Is the universe still accelerating?

Sean Carroll, University of Chicago
To most cosmologists, it came as something of a surprise when, in 1998, two groups (the Supernova Cosmology Project [1] and the High-Z Supernova Team [2,3] presented evidence that the expansion of the universe is accelerating rather than slowing down. Applied to a Robertson-Walker metric

 \begin{displaymath}{\rm d}s^2 = -{\rm d}t^2 + R^2(t)\left[
{{{\rm d}r^2}\over{1-kr^2}} + r^2 {\rm d}\Omega^2\right]\ ,
\end{displaymath} (1)

Einstein's equations imply the Friedmann equation,

 \begin{displaymath}{\dot R}^2 =
{{8\pi G}\over 3}R^2 \rho - k\ ,
\end{displaymath} (2)

where R is the scale factor, $\rho$ the energy density, and k the spatial curvature parameter. The energy density in a species of non-relativistic massive particles (``matter'') is given by the species' rest mass times its number density, and correspondingly diminishes as $\rho_{\rm M}\propto R^{-3}$ as the number density becomes increasingly rarified. In a matter-dominated universe, then, the right-hand side of (2) is decreasing as the universe expands, resulting in deceleration. To provide acceleration ( $\ddot R > 0$), the energy density must decay more slowly than R-2; the simplest candidate for such a source is the cosmological constant $\Lambda$, equivalent to a ``vacuum'' energy density

\begin{displaymath}\rho_\Lambda = {{\Lambda}\over{8\pi G}}\ ,
\end{displaymath} (3)

which remains constant as the universe expands. The supernova teams have measured the distances to cosmological supernovae by using the fact that the intrinsic luminosity of Type Ia supernovae, while not always the same, is closely correlated with their decline rate from maximum brightness, which can be independently measured. Their apparent magnitude then provides an indication of their distance, and their redshift z (related to the value of the scale factor R at the time of explosion by z=R0/R - 1) can be straightforwardly determined from spectroscopic data. The results to date favor a positive value of $\rho_\Lambda$. Along with constraints on the matter density as derived from dynamical measurements of galaxies and clusters, and additional constraints from the anisotropies of the cosmic microwave background, a consistent picture emerges with $\rho_\Lambda/\rho_{\rm M}
\sim 3$, with the total energy density $\rho_{\rm M}+\rho_\Lambda$ approximately equal to the critical density necessary to solve (2) with k=0.

Despite its excellent fit to the data, such a universe seems quite unnatural. For one thing, the implied vacuum energy $\rho_\Lambda \sim 10^{-10}$ erg/cm3 is less by many orders of magnitude than any sensible estimate based on particle physics. For another, $\rho_{\rm M}$ and $\rho_\Lambda$ evolve at different rates, with $\rho_{\rm M}/\rho_\Lambda \propto R^{-3}$, and it would seem quite unlikely that they would differ today by a factor of order unity. Since any effect which would diminish the brightness of distant supernovae without noticeably affecting their spectra could mimic the effects of an accelerating universe, it is sensible to ask whether these apparently dramatic results can be explained in terms of conventional astrophysics without invoking new cosmological phenomena. The most plausible candidates for such effects are evolution of the supernova population from high to low redshifts, and obscuring dust between us and the high-redshift objects. Both possibilities are being carefully investigated.

Type Ia supernovae are thought to result from thermonuclear explosions of white dwarfs which have reached the Chandrasekhar limit. Therefore, they can occur in a wide variety of environments, and a simple argument against evolution is that the high-redshift environments, while chronologically younger, should be a subset of all possible low-redshift environments, which include regions that are ``young'' in terms of chemical and stellar evolution. Nevertheless, even a small amount of evolution could ruin our ability to reliably constrain cosmological parameters [4]. In their original papers [1,2,3], the supernova teams found impressive consistency in the spectral and photometric properties of Type Ia supernovae over a variety of redshifts and environments (e.g., in elliptical vs. spiral galaxies). More recently, however, Riess et al. [5] have presented tentative evidence for a systematic difference in the properties of high- and low-redshift supernovae, claiming that the risetimes (from initial explosion to maximum brightness) were higher in the high-redshift events. It is not immediately clear that such a difference is relevant to the distance determinations; first, because the risetime is not used in determining the absolute luminosity at peak brightness, and second, because a process which only affects the very early stages of the light curve is most plausibly traced to differences in the outer layers of the progenitor, which may have a negligible affect on the total energy output. Nevertheless, any indication of evolution brings into question the fundamental assumptions behind the entire program. However, Aldering et al. [6] have argued that the discrepancy in risetimes goes away once one properly takes into account correlations in the uncertainties of the light curve fit parameters. In that case, all of the data presently available are consistent with no evolution of any sort between high and low redshifts. It is clearly important to improve both our empirical and theoretical understanding of the high-redshift supernovae, but to date there is no compelling reason to doubt the distance determinations (and cosmological conclusions) of the original studies.

Other than evolution, obscuration by dust is the leading concern about the reliability of the supernova results. Ordinary astrophysical dust does not obscure equally at all wavelengths, but scatters blue light preferentially, leading to the well-known phenomenon of ``reddening''. Spectral measurements by the two supernova teams reveal a negligible amount of reddening, implying that any hypothetical dust must be a novel ``grey'' variety. This possibility has been investigated by a number of authors [7] These studies have found that even grey dust is highly constrained by observations: first, it is likely to be intergalactic rather than within galaxies, or it would lead to additional dispersion in the magnitudes of the supernovae; and second, intergalactic dust would absorb ultraviolet/optical radiation and re-emit it at far infrared wavelengths, leading to stringent constraints from observations of the cosmological far-infrared background. Moreover, even relatively grey dust would inevitably lead to some reddening, and recent near-infrared observations of a high-reshift supernova [8] have failed to find any evidence for such an effect. Thus, while the possibility of obscuration has not been entirely eliminated, it requires a novel kind of dust which is already highly constrained (and may be convincingly ruled out by further observations).

Meanwhile, measurements of the anisotropy spectrum of the cosmic microwave background continue to improve. Two groups [9] have reported measurements on the angular scale of the first ``Doppler peak'', whose location is tied to the total energy density of the universe. Both experiments provide independent evidence that the energy density is approximately equal to the critical density of a spatially flat universe; along with increasing confidence that ordinary matter constitutes approximately $30\%$ if the critical density, this provides additional support for the existence of a positive cosmological constant. Data to come in the near future, from satellite, ground-based, and balloon-borne experiments, will test this scenario to much greater precision. Measurements of additional supernovae at even higher redshifts have the potential of separating out the effects of evolution and extinction from those of cosmology; along with continued ground-based and Space Telescope observations, a dedicated satellite has been proposed [10] which could observe 2000 high-redshift supernovae per year. Our best current understanding, therefore, continues to favor an accelerating universe, and in a short while the case could be nailed down to a near certainty; in that case the task of theorists to explain a small but nonzero vacuum energy will become especially urgent.


[1] S. Perlmutter et al. [Supernova Cosmology Project Collaboration], Astrophys. Journ. 517, 565 (1999); astro-ph/9812133.

[2] B. P. Schmidt et al. [Hi-Z Supernova Team Collaboration], Astrophys. Journ. 507, 46 (1998); astro-ph/9805200.

[3] A.G. Riess et al. [Hi-Z Supernova Team Collaboration], Astron. Journ. 116, 1009 (1998); astro-ph/9805201.

[4] P. S. Drell, T. J. Loredo and I. Wasserman, astro-ph/9905027.

[5] A. G. Riess, A. V. Filippenko, W. Li and B. P. Schmidt, Astron. Journ. 118, 2668 (1999); astro-ph/9907038.

[6] G. Aldering, R. Knop and P. Nugent, astro-ph/0001049.

[7] A. Aguirre, Astrophys. Journ. 512, L19 (1999); astro-ph/9811316; Astrophys. Journ. 525, 583 (1999); astro-ph/9904319; A. Aguirre and Z. Haiman, astro-ph/9907039; J.T. Simonsen and S. Hannestad, Astron. Astrophys. 351, 1 (1999); astro-ph/9909225; T. Totani and C. Kobayashi, Astrophys. Journ. 526, L65 (1999); astro-ph/9910038.

[8] A.G. Riess et al., astro-ph/0001384.

[9] A. D. Miller et al., Astrophys. Journ. 524, L1 (1999); astro-ph/9906421; A. Melchiorri et al., astro-ph/9911445.

[10] See the web page at

Jorge Pullin