Scalar field models for an accelerating universe

I describe a new class of quintessence+CDMmodels in which late time scalar field oscillations can give rise to both quintessence and cold dark matter. Additionally, a versatile ansatz for the luminosity distance is used to reconstruct the quintessence equation of state in a model independent manner from observations of high redshift supernovae. 1. A new model of quintessence and cold dark matter The supernova-based discovery that the universe may be accelerating can be explained within a general relativistic framework provided one speculates the presence of a matter component with negative pressure, the most famous example of which is the cosmological constant ‘Λ’ (Perlmutter et al. 1998,1999; Riess et al. 1999). Λ runs into formidable fine tuning problems since its value must be set ∼ 10 times smaller than the energy density in the universe at the Planck time in order to ensure that Λ dominates the total energy density at precisely the present cosmological epoch. This involves a fine tuning of one part in 10 at the Planck scale or one part in 10 at the Electroweak scale. One way around this difficulty is to make Λ time-dependent, perhaps by using scalar field models which successfully generate a time-dependent Λ-term during an early Inflationary epoch. In this context the exponential potential provides an interesting illustration, since the density in the φ-field tracks the background matter/radiation density when the latter is cosmologically dominant (Ratra & Peebles 1988, Wetterich 1988, Ferreira & Joyce 1997): ρφ ρB + ρφ = 3(1 + wB) pλ ≪ 1 (1) (wB = 0, 1/3 respectively for dust, radiation). This behaviour allows ρφ to be fairly large initially. Based on this property we introduce a new class of cosmological models which can describe both a time-dependent Λ-term (quintessence) and cold dark matter (CDM) within the unified framework of the class of potentials (Sahni & Wang 2000) V (φ) = V0(coshλφ− 1). (2) V (φ) has asymptotic forms: V (φ) ≃ Ṽ0e for |λφ| ≫ 1 (φ < 0), (3) V (φ) ≃ Ṽ0(λφ) for |λφ| ≪ 1 (4) 1