Cosmological perturbation theory and conserved quantities in the large-scale limit

AbstractThe origin of large-scale magnetic fields is an unsolved problem in cosmology. In order to overcome, a possible scenario comes from the idea that these fields emerged from a small primordial magnetic field (PMF), produced in the early universe. This field could lead to the observed large-scales magnetic fields but also, would have left an imprint on the cosmic microwave background (CMB). In this work we summarize some statistical properties of this PMFs on the FLRW background. Then, we show the resulting PMF power spectrum using cosmological perturbation theory and some effects of PMFs on the CMB anisotropies.

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COSMOLOGICAL CONSTRAINT ON BRANS-DICKE THEORY

International Journal of Modern Physics Conference Series ◽

10.1142/s2010194511000274 ◽

2011 ◽

Vol 01 ◽

pp. 195-202

Author(s):

XUELEI CHEN ◽

FENGQUAN WU

Keyword(s):

Monte Carlo ◽

Perturbation Theory ◽

Markov Chain ◽

Large Scale ◽

Mcmc Method ◽

Covariant Formalism ◽

Microwave Background ◽

Cosmological Perturbation ◽

Cosmological Perturbation Theory ◽

Cosmological Constraint

We develop the covariant formalism of the cosmological perturbation theory for the Brans-Dicke gravity, and use it to calculate the cosmic microwave background (CMB) anisotropy and large scale structure (LSS) power spectrum. We introduce a new parameter ζ which is related to the Brans-Dicke parameter ζ = ln (1/ω + 1), and use the Markov-Chain Monte Carlo (MCMC) method to explore the parameter space. Using the latest CMB data published by WMAP, ACBAR, CBI, Boomerang teams, and the LSS data from the SDSS survey DR4, we find that the the 2σ (95.5%) bound on ζ is about |ζ| > 10-2, or |ω| > 102, the precise limit depends somewhat on the prior used.

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On Decoupling the Integrals of Cosmological Perturbation Theory

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa1789 ◽

2020 ◽

Author(s):

Zachary Slepian

Keyword(s):

Perturbation Theory ◽

Large Scale ◽

Cosmological Perturbation ◽

Cosmological Perturbation Theory ◽

Space Technique ◽

Gegenbauer Polynomial ◽

Sum Of Products ◽

Grid Points ◽

Higher Order Corrections ◽

Computational Resources

Abstract Perturbation theory (PT) is often used to model statistical observables capturing the translation and rotation-invariant information in cosmological density fields. PT produces higher-order corrections by integration over linear statistics of the density fields weighted by kernels resulting from recursive solution of the fluid equations. These integrals quickly become high-dimensional and naively require increasing computational resources the higher the order of the corrections. Here we show how to decouple the integrands that often produce this issue, enabling PT corrections to be computed as a sum of products of independent 1-D integrals. Our approach is related to a commonly used method for calculating multi-loop Feynman integrals in Quantum Field Theory, the Gegenbauer Polynomial x-Space Technique (GPxT). We explicitly reduce the three terms entering the 2-loop power spectrum, formally requiring 9-D integrations, to sums over successive 1-D radial integrals. These 1-D integrals can further be performed as convolutions, rendering the scaling of this method Nglog Ng with Ng the number of grid points used for each Fast Fourier Transform. This method should be highly enabling for upcoming large-scale structure redshift surveys where model predictions at an enormous number of cosmological parameter combinations will be required by Monte Carlo Markov Chain searches for the best-fit values.

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Cosmological perturbation theory revisited

Classical and Quantum Gravity ◽

10.1088/0264-9381/28/17/175017 ◽

2011 ◽

Vol 28 (17) ◽

pp. 175017 ◽

Cited By ~ 6

Author(s):

Claes Uggla ◽

John Wainwright

Keyword(s):

Perturbation Theory ◽

Cosmological Perturbation ◽

Cosmological Perturbation Theory

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Maximum turnaround radius in f(R) gravity

International Journal of Modern Physics D ◽

10.1142/s0218271819500585 ◽

2019 ◽

Vol 28 (03) ◽

pp. 1950058 ◽

Cited By ~ 8

Author(s):

Salvatore Capozziello ◽

Konstantinos F. Dialektopoulos ◽

Orlando Luongo

Keyword(s):

Large Scale ◽

A Priori ◽

Spherically Symmetric ◽

Cosmological Perturbation ◽

Suitable Alternative ◽

Cosmological Perturbation Theory ◽

Large Scale Structures ◽

Scale Structures ◽

Analytic Expression ◽

Prescription Rules

The accelerating behavior of cosmic fluid opposes gravitational attraction at present epoch, whereas standard gravity is dominant at small scales. As a consequence, there exists a point where the effects are counterbalanced, dubbed turnaround radius, [Formula: see text]. By construction, it provides a bound on maximum structure sizes of the observed universe. Once an upper bound on [Formula: see text] is provided, i.e. [Formula: see text], one can check whether cosmological models guarantee structure formation. Here, we focus on [Formula: see text] gravity, without imposing a priori the form of [Formula: see text]. We thus provide an analytic expression for the turnaround radius in the framework of [Formula: see text] models. To figure this out, we compute the turnaround radius in two distinct cases: (1) under the hypothesis of static and spherically symmetric spacetime, and (2) by using the cosmological perturbation theory. We thus find a criterion to enable large scale structures to be stable in [Formula: see text] models, circumscribing the class of [Formula: see text] theories as suitable alternative to dark energy. In particular, we get that for constant curvature, the viability condition becomes [Formula: see text], with [Formula: see text] and [Formula: see text], respectively, the observed cosmological constant and the Ricci curvature. This prescription rules out models which do not pass the aforementioned [Formula: see text] limit.

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