skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Ray tracing and Hubble diagrams in post-Newtonian cosmology

Abstract

On small scales the observable Universe is highly inhomogeneous, with galaxies and clusters forming a complex web of voids and filaments. The optical properties of such configurations can be quite different from the perfectly smooth Friedmann-Lemaȋtre-Robertson-Walker (FLRW) solutions that are frequently used in cosmology, and must be well understood if we are to make precise inferences about fundamental physics from cosmological observations. We investigate this problem by calculating redshifts and luminosity distances within a class of cosmological models that are constructed explicitly in order to allow for large density contrasts on small scales. Our study of optics is then achieved by propagating one hundred thousand null geodesics through such space-times, with matter arranged in either compact opaque objects or diffuse transparent haloes. We find that in the absence of opaque objects, the mean of our ray tracing results faithfully reproduces the expectations from FLRW cosmology. When opaque objects with sizes similar to those of galactic bulges are introduced, however, we find that the mean of distance measures can be shifted up from FLRW predictions by as much as 10%. This bias is due to the viable photon trajectories being restricted by the presence of the opaque objects, which means thatmore » they cannot probe the regions of space-time with the highest curvature. It corresponds to a positive bias of order 10% in the estimation of Ω{sub Λ} and highlights the important consequences that astronomical selection effects can have on cosmological observables.« less

Authors:
;  [1];  [2]
  1. School of Physics and Astronomy, Queen Mary University of London, 327 Mile End Road, London E1 4NS (United Kingdom)
  2. Départment de Physique Théorique, Université de Genève, 24 quai Ernest-Ansermet, 1211 Genève 4 (Switzerland)
Publication Date:
OSTI Identifier:
22676098
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Cosmology and Astroparticle Physics; Journal Volume: 2017; Journal Issue: 07; Other Information: Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
79 ASTROPHYSICS, COSMOLOGY AND ASTRONOMY; COMPUTERIZED SIMULATION; COSMOLOGICAL MODELS; COSMOLOGY; DENSITY; DISTANCE; FORECASTING; GALAXIES; LUMINOSITY; OPTICS; PHOTONS; RED SHIFT; SPACE-TIME; TRAJECTORIES; UNIVERSE

Citation Formats

Sanghai, Viraj A.A., Clifton, Timothy, and Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk. Ray tracing and Hubble diagrams in post-Newtonian cosmology. United States: N. p., 2017. Web. doi:10.1088/1475-7516/2017/07/028.
Sanghai, Viraj A.A., Clifton, Timothy, & Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk. Ray tracing and Hubble diagrams in post-Newtonian cosmology. United States. doi:10.1088/1475-7516/2017/07/028.
Sanghai, Viraj A.A., Clifton, Timothy, and Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk. Sat . "Ray tracing and Hubble diagrams in post-Newtonian cosmology". United States. doi:10.1088/1475-7516/2017/07/028.
@article{osti_22676098,
title = {Ray tracing and Hubble diagrams in post-Newtonian cosmology},
author = {Sanghai, Viraj A.A. and Clifton, Timothy and Fleury, Pierre, E-mail: v.a.a.sanghai@qmul.ac.uk, E-mail: pierre.fleury@unige.ch, E-mail: t.clifton@qmul.ac.uk},
abstractNote = {On small scales the observable Universe is highly inhomogeneous, with galaxies and clusters forming a complex web of voids and filaments. The optical properties of such configurations can be quite different from the perfectly smooth Friedmann-Lemaȋtre-Robertson-Walker (FLRW) solutions that are frequently used in cosmology, and must be well understood if we are to make precise inferences about fundamental physics from cosmological observations. We investigate this problem by calculating redshifts and luminosity distances within a class of cosmological models that are constructed explicitly in order to allow for large density contrasts on small scales. Our study of optics is then achieved by propagating one hundred thousand null geodesics through such space-times, with matter arranged in either compact opaque objects or diffuse transparent haloes. We find that in the absence of opaque objects, the mean of our ray tracing results faithfully reproduces the expectations from FLRW cosmology. When opaque objects with sizes similar to those of galactic bulges are introduced, however, we find that the mean of distance measures can be shifted up from FLRW predictions by as much as 10%. This bias is due to the viable photon trajectories being restricted by the presence of the opaque objects, which means that they cannot probe the regions of space-time with the highest curvature. It corresponds to a positive bias of order 10% in the estimation of Ω{sub Λ} and highlights the important consequences that astronomical selection effects can have on cosmological observables.},
doi = {10.1088/1475-7516/2017/07/028},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 07,
volume = 2017,
place = {United States},
year = {Sat Jul 01 00:00:00 EDT 2017},
month = {Sat Jul 01 00:00:00 EDT 2017}
}
  • In this paper, we continue to build support for the proposal to use gamma-ray bursts (GRBs) as standard candles in constructing the Hubble diagram at redshifts beyond the current reach of Type Ia supernova observations. We confirm that correlations among certain spectral and light-curve features can indeed be used as luminosity indicators, and demonstrate from the most up-to-date GRB sample appropriate for this work that the {Lambda}CDM model optimized with these data is characterized by parameter values consistent with those in the concordance model. Specifically, we find that ({Omega}{sub m},{Omega}{sub {Lambda}}){approx}(0.25{sub -0.06}{sup +0.05}, 0.75{sub -0.05}{sup +0.06}), which are consistent, tomore » within 1{sigma}, with (0.29, 0.71) obtained from the 9 yr Wilkinson Microwave Anisotropy Probe data. We also carry out a comparative analysis between {Lambda}CDM and the R{sub h} = ct universe and find that the optimal {Lambda}CDM model fits the GRB Hubble diagram with a reduced {chi}{sup 2}{sub dof}{approx}2.26, whereas the fit using R{sub h} = ct results in a {chi}{sup 2}{sub dof}{approx}2.14. In both cases, about 20% of the events lie at least 2{sigma} away from the best-fit curves, suggesting that either some contamination by non-standard GRB luminosities is unavoidable or that the errors and intrinsic scatter associated with the data are being underestimated. With these optimized fits, we use three statistical tools-the Akaike information criterion, the Kullback information criterion, and the Bayes information criterion-to show that, based on the GRB Hubble diagram, the likelihood of R{sub h} = ct being closer to the correct model is {approx}85%-96%, compared to {approx}4%-15% for {Lambda}CDM.« less
  • We construct the Hubble diagram of gamma-ray bursts (GRBs) with redshifts reaching up to z{approx}6, by using five luminosity versus luminosity indicator relations calibrated with the Cardassian cosmology. This model has a major interesting feature: despite being matter dominated and flat, it can explain the present accelerated expansion of the universe. This is the first study of this class of models using high redshift GRBs. We have performed a {chi} squared statistical analysis of the GRBs calibrated with the Cardassian model, and also combined them with both the current cosmic microwave background and baryonic acoustic oscillation data. Our results showmore » consistency between the current observational data and the model predictions; in particular, the best fit parameters obtained from that {chi}{sup 2} analysis are in agreement with those obtained from previous investigations. The influence of these best fit parameters on the redshift at which the universe would start to follow the Cardassian expansion, i.e., z{sub card}, and on both the redshift at which the universe supposedly had started to accelerate, i.e., z{sub acc}, and the age-redshift relation, H{sub 0}t{sub 0}, are also discussed. Our results also show that the universe, from the point of view of GRBs, had undergone a transition to acceleration at a redshift z Almost-Equal-To 0.2-0.7, which agrees with the type Ia supernovae results. One important point that we notice is that despite the statistical analysis being performed with a model that does not need any vacuum energy, we found that the results attained using this cosmological model are compatible with those obtained with the concordance cosmology ({Lambda}-CDM; CDM: cold dark matter), as far as GRBs are concerned. Hence, after confronting the Cardassian scenario with the GRB Hubble diagram, our main conclusion is that GRBs should indeed be considered a tool complementary to several other observational studies for doing precision cosmology.« less
  • Using post-Newtonian equations of motion for fluid bodies valid to the second post-Newtonian order, we derive the equations of motion for binary systems with finite-sized, nonspinning but arbitrarily shaped bodies. In particular we study the contributions of the internal structure of the bodies (such as self-gravity) that would diverge if the size of the bodies were to shrink to zero. Using a set of virial relations accurate to the first post-Newtonian order that reflect the stationarity of each body, and redefining the masses to include 1PN and 2PN self-gravity terms, we demonstrate the complete cancellation of a class of potentiallymore » divergent, structure-dependent terms that scale as s{sup -1} and s{sup -5/2}, where s is the characteristic size of the bodies. This is further evidence of the strong equivalence principle, and supports the use of post-Newtonian approximations to derive equations of motion for strong-field bodies such as neutron stars and black holes. This extends earlier work done by Kopeikin.« less
  • A precise definition of the Newtonian and post-Newtonian hierarchy of approximations to general relativity is given by studying a C/sup infinity/ sequence of solutions to Einstein's equations that is defined by initial data having the Newtonian scaling property: v/sup i/approx.epsilon, rhoapprox.epsilon/sup 2/, papprox.epsilon/sup 4/, where epsilon is the parameter along the sequence. We map one solution in the sequence to another by identifying them at constant spatial position x/sup i/ and Newtonian dynamical time tau = epsilont. This mapping defines a congruence parametrized by epsilon, and the various post-Newtonian approximations emerge as derivatives of the relativistic solutions along this congruence.more » We thereby show for the first time that the approximations are genuine asymptotic approximations to general relativity. The proof is given in detail up to first post-Newtonian order, but is easily extended. The results will be applied in the following paper to radiation reaction in binary star systems, to give a proof of the validity of the ''quadrupole formula'' free from any divergences.« less
  • The time delay in galaxy gravitational lensing systems has been used to determine the value of the Hubble constant. As with other dynamical phenomena on the galaxy scale, dark matter is often invoked in gravitational lensing to account for the 'missing mass' (the apparent discrepancy between the dynamical mass and the luminous mass). Alternatively, modified gravity can be used to explain the discrepancy. In this paper, we adopt the tensor-vector-scalar gravity (TeVe S), a relativistic version of Modified Newtonian Dynamics, to study gravitational lensing phenomena and derive the formulae needed to evaluate the Hubble constant. We test our method onmore » quasar lensing by elliptical galaxies in the literature. We focus on double-image systems with time delay measurement. Three candidates are suitable for our study: HE 2149-2745, FBQ J0951+2635, and SBS 0909+532. The Hubble constant obtained is consistent with the value used to fit the cosmic microwave background result in a neutrino cosmological model.« less