Gravitational Energy as Dark Energy: Concordance of Cosmological Tests

We provide quantitative evidence that a new solution to averaging the observed inhomogeneous structure of matter in the universe (Wiltshire 2007a,b), leads to an observationally viable cosmology without exotic dark energy. We find concordance parameters which simultaneously satisfy three independent tests: the match to the angular scale of the sound horizon detected in the cosmic microwave background anisotropy spectrum; the effective comoving baryon acoustic oscillation scale detected in galaxy clustering statistics; and type Ia supernova luminosity distances. Independently of the supernova data, concordance is obtained for a value of the Hubble constant which agrees with the measurement of the Hubble Key team of Sandage et al. (2006). Combining all three tests, best–fit parameters include a global average Hubble constant H0 = 61.7 +1.4 −1.3 km sec −1 Mpc, a present epoch void volume fraction of fv0 = 0.76 ± 0.05, and an age of the universe of 14.7 +0.6 −0.5 billion years as measured by observers in galaxies. The mass ratio of non–baryonic dark matter to baryonic matter is 3.1 −1.1, computed with a baryon–to–photon ratio that concords with primordial lithium abundances. Subject headings: Cosmology: theory — Cosmology: large-scale structure of universe — Cosmological parameters — Cosmology: dark matter The apparent acceleration of the rate of expansion of the universe at the present epoch is usually attributed to a smooth “dark energy”, the nature of which poses a foundational mystery to physics. Our present standard ΛCDM cosmology, with a cosmological constant, Λ, as dark energy, fits three independent observational tests: type Ia supernovae (SneIa) luminosity distances; the angular scale of the Doppler peaks in the spectrum of temperature anisotropies in the cosmic microwave radiation; and the baryon acoustic oscillation scale detected in galaxy clustering statistics. In this Letter we provide quantitative evidence that these same tests can all be satisfied in ordinary general relativity without exotic dark energy, within a model (Wiltshire 2007a,b) which takes a new approach to averaging the observed structure of the universe, which is presently dominated by voids. In recent years a number of cosmologists have questioned whether the apparent acceleration of the universe might in fact be an artifact of replacing the actual observed structure of the universe by a smooth featureless dust fluid in Einstein’s equations. (For a review see Buchert (2007).) The specific solution to the averaging problem we investigate here (Wiltshire 2007a) realises cosmic acceleration as an apparent effect that arises in the decoupling of bound systems from the global expansion of the universe. In particular, gradients in the kinetic energy of expansion, and more importantly, in the quasilocal energy associated with spatial curvature gradients between bound systems and a volume–average position in freely expanding space, can manifest themselves in a significant difference in clock rates between the two locations. The difference in clock rates is negligible in the early universe when the assumption of homogeneity is valid, but becomes important after the transition 1 Department of Physics & Astronomy, University of Canterbury, Private Bag 4800, Christchurch 8140, New Zealand 2 Physics Department, National University of Singapore, 2 Science Drive 3, Singapore 117542 to void dominance, making apparent acceleration a phenomenon registered by observers in galaxies at relatively late epochs. Galaxies and other objects dense enough to be observed at cosmological distances are bound systems, leading to a selection bias in our sampling of cosmic clocks. Since the clock rates within bound systems are closely tied to a universal finite infinity scale (Ellis 1984; Wiltshire 2007a), gross variations in cosmic clock rates are not directly observable in any observational test yet devised. However, relative to observers in bound systems an ideal comoving observer within a void would measure an older age of the universe, and an isotropic CMB with a lower mean temperature and an angular anisotropy scale shifted to smaller angles. A systematic variation in clock rates between bound systems and the volume average, which we will find to be 38% at the present epoch, seems implausible given our familiarity of large gravitational time dilation effects occurring only for extreme density contrasts, such as with black holes. However, cosmology presents a circumstance in which conventional intuition based on static Newtonian potentials can fail, because spacetime itself is dynamical and the definition of gravitational energy is extremely subtle. The normalization of clock rates in bound systems relative to expanding regions can accumulate significant differences, given that the entire age of the universe has been available for this to occur. In this Letter we find concordance parameters for the two–scale fractal bubble (FB) model (Wiltshire 2007a,b) which satisfy the three major independent observational tests. The two scales represent voids, and the filaments and bubble walls which surround them, within which clusters of galaxies are located. The geometry within finite infinity regions in the bubble walls is assumed to be spatially flat, but the geometry beyond these regions is not spatially flat. The relationship between the geometry in galaxies and the volume–average geometry within our 2 Leith, Ng & Wiltshire present horizon volume is fixed by the assumption that the regionally “locally” measured expansion is uniform despite variations in spatial curvature and clock rates. This provides an implicit resolution of the Sandage–de Vaucouleurs paradox (Wiltshire 2007a): the “locally” measured or “bare” Hubble flow is uniform, but since clock rates vary it will appear that voids expand faster than walls when referred to any single set of clocks. As observers in galaxies, our local average geometry at the boundary of a finite infinity region is spatially flat, with the metric ds F I = −dτ + aw (τ) [