Reconstructing the Cosmic Equation of State from Supernova Distances

Abstract

Observations of high-redshift type Ia supernovae indicate that the universe is accelerating, fueled perhaps by a cosmological constant or by a self-interacting scalar field. In this letter, we develop a model-independent method for estimating the form of the scalar field potential V (φ) and the associated equation of state w φ ≡ p/ε φ . Our method is based on a simple yet powerful analytical form for the luminosity distance DL which is optimized to fit observed distances to distant extragalactic supernovae, and then differentiated to yield V (φ) and w φ . Our results favor w φ −1 at the present epoch, steadily increasing with redshift. However, a cosmological constant is consistent with our results. A model-independent way of obtaining the age of the universe is also proposed.PACS numbers: 98.80. Es, 98.80.Cq, 98.80.Hw, 97.60.Bw The relation between luminosity distance and redshift for extragalactic Type Ia Supernovae (SNe) appears to favor an accelerating Universe, where almost two-thirds of the critical energy density may be in the form of a component with negative pressure [1,2]. On the other hand, several studies of large-scale structure, including those of the abundances of rich galaxy clusters [3] and clustering of galaxies [4] and Lyman-α clouds [5] (for recent reviews, see [6]) indicate low baryonic and matterThis consistency is encouraging since it is well-known that a flat Cold Dark matter Universe with Ω M < 1 and a Cosmological Constant Λ > 0 fits observations of large-scale structure [6,7] better than any other theoretical model.Although Λ = 0 does agree well with the recent SNe observations, it is clear that at a theoretical level a constant Λ runs into serious difficulties, since the present value of Λ is ∼10 123 times smaller than predicted by most particle physics models [7].A time-dependent Λ-like term, which considerably alleviates this fine-tuning problem, can be described in a simple and natural way in terms of a scalar field (referred to here as the Λ-field) with a self-interaction potential V (φ) which is minimally coupled to the Einstein gravity field, and has little or no coupling to any other known physical field. Actually, this model mimics the simplest variant of the inflationary scenario of the early Universe. Since we have not yet got a definite prediction for the form of V (φ) from theoretical considerations, it has to be reconstructed from present-day observations.The aim of the present letter is to go from observations to theory, i.e. from D L (z) to V (φ), following the prescription outlined by Starobinsky [8] (see also [9]). This is the first attempt at reconstructing V (φ) from real observational data without resorting to specific models (e.g. cosmological constant, quintessence etc.).Since the spatially flat Universe (Ω φ + Ω M = 1) is both predicted by the simplest inflationary models and agrees well with observational evidence, we will not consider spatially curved Friedmann-Robertson-Walker (FRW) cosmological models. In a flat FRW cosmology, the luminosity distance D L ...

Direct reconstruction of the dark energy scalar-field potential

“…This is because the parameters in the Padé approximation are additionally constrained to satisfy criteria related to the behavior of r z as z ! 1, as well as by the assumption of a flat universe [15]. When fitting the w z parametrizations to the data, we were able to impose a prior on m based on existing cosmological information [this was not possible when using r z fitting functions].…”

“…We compare and contrast a variety of methods to reconstruct the potential and the dark energy EOS. We write the luminosity distance either as a simple polynomial expansion in redshift, or as a Padé approximation [15] (which avoids some of the known problems in the polynomial expansion when taking derivatives [8,10,16]). In addition to approximating the luminosity distance, we also explore two approximations to the EOS: w z w 0 w a 1 ÿ a [17,18] and w z w 0 ÿ ln 1 z [10].…”

Untitled

“…where S(u) = sin u for a closed universe, S(u) = sinh u for an open universe and S is the identity for a flat universe 8,9,10 . This reconstruction can actually be extended to non minimally coupled scalar fields in the framework of scalar-tensor theories 11,12 .…”

From brane assisted inflation to quintessence through a single scalar field

“…It is hoped that programmes such as the ones initiated in Ref. [26] using red shift -luminosity distance correlations and in Ref. [15] using CMB data [27] will enable the enforcement of tighter constraints on the signature and value of the parameters A and β.…”