The Revised Evolutionary Volume Tolman Test: Cosmological Constraints from Galaxy Evolution

Abstract

In this study we adapt a classical cosmology measurement, the volume or number density test, to a modern synthesis of observed galaxy evolution. We do this by using measured galaxy mass functions and the history of galaxy evolution through star formation and galaxy mergers, inspired by the latest results from deep extragalactic surveys. We develop a new framework using measured galaxy volume number densities as a function of redshift and volume to determine cosmological parameters, especially those which alter the volume of the Universe at a given redshift. Whilst this is a classic cosmology test proposed since at least the 1930s, it has largely been abandoned for decades due to uncertainties in galaxy evolution which make it difficult to trace galaxy populations through time. However, recent advances in our understanding of star formation and the merging history of galaxies allow us to revise this method to uncover and measure cosmological parameters, especially those which involve the nature of dark energy. We present a modified version of the volume test, called the revised evolutionary volume Tolman test, using properties of known galaxy evolution as part of the cosmological calculation. We show how this method can successfully be applied and is competitive with other major cosmological measurement methods, including those using supernova and the CMB, when the merger and star formation histories can be measured accurately to between 1 to 10 percent. This accuracy is not yet achievable, but we discuss how future missions will allow these astrophysical quantities to be known at this level. Within this measurement accuracy we can measure the dynamical properties of dark energy, including its evolution through its equation of state. We also give a fuller accounting of the future use of this new method with upcoming galaxy surveys such as Euclid and LSST/Rubin.

Figures (7)

• Figure 1: Total comoving volume (left, as given in Eq. \ref{['eq:dv']}) and number galaxy counts (right, as given by dividing Eq. \ref{['Ntot1']} by $\Omega_{deg}$) for the different parametrisations outlined in Table \ref{['tab:gwmodels']}. Upper plots show the absolute values, taken to best fit our Universe (dashed lines corresponding to the errors as given in the corresponding references), hence explaining why they agree with $\Lambda$CDM results (black dashed line). Lower plots show the relative difference of each Quintessence best-fit parametrisation compared to $\Lambda$CDM.
• Figure 2: Number of galaxies per square degree within redshift bins of width $\delta z=0.25$, as given by Eq. \ref{['eq:Nfunction']}. On the top plot, the absolute values are shown, with $\Lambda$CDM corresponding to the black line and the colored lines to the best-fit parametrisations and errors from the models in Table \ref{['tab:gwmodels']}. The lower plot shows the relative difference of each model to $\Lambda$CDM.
• Figure 3: Plot of the average star formation rate per galaxy which we use in this paper. We show a modified version of the standard Madau & Dickinson star formation history (blue line) and the modified versions, based on theory (see text), designed such that the integral of the star formation provides a total stellar mass of M$_{*} = 10^{11}$ M$_{\odot}$ or M$_{*} = 10^{11.5}$ M$_{\odot}$ over redshifts from $0 < z < 10$. These forms use the models of Mostar2013. Within this paper, we assume M$_{*} = 10^{11}$ M$_{\odot}$ is the typical final stellar mass of a galaxy in our sample.
• Figure 4: Evolution of the total galaxy number density as given in Eq. (\ref{['eq: phiT(zf)']}) for a $\Lambda$CDM cosmology, including star formation effects and galaxy mergers, with step size $\delta z = 0.25$. The black line shows the constant Schechter function with no galaxy evolution, as calculated in § \ref{['sec:theory']}. Coloured regions show the effect that the errors on merger rates have on the evolution of the Schechter function, parametrised by $\varepsilon$ as shown in the text below.
• Figure 5: Number of galaxies per square degree within redshift bins of width $\delta z=0.25$, as given by Eqs. \ref{['eq:Nfunction']} and (\ref{['eq: phiT(zf)']}) for a $\Lambda$CDM cosmology. As with Figure \ref{['fig: phiT LCDM']}, the black line shows the galaxy counts with no galaxy evolution history, as calculated in § \ref{['sec:theory']}. Coloured regions show the effect that the errors on merger rates have on the galaxy counts, parametrised by $\varepsilon$ as shown in the text below.