Looking for the imprints of nonlinear structures on the cosmic microwave background

Fullana, M. J.; Arnau, J. V.; Sáez, D.

doi:10.1016/s0083-6656(98)00032-4

Cited by 2 publications

(4 citation statements)

References 76 publications

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“…Moreover, we have the following papers about CMB anisotropies in LTB universes: [51][52][53][54][55][56]. The reader may find comprehensive explanations, including important consequences of previous applications performed with our algorithm, in the book [17] and in the review paper of the Ref.…”

Section: Resultsmentioning

confidence: 99%

“…The reader may find comprehensive explanations, including important consequences of previous applications performed with our algorithm, in the book [17] and in the review paper of the Ref. [18]. The latter paper also outlines an overview of CMB and CMB anisotropies research so far.…”

Section: Resultsmentioning

confidence: 99%

“…Theoretically, one only has to compute K 4 D by integrating (backwards in time) the system of equations. In any way, it can be supposed that problems with the stability of the system will appear in the case where you need to obtain δ B of the order of 10 −5 with Equation (18), which should be the precision required in K 4 D to obtain at least seven correct decimals in the quotient and to be able to guarantee that δ B has at least three correct significative digits. If what one tries to do is to obtain quasi null anisotropy (FLRW limit), the precision requirements should be even greater.…”

Section: Resolution Of the Null Geodesics Edosmentioning

confidence: 99%

“…These null geodesics describe the Cosmic Microwave Background (CMB) Radiation. We numerically compute the anisotropies on CMB caused by a great inhomogeneity in the universe [11][12][13][14][15][16][17][18]. A detailed explanation of the main physical results and where they were published are presented in Section 8.…”

Section: Introductionmentioning

confidence: 99%

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Resolution of Initial Value Problems of Ordinary Differential Equations Systems

Córdoba

Alfonso

2022

Mathematics

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In this work, we present some techniques applicable to Initial Value Problems when solving a System of Ordinary Differential Equations (ODE). Such techniques should be used when applying adaptive step-size numerical methods. In our case, a Runge-Kutta-Fehlberg algorithm (RKF45) has been employed, but the procedure presented here can also be applied to other adaptive methods, such as N-body problems, as AP3M or similar ones. By doing so, catastrophic cancellations were eliminated. A mathematical optimization was carried out by introducing the objective function in the ODE System (ODES). Resizing of local errors was also utilised in order to adress the problem. This resize implies the use of certain variables to adjust the integration step while the other variables are used as parameters to determine the coefficients of the ODE system. This resize was executed by using the asymptotic solution of this system. The change of variables is necessary to guarantee the stability of the integration. Therefore, the linearization of the ODES is possible and can be used as a powerful control test. All these tools are applied to a physical problem. The example we present here is the effective numerical resolution of Lemaitre-Tolman-Bondi space-time solutions of Einstein Equations.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%