Relativistic Euler equations in cosmologies with nonlinear structures

Gallagher, Christopher; Clifton, Timothy

doi:10.1103/physrevd.98.103516

Cited by 10 publications

(17 citation statements)

References 37 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A more comprehensive approach, in which both expansions are deployed together, was only recently introduced in Refs. [11][12][13][14]. In this paper we will consider cosmological perturbation theory and post-Newtonian theory separately, in order to identify suitable gauge choices in each case.…”

Section: Weak-field Expansions In Cosmologymentioning

confidence: 99%

Viable gauge choices in cosmologies with nonlinear structures

et al. 2020

Self Cite

View full text Add to dashboard Cite

A variety of gauges are used in cosmological perturbation theory. These are often chosen in order to attribute physical properties to a particular choice of coordinates, or otherwise to simplify the form of the resultant equations. Calculations are then performed with the understanding that they could have been done in any gauge, and that transformations between different gauges can be made at will. We show that this logic can be extended to the domain of large density contrasts, where different types of perturbative expansion are required, but that the way in which gauges can be chosen in the presence of such structures is severely constrained. In particular, most gauges that are commonly considered in the cosmology literature are found to be unviable in the presence of nonlinear structures. This includes spatially flat gauge, synchronous gauge, comoving orthogonal gauge, total matter gauge, N-body gauge, and the uniform density gauge. In contrast, we find that the longitudinal gauge and the Newtonian motion gauge are both viable choices in both standard cosmological perturbation theory, and in the post-Newtonian perturbative expansions that are required in order to model non-linear structures.

show abstract

Section: Weak-field Expansions In Cosmologymentioning

confidence: 99%

Viable gauge choices in cosmologies with nonlinear structures

et al. 2020

Self Cite

View full text Add to dashboard Cite

show abstract

“…Equations (2.9) and (2.10) are identical to the Friedmann equations for an Einstein-de Sitter (EdS) universe, and admit the well-known solution As was demonstrated in Ref. [15], conservation of the Einstein constraint equations under time evolution demands that δ N ≡ δρ N /ρ and v Ni satisfy the continuity equation and Euler equations:…”

Section: Field Equationsmentioning

confidence: 88%

“…In this section we will introduce the two-parameter perturbation theory (2PPT) constructed in Refs. [13][14][15], as well as the method we will use to solve them. The 2PPT approach simultaneously expands the metric and matter fields in both Cosmological Perturbation Theory (CPT) and post-Newtonian (PN) approximations, and uses the labels ∼ 10 −4 and η ∼ 10 −2 to label the smallness parameter in each of these two expansions, respectively.…”

Section: Two-parameter Perturbation Theory In Einstein-de Sitter Univmentioning

confidence: 99%

See 1 more Smart Citation

Multi-scale perturbation theory. Part I. Methodology and leading-order bispectrum corrections in the matter-dominated era

Gallagher

Clifton

Clarkson

2020

J. Cosmol. Astropart. Phys.

Self Cite

View full text Add to dashboard Cite

Two-parameter perturbation theory is a scheme tailor-made to consistently include nonlinear density contrasts on small scales (< 100 Mpc), whilst retaining a traditional approach to cosmological perturbations in the long-wavelength universe. In this paper we study the solutions that arise from this theory in a spatially-flat dust-filled cosmology, and what these imply for the bispectrum of matter. This is achieved by using Newtonian perturbation theory to model the gravitational fields of nonlinear structures in the quasi-linear regime, and then using the resulting solutions as source terms for the cosmological equations. We find that our approach results in the leading-order part of the cosmological gravitational potentials being identical to those that result from standard cosmological perturbation theory at second-order, while the dark matter bispectrum itself yields some differences on Hubble scales. This demonstrates that our approach is sufficient to capture most leading-order relativistic effects, but within a framework that is far easier to generalize. We expect this latter property to be particularly useful for calculating leading-order relativistic corrections to the matter power spectrum, as well as for deriving predictions for relativistic effects in alternative theories of gravity.

show abstract

“…Several groups have already computed the galaxy bispectrum in relativistic perturbation theory [26][27][28][29][30][31][32][33][34], and conclude that these effects are degenerate with f loc NL ∼ 1 [35]. In particular, the impact of general relativity on the dynamics of dark matter was investigated in [36][37][38]. Second order analyses are valid when all scales involved are large, such that the tree level bispectrum is enough.…”

Section: Contentsmentioning

confidence: 99%

Relativistic cosmological large scale structures at one-loop

Castiblanco¹,

Gannouji²,

Noreña³

et al. 2019

J. Cosmol. Astropart. Phys.

View full text Add to dashboard Cite

The large scale structure bispectrum in the squeezed limit couples large with small scales. Since relativity is important at large scales and non-linear loop corrections are important at small scales, the proper calculation of the observed bispectrum in this limit requires a non-linear relativistic calculation. We compute the matter bispectrum in general relativity in the weak field approximation. The calculation is as involved as existing second-order results. We find several differences with the Newtonian calculation such as the non-cancellation of IR divergences, the need to renormalize the background, and the fact that initial conditions must be set at second order in perturbation theory. For the bispectrum, we find relativistic corrections to be as large as the newtonian result in the squeezed limit. In that limit relativistic one-loop contributions, which we compute for the first time, can be as large as tree level results and have the same 1/k 2 dependence as a primordial local non-Gaussianity signal where k is the momentum approaching zero. Moreover, we find the time dependence of the relativistic corrections to the bispectrum to be the same as that of a primordial non-Gaussianity signal.

show abstract

Relativistic Euler equations in cosmologies with nonlinear structures

Cited by 10 publications

References 37 publications

Viable gauge choices in cosmologies with nonlinear structures

Viable gauge choices in cosmologies with nonlinear structures

Multi-scale perturbation theory. Part I. Methodology and leading-order bispectrum corrections in the matter-dominated era

Relativistic cosmological large scale structures at one-loop

Contact Info

Product

Resources

About