Determining the Equation of State of the Expanding Universe: Inverse Problem in Cosmology

Abstract

Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely but depends on one free parameter ${\Omega }_{k0}=k/(a_0^2{H}_0^2)$, where $a_0$ and $H_0$ are the present scale factor and the Hubble parameter, respectively. This degeneracy might be resolved if, for example, the time variations of the redshift of quasars are measured as proposed recently by Loeb. Therefore the equation of state of the Universe (or the metric of the universe) might be determined without any theoretical assumption on the matter content of the Universe in future.

5 pages, accepted for publication in MNRAS

References in corpus (9)

• Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant
• Cosmological Imprint of an Energy Component with General Equation of State
• Discovery of a Supernova Explosion at Half the Age of the Universe and its Cosmological Implications
• The High-Z Supernova Search: Measuring Cosmic Deceleration and Global Cur vature of the Universe Using Type Ia Supernovae
• Constraints on Cosmological Models from Hubble Space Telescope Observations of High-z Supernovae
• Gamma-Ray Bursts From Neutron Star Phase Transitions
• Direct Measurement of Cosmological Parameters from the Cosmic Deceleration of Extragalactic Objects
• The Luminosity Distance, the Equation of State, and the Geometry of the Universe
• Observational tests of x-matter models

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