Supernovae Ia , Evolution and Quintessence ∗

Quintessence models with a dark energy generated by pseudo Nambu– Goldstone bosons provide a natural framework in which to test the possibility that type Ia supernovae luminosity distance measurements are at least partially due to an evolution of the sources, since these models can have parameter values for which the expansion of the Universe is decelerating as well as values for which it is accelerating, while being spatially flat in all cases and allowing for a low density of clumped matter. The results of a recent investigation [1] of current observational bounds which allow for SNe Ia source evolution are discussed. It is found that models with source evolution still favour cosmologies with an appreciable amount of acceleration in the recent past, but that the region of parameter space which is most favoured shifts significantly. As has been described in many other talks at this conference, many independent measurements – for example, the spectrum of cosmic microwave background radiation (CMBR) anisotropies, galaxy clustering statistics, peculiar velocities, the baryon mass fraction in clusters of galaxies – all appear to agree in estimating that the density of matter which is clumped is relatively low compared to the critical density, being of order Ωm0 ∼ 0.2–0.3. On the other hand, the recent measurement of the position of the first acoustic peak in the angular power spectrum of CMBR anisotropies by the BOOMERANG-98 and MAXIMA-I experiments now gives unequivocal evidence that the Universe is close to being spatially flat [2]. A natural conclusion to draw from these observations is that a significant proportion of the energy density of the Universe is in the form of a dark component which is smooth, rather than clumped, on cosmological scales. The form of dark energy which we are most familiar with, for historical reasons, is a cosmological constant. It leads to models in which the expansion of the universe is accelerating. In the last few years, Type Ia supernovae (SNe Ia) have come to be used as a cosmological distance indicator, with the conclusion that there is very good evidence that the expansion of the Universe is indeed accelerating [3,4]. Unfortunately, in terms of the physical basis of the measurements, the SNe Ia result remains the most poorly understood component of the present “concordance model”, and it remains possible that there are systematic uncertainties that have not been accounted for, ∗) To appear in “Cosmology and Particle Physics”, Proc. of the CAPP’2000 Conference, Verbier, eds. J. Garćıa-Bellido, R. Durrer and M. Shaposhnikov, (American Institute of Physics, 2001) such as an evolution of the sources or extinction by dust. In particular, cosmological parameters are fitted by normalizing the peak luminosities of supernovae on the basis of a purely empirical correlation which has been observed at low redshifts between the peak luminosity and the decay time of SNe Ia events as measured in their rest frames: the resulting “Phillips relations” [5]– [7] reduce the dispersion in the distance moduli to about 0.15 [6,7] as compared to an intrinsic dispersion of 0.3–0.5 in peak absolute B − V magnitudes of suitably selected nearby events. Many of the details of the physics behind SNe Ia remain unclear. It is believed that each SNe Ia event is formed by a white dwarf in a binary system, accreting matter from its companion until it undergoes a catastrophic thermonuclear conflagration, possibly at a sub-Chandrasekhar limit stage. Given their common physical origin such systems might be reasonably expected to be somewhat “insensitive” to much of the individual histories of the progenitor systems, which provides the basis for their use as a standard candle. However, while much progress has been made in attempting to numerically model the explosions [8], huge uncertainties remain because of a lack of knowledge of the details of particular nuclear cross–sections and the fluid dynamics of flame propagation. Attempts to find a physical origin for the Phillips relations are at a very preliminary stage [9]. Given that the prospect of understanding the physical basis of the SNe Ia events is not going to be resolved without much more detailed measurements and calculations, it would be prudent to test the conclusions that have been derived cosmologically, allowing for the possibility that there has been some evolution of the peak luminosities insofar as they affect the Phillips relations over cosmological timescales. Such an analysis has been instigated by Drell, Loredo and Wasserman [10] in the case of open Friedmann–Robertson–Walker (FRW) models. I wish to argue, however, that since we now have remarkably good evidence that the Universe is close to flat with a low density fraction of ordinary clumped matter, Ωm0 ∼ 0.2–0.3, it makes much better sense to test the evolution hypothesis in the context of models which have these features but which make no assumptions regarding the acceleration or deceleration of the Universe at the present epoch. This is not possible within the class of Friedmann-Lemâıtre models with Ωm + ΩΛ = 1. However, cosmological models with a quintessence field in the form of a dynamical pseudo Nambu–Goldstone boson have precisely the desired properties. It may come as a surprise that “quintessence” does not necessarily entail an accelerated expansion of the Universe, since one of the most common approaches to seeking a particle physics origin for the vacuum energy is to look for a scalar field, φ, with a potential, V (φ), which gives homogeneous isotropic cosmological solutions for which the Universe undergoes an accelerated expansion at late times. However, such an approach does not fully utilize the fact that the effective equation of state for the quintessence field, Pφ = wφρφ, has a variable coefficient wφ which can generically take all values consistent with the dominant energy condition. Furthermore, such an approach often leads to the study of potentials whose physical origin is not particularly well motivated. The PNGB model, on the other hand, is well–motivated from a particle physics