotropy

Cited by 5 publications

References 17 publications

Covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations

Covariant and gauge-invariant analysis of cosmic microwave background anisotropies from scalar perturbations

Recent Developments in the Calculation of CMB Anisotropies

Cosmic Microwave Background Anisotropies in the Cold Dark Matter Model: A Covariant and Gauge‐invariant Approach

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