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Register a new userRadiative transport of relativistic species in cosmology
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Cyril Pitrou
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We review the general construction of distribution functions for gases of fermions and bosons (photons), emphasizing the similarities and differences between both cases. The central object which describes polarization for photons is a tensor-valued distribution function, whereas for fermions it is a vector-valued one. The collision terms of Boltzmann equations for fermions and bosons also possess the same general structure and differ only in the quantum effects associated with the final state of the reactions described. In particular, neutron-proton
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This paper studies the connection between the relativistic number density of galaxies down the past light cone in a Friedmann-Lemaitre-Robertson-Walker spacetime with non-vanishing cosmological constant and the galaxy luminosity function (LF) data. It extends the redshift range of previous results presented in Albani et al. (2007:astro-ph/0611032) where the galaxy distribution was studied out to z=1. Observational inhomogeneities were detected at this range. This research also searches for LF evolution in the context of the framework advanced by Ribeiro and Stoeger (2003:astro-ph/0304094), further developing the theory linking relativistic cosmology theory and LF data. Selection functions are obtained using the Schechter parameters and redshift parametrization of the galaxy luminosity functions obtained from an I-band selected dataset of the FORS Deep Field galaxy survey in the redshift range 0.5<z<5.0 for its blue bands and 0.75<z<3.0 for its red ones. Differential number counts, densities and other related observables are obtained, and then used with the calculated selection functions to study the empirical radial distribution of the galaxies in a fully relativistic framework. The redshift range of the dataset used in this work, which is up to five times larger than the one used in previous studies, shows an increased relevance of the relativistic effects of expansion when compared to the evolution of the LF at the higher redshifts. The results also agree with the preliminary ones presented in Albani et al. (2007:astro-ph/0611032), suggesting a power-law behavior of relativistic densities at high redshifts when they are defined in terms of the luminosity distance.
In relativistic inhomogeneous cosmology, structure formation couples to average cosmological expansion. A conservative approach to modelling this assumes an Einstein--de Sitter model (EdS) at early times and extrapolates this forward in cosmological time as a background model against which average properties of todays Universe can be measured. This requires adopting an early-epoch--normalised background Hubble constant $H_1^{bg}$. Here, we show that the $Lambda$CDM model can be used as an observational proxy to estimate $H_1^{bg}$ rather than choose it arbitrarily. We assume (i) an EdS model at early times; (ii) a zero dark energy parameter; (iii) bi-domain scalar averaging---division of the spatial sections into over- and underdense regions; and (iv) virialisation (stable clustering) of collapsed regions. We find $H_1^{bg}= 37.7 pm 0.4$ km/s/Mpc (random error only) based on a Planck $Lambda$CDM observational proxy. Moreover, since the scalar-averaged expansion rate is expected to exceed the (extrapolated) background expansion rate, the expected age of the Universe should be much less than $2/(3 H_1^{bg}) = 17.3$ Gyr. The maximum stellar age of Galactic Bulge microlensed low-mass stars (most likely: 14.7 Gyr; 68% confidence: 14.0--15.0 Gyr) suggests an age about a Gyr older than the (no-backreaction) $Lambda$CDM estimate.
The study of relativistic, higher order and nonlinear effects has become necessary in recent years in the pursuit of precision cosmology. We develop and apply here a framework to study gravitational lensing in exact models in general relativity that are not restricted to homogeneity and isotropy, and where full nonlinearity and relativistic effects are included. We apply the framework to a specific, anisotropic galaxy cluster model which is based on a modified NFW halo density profile and described by the Szekeres metric. We examine the effects of increasing levels of anisotropy in the galaxy cluster on lensing observables like the convergence and shear for various lensing geometries, finding a strong nonlinear response in both the convergence and shear for rays passing through anisotropic regions of the cluster. Deviation from the expected values in a spherically symmetric structure are asymmetric with respect to path direction and thus will persist as a statistical effect when averaged over some ensemble of such clusters. The resulting relative difference in various geometries can be as large as approximately 2%, 8%, and 24% in the measure of convergence for levels of anisotropy of 5%, 10%, and 15%, respectively, as a fraction of total cluster mass. For the total magnitude of shear, the relative difference can grow near the center of the structure to be as large as 15%, 32%, and 44% for the same levels of anisotropy, averaged over the two extreme geometries. The convergence is impacted most strongly for rays which pass in directions along the axis of maximum dipole anisotropy in the structure, while the shear is most strongly impacted for rays which pass in directions orthogonal to this axis, as expected. These effects due to anisotropic structures will affect lensing measurements and must be fully examined in an era of precision cosmology.
We address the generation of initial conditions (ICs) for GRAMSES, a code for nonlinear general relativistic (GR) $N$-body cosmological simulations recently introduced in Ref. [1]. GRAMSES adopts a constant mean curvature slicing with a minimal distortion gauge, where the linear growth rate is scale-dependent, and the standard method for realising initial particle data is not straightforwardly applicable. A new method is introduced, in which the initial positions of particles are generated from the displacement field realised for a matter power spectrum as usual, but the velocity is calculated by finite-differencing the displacement fields around the initial redshift. In this way, all the information required for setting up the initial conditions is drawn from three consecutive input matter power spectra, and additional assumptions such as scale-independence of the linear growth factor and growth rate are not needed. We implement this method in a modified 2LPTic code, and demonstrate that in a Newtonian setting it can reproduce the velocity field given by the default 2LPTic code with subpercent accuracy. We also show that the matter and velocity power spectra of the initial particle data generated for GRAMSES simulations using this method agree very well with the linear-theory predictions in the particular gauge used by GRAMSES. Finally, we discuss corrections to the finite difference calculation of the velocity when radiation is present, as well as additional corrections implemented in GRAMSES to ensure consistency. This method can be applied in ICs generation for GR simulations in generic gauges, and simulations of cosmological models with scale-dependent linear growth rate.
We present GRAMSES, a new pipeline for nonlinear cosmological $N$-body simulations in General Relativity (GR). This code adopts the Arnowitt-Deser-Misner (ADM) formalism of GR, with constant mean curvature and minimum distortion gauge fixings, which provides a fully nonlinear and background independent framework for relativistic cosmology. Employing a fully constrained formulation, the Einstein equations are reduced to a set of ten elliptical equations which are solved using multigrid relaxation with adaptive mesh refinements (AMR), and three hyperbolic equations for the evolution of tensor degrees of freedom. The current version of GRAMSES neglects the latter by using the conformal flatness approximation, which allows it to compute the two scalar and two vector degrees of freedom of the metric. In this paper we describe the methodology, implementation, code tests and first results for cosmological simulations in a $Lambda$CDM universe, while the generation of initial conditions and physical results will be discussed elsewhere. Inheriting the efficient AMR and massive parallelisation infrastructure from the publicly-available $N$-body and hydrodynamic simulation code RAMSES, GRAMSES is ideal for studying the detailed behaviour of spacetime inside virialised cosmic structures and hence accurately quantifying the impact of backreaction effects on the cosmic expansion, as well as for investigating GR effects on cosmological observables using cosmic-volume simulations.
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