Evidence against Ryskin’s model of cosmic acceleration

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Abstract

In this paper I examine how well Ryskin’s model of emergent cosmic acceleration fits several sets of cosmological observations. I find that while Ryskin’s model is somewhat compatible with the standard model of cosmic acceleration (ΛCDM) for low redshift (z ≲ 1) measurements, its predictions diverge considerably from those of the standard model for measurements made at high redshift (for which z ≳ 1), and it is therefore not a compelling substitute for the standard model.

Introduction

Observations show that the universe is currently undergoing an accelerated phase of expansion, which was preceded by a decelerated phase of expansion at z ≳ 0.75 (for reviews of the standard paradigm, see e.g. Refs. [9], [12]; for a discussion of the deceleration-acceleration transition, see Ref. [3] and references therein). In the standard cosmological model, ΛCDM, this acceleration is powered by a spatially homogeneous energy density in the form of a cosmological constant, Λ. Although the cosmological constant has successfully explained many observations to date (see e.g. Refs. [10], [11]), an explanation of its origin in terms of fundamental physics remains elusive (see e.g. Refs. [7], [17], [18], [19]). Many researchers have therefore attempted to construct models of cosmic acceleration that do not incorporate the cosmological constant, or any other form of dark energy (for a review of which, see e.g. Ref. [2]). One such model (not covered in Ref. [2]) is Gregory Ryskin’s model of emergent cosmic acceleration (presented in Ref. [16]). In this model, the observed acceleration of the universe is argued to emerge naturally as a consequence of applying a mean-field treatment to Einstein’s gravitational field equations on cosmic scales. In this way, Ryskin claims to have arrived at an explanation of cosmic acceleration that does not require any fundamentally new physics. According to Ref. [16], Ryskin’s model accurately fits the Hubble diagram built from SNe Ia data, but I will show in this paper that there are other data sets with which Ryskin’s model is much less compatible. In addition to predicting a value of the Hubble constant (H0) that is larger than the values obtained from the CMB and from local measurements (see Refs. [11] and [13], respectively, for these measurements), Ryskin’s model fails to predict the trend in high-redshift (z ≳ 1) Hubble parameter data when its predicted Hubble parameter curve is plotted together with these data.

Recently, another group found that Ryskin’s model cannot accurately describe structure formation (see Ref. [6]), while leaving open the possibility that other types of observations may be compatible with this model. This paper is complementary to, and independent of, the analysis presented in Ref. [6]; I will show that none of the data sets I have collected favor Ryskin’s model over ΛCDM, making it unlikely that Ryskin’s model will be saved by future measurements.

In Section 2 I briefly describe Ryskin’s model, in Section 3 I describe the data that I use, and in Section 4 I present my results.

Section snippets

Emergent cosmic acceleration

The central claim of Ryskin’s paper is that the standard gravitational field equations of General Relativity,Rμν−12Rgμν=κTμν,where κ:=8πGc4, which are well-tested on the scale of the solar system, must be modified when applied to cosmological scales. Ryskin contends, in Ref. [16], that moving from sub-cosmological scales (in which matter is distributed inhomogeneously) to cosmological scales (in which matter is distributed homogeneously) introduces emergent properties to the description of the

Data

In this paper I use 31 measurements of the Hubble parameter H(z), 11 distance measurements derived from baryon acoustic oscillation (“BAO”) data, and 120 quasar (“QSO”) angular size measurements. The H(z) data are listed in Ref. [15]; see that paper for a description. The BAO data are listed in Ref. [14]. My method of analyzing these data is slightly different from the method employed in Ref. [14]; see below for a discussion. The QSO data are listed in Ref. [1]; see that paper and Ref. [14] for

Results

My results for the fit of Ryskin’s model to the data are presented in Table 1 and Fig. 1. In the first column of Table 1 I list the data combination, in the second column I list the one-dimensional best-fitting values of H0 with their respective 1σ and 2σ uncertainties (σ here being defined in the same way as the one-sided confidence limits used in Ref. [14]), and in the third column I list the corresponding value of χmin2/ν, where χmin2 is computed from Eq. (7), and ν is the number of degrees

Conclusion

I conclude, based on these results and the earlier findings of Ref. [6], that Ryskin’s model of emergent cosmic acceleration does not provide an adequate fit to available cosmological data, and so cannot replace the standard spatially-flat ΛCDM cosmological model. The fit to the SNe Ia data presented in Ryskin’s original paper is primarily a fit to low-redshift (z ≲ 1) measurements; as can be seen from Figs. 2 and 4, as well as Tables 1 and 2, low-redshift measurements do not clearly

Declaration of Competing Interest

None.

Acknowledgments

Some of the computing for this project was performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF grants CNS-1006860, EPS-1006860, EPS-0919443, ACI-1440548, CHE-1726332, and NIH P20GM113109. This work was partially funded by DOE grant DE-SC0019038. I thank Gregory Ryskin for bringing his work to my attention, and I thank Bharat Ratra and the anonymous referee for their helpful comments on drafts of this paper.

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