Galaxy number counts at second order: an independent approach

Fuentes, Jorge L.; Hidalgo, Juan Carlos; Malik, Karim A.

doi:10.1088/1361-6382/abd95c

Cited by 6 publications

(9 citation statements)

References 39 publications

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“…In order to account for relativistic contributions to observables, a complementary strategy is to integrate the signals produced by galaxies along the line of sight to determine the distance-redshift relation. The resulting distortions of redshift-space due to structure have been reported in terms of the number counts of galaxy clustering at linear order [12][13][14][15][16], and at second order [17][18][19][20][21][22][23][24][25]. Moreover, the observed bispectrum receives contributions from this relation as shown recently in [19,[26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 68%

Relativistic and non-Gaussianity contributions to the one-loop power spectrum

Martinez-Carrillo

De-Santiago

Hidalgo

et al. 2020

J. Cosmol. Astropart. Phys.

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We compute the one-loop density power spectrum including Newtonian and relativistic contributions, as well as the primordial non-Gaussianity contributions from f NL and g NL in the local configuration. To this end we take solutions to the Einstein equations in the long-wavelength approximation and provide expressions for the matter density perturbation at second and third order. These solutions have shown to be complementary to the usual Newtonian cosmological perturbations. We confirm a sub-dominant effect from pure relativistic terms, manifested at scales dominated by cosmic variance, but find that a sizable effect of order one comes from g NL values allowed by Planck-2018 constraints, manifested at scales probed by forthcoming galaxy surveys like DESI and Euclid. As a complement, we present the matter bispectrum at the tree-level including the mentioned contributions.

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Section: Introductionmentioning

confidence: 68%

Relativistic and non-Gaussianity contributions to the one-loop power spectrum

Martinez-Carrillo

De-Santiago

Hidalgo

et al. 2020

J. Cosmol. Astropart. Phys.

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“…To exercise our notation and for convenience of use we define in this section the basic quantities required to calculate the Galaxy number density up to second order in cosmological perturbation theory. We follow very closely our previous paper, reference [13]. However, we do not reproduce the rather lengthy calculations presented there, and focus here on the results.…”

Section: Basic Definitions For the Galaxy Number Densitymentioning

confidence: 78%

“…In reference [12] the authors use a straight-forward derivation to reproduce the result of reference [8], finding disagreements concerning lensing terms and a double counting of volume distortion effects in references [9,11], respectively. Given the importance of the number density for current and future LSS surveys, we decided to have an independent calculation of this quantity up to second order in the perturbations and published the results in reference [13]. In this paper, we use the derivation of the second order number count given in reference [13] and follow a similar approach as the one made in reference [12] comparing leading terms in the aforementioned literature, however not constraining our comparison to sub-horizon scales Notation.…”

Section: Introductionmentioning

confidence: 99%

“…Given the importance of the number density for current and future LSS surveys, we decided to have an independent calculation of this quantity up to second order in the perturbations and published the results in reference [13]. In this paper, we use the derivation of the second order number count given in reference [13] and follow a similar approach as the one made in reference [12] comparing leading terms in the aforementioned literature, however not constraining our comparison to sub-horizon scales Notation. Greek indices (μ, ν, .…”

Section: Introductionmentioning

confidence: 99%

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Galaxy number counts at second order in perturbation theory: a leading-order term comparison

Fuentes

Hidalgo

Malik

2021

Class. Quantum Grav.

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The Galaxy number density is a key quantity to compare theoretical predictions to the observational data from current and future large scale structure surveys. The precision demanded by these stage IV surveys requires the use of second order cosmological perturbation theory. Based on the independent calculation published previously, we present the result of the comparison with the results of three other groups at leading order. Overall we find that the differences between the different approaches lie mostly on the definition of certain quantities, where the ambiguity of signs results in the addition of extra terms at second order in perturbation theory.

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“…The linear order perturbation theory around the homogeneous and isotropic solution is well understood and documented, but is often insufficient for matching the aforementioned precision requirements. This is why, in the last decade, the community has been actively investigating the impact of second-order effects in the CMB lensing [10][11][12][13][14][15][16][17][18][19][20][21], in galaxy number counts [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36] and cosmological distances and weak lensing [37][38][39][40][41][42][43][44][45].…”

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confidence: 99%

Tetrad formalism for exact cosmological observables

Mitsou,

Yoo

2019

Preprint

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The standard description of cosmological observables is incomplete, because it does not take into account the correct angular parametrization of the sky, i.e. the one determined by the observer frame. The corresponding corrections must be taken into account for reliable results at non-linear orders. This can be accomplished by introducing an orthonormal basis, or "tetrad", at the observer point, representing the frame with respect to which observations are performed. In this paper we consider the tetrad formalism of General Relativity, thus associating tetrads to sources as well, and develop a new formalism for describing cosmological observables. It is based on a manifold which we call the "observer space-time", whose coordinates are the proper time, redshift and angles an observer uses to parametrize measurements, and on which the rest of the observables are defined. This manifold does not have to be diffeomorphic to the true space-time and allows us to resolve caustics in the latter, in contrast with similar coordinate-based formalisms. As a concrete example, we work out the definitions and equations for the angular diameter distance, weak lensing and number count observables. As for the observables associated to the CMB, they lie inside the phase space matrix distribution of the photon fluid evaluated at the observer point and pulled back on the observer sky. The second part of this paper is therefore devoted to general-relativistic matrix kinetic theory. Here too the tetrad formalism appears as the natural approach for relating the macroscopic dynamics to the microscopic QFT and therefore for constructing the matrix Boltzmann equations. Part of the presented material is known and is included for completeness, but we provide more detailed discussions over some subtle issues and we also consider an alternative construction of the collision term which deviates from the standard one at higher order in the loop corrections. In summary, the present paper contains all the required structures for computations in cosmology with exact and model-independent cosmological observables. The associated linear perturbation theory will be given in a companion paper.

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Galaxy number counts at second order: an independent approach

Cited by 6 publications

References 39 publications

Relativistic and non-Gaussianity contributions to the one-loop power spectrum

Relativistic and non-Gaussianity contributions to the one-loop power spectrum

Galaxy number counts at second order in perturbation theory: a leading-order term comparison

Tetrad formalism for exact cosmological observables

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