Testing the Copernican principle with the Hubble parameter

Abstract

Using the longitudinal expression of Hubble expansion rate for the general Lemaître-Tolman-Bondi (LTB) metric as a function of cosmic time, we examine the scale on which the Copernican Principle holds in the context of a void model. By way of performing parameter estimation on the CGBH void model, we show that the Hubble parameter data favors a void with characteristic radius of 2 ∼ 3 Gpc. This brings the void model closer, but not yet enough, to harmony with observational indications given by the background kinetic Sunyaev-Zel'dovich effect and the normalization of near-infrared galaxy luminosity function. However, the test of such void models may ultimately lie in the future detection of the discrepancy between longitudinal and transverse expansion rates, a touchstone of inhomogeneous models. With the proliferation of observational Hubble parameter data and future large-scale structure observation, a definitive test could be performed on the question of cosmic homogeneity. Particularly, the spherical LTB void models have been ruled out, but more general non-spherical inhomogeneities still need to be tested by observation. In this paper, we utilise a spherical void model to provide guidelines into how observational tests may be done with more general models in the future.

Exploring the evidence for a large local void with supernovae Ia data

“…Contrasting the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) models, the LTB metric (Lemaître 1927(Lemaître , 1933Tolman 1934;Bondi 1947) describes an isotropic but inhomogeneous dust system, which on cosmological scales can be used for studying cold dark matter density distribution. Since the discovery of cosmic acceleration, LTB metric was used to construct toy models that challenge the cosmological constant paradigm with an alternative scenario in which the apparent accelerated expansion is a result of the strongly underdense local Universe that smoothly converges to Einstein de Sitter (EdS) solution on higher redshifts (Célérier 2000;Alnes et al 2006;Clifton et al 2008;February et al 2010;Nadathur & Sarkar 2011;Bolejko & Sussman 2011;Zhang et al 2015). Certainly, as the deceleration-acceleration transition redshift is well constrained at z t ≈ 0.6 (see e.g.…”

Testing the cosmic anisotropy with supernovae data: Hemisphere comparison and dipole fitting

“…For instance, giving up the cosmic homogeneity, it is reasonable to imagine that we are living in a locally underdense void. One of such models is the well-known Lemaître-Tolman-Bondi (LTB) void model [11][12][13][14][15][16][17][18][19][20]. In this model, the universe is spherically symmetric and radially inhomogeneous, and we are living in a locally underdense void centered nearby our location.…”

“…In this model, the universe is spherically symmetric and radially inhomogeneous, and we are living in a locally underdense void centered nearby our location. The Hubble diagram inferred from lines-of-sight originating at the center of the void might be misinterpreted to indicate cosmic acceleration [13][14][15][16][17][18][19][20]. In fact, the LTB-like models violating the cosmological principle have been extensively considered in the literature nowadays.…”

“…In the literature, the cosmic homogeneity has been tested by using e.g. type Ia supernovae (SNIa) [16,18,21], cosmic microwave background (CMB) [5,[22][23][24][25][26], time drift of cosmological redshifts [27,28], baryon acoustic oscillations (BAO) [29][30][31], integrated Sachs-Wolfe effect [32], galaxy surveys [33], kinetic Sunyaev Zel'dovich effect [34][35][36][37][38], ages of old high-redshift objects [20], observational H(z) data [19], and growth of large-scale structure [16]. However, the debate on the inhomogeneous universe has not been settled by now.…”

A simple and novel amide ligand based on quinoline derivative used for palladium-catalyzed Suzuki coupling reaction

“…According to these results, a working mechanism was proposed on the basis of the previously proposed mechanism as outlined in Scheme 2 [12,31,40,43e45]. This proposed catalytic cycle involves oxidative addition of Pd(0)L 4 to the halide (R 1 X) to form the organopalladium interme-diate Pd(L 2 )R 1 X, transmetalation reaction of Pd(L 2 )R 1 X with the boron acid to form a diarylpalladium species Pd(L 2 )R 1 R 2 , and reductive elimination of Pd(L 2 )R 1 R 2 to release the desired coupling product (R1eR2) [1,12].…”