On the luminosity distance and the epoch of acceleration

Abstract

Standard cosmological models based on general relativity (GR) with dark energy predict that the Universe underwent a transition from decelerating to accelerating expansion at a moderate redshift z acc ∼ 0.7. Clearly, it is of great interest to directly measure this transition in a model-independent way, without the assumption that GR is the correct theory of gravity. We explore to what extent supernova (SN) luminosity distance measurements provide evidence for such a transition: we show that, contrary to intuition, the well-known "turnover" in the SN distance residuals ∆µ relative to an empty (Milne) model does not give firm evidence for such a transition within the redshift range spanned by SN data. The observed turnover in that diagram is predominantly due to the negative curvature in the Milne model, not the deceleration predicted by Λ cold dark matter and relatives. We show that there are several advantages in plotting distance residuals against a flat, non-accelerating model (w = −1/3), and also remapping the z−axis to u = ln(1 + z); we outline a number of useful and intuitive properties of this presentation. We conclude that there are significant complementarities between SNe and baryon acoustic oscillations (BAOs): SNe offer high precision at low redshifts and give good constraints on the net amount of acceleration since z ∼ 0.7, but are weak at constraining z acc ; while radial BAO measurements are probably superior for placing direct constraints on z acc .

The effects of peculiar velocities in SN Ia environments on the local H0 measurement

“…In terms of the methods of the present work, analyses of biases in fractional H 0 error estimates can be built upon with vari-ous improvements to assessments of the galaxy density field. These improvements could include: a replacement of 2MRS with 2M++ galaxies (Lavaux & Hudson 2011); an assessment of the density structure within the 'Zone of Avoidance' (Hubble 1934); and increased magnitude-depth of all-sky near-IR galaxy surveys from, for example, the UKIRT Hemisphere Survey (Dye et al 2018), the VISTA Hemisphere Survey (Sutherland et al 2015) and LSST (Ivezić et al 2019). Assessments of galaxy cluster densities from deep X-ray surveys such as eROSITA (Merloni et al 2012) also promise to put state-of-the-art constraints on the local density structure.…”

“…the other is a 'coasting' model with w = −1/3. Notably, none of these versions of the Hubble law are accurate except in the case of (d) v = c ln(1 + z) = H 0 D C for the coasting model (Sutherland & Rothnie 2015). Note this exact law also is valid for a non-flat coasting model such as an empty universe [though in this case, D L…”

“…This form tends to the exact law with q 0 → 0, and the right-hand term [1−(q 0 /2)(v/c)] represents an average of (1+z)/E(z) assuming constant acceleration (c.f. the quadratic fitting function given by Sutherland & Rothnie (2015) for improved precision). For ΛCDM cosmologies, the approximation is accurate to within 0.1% at z 0.1.…”

What do the cosmological supernova data really tell us?

“…The second and third families are polynomials multiplied by an exponential function where the exponent is linear and quadratic in y i , respectively. We extend the spectrum by introducing three more families 2 During the writing of this manuscript, we became aware of another work [11] introducing the same variable. which are the first three families multiplied by 1 + z; this is done to simplify (4) where division of d L by 1 + z is present.…”

Reinventing the slide rule for redshifts: the case for logarithmic wavelength shift

“…See, for example, fig.2ofAubourg et al (2015) for related plots [using ȧ and ln(1 + z)] comparing different models of dark energy, andSutherland & Rothnie (2015) who advocated changing the redshift variable to ln(1 + z) in analysis of luminosity distance residuals.…”