Scalar field models for dark energy

Abstract

The accelerated expansion of the universe was discovered in 1998 through studying high–redshift Type Ia supernovae. “Dark energy” has been proposed to account for this acceleration. There have been sundry candidates for dark energy, which remains one of the greatest unresolved mysteries in science today. Einstein's cosmological constant Λ originally introduced in 1917 became a strong candidate for dark energy. A model of the universe with cold dark matter (CDM) and a cosmological constant, the ΛCDM, became the currently accepted model of the universe. However, there are distinct unresolved issues with the ΛCDM cosmology, one major one being the coincidence problem. There are also realistic models of the universe, such as quintessence cosmologies which contain a scalar field <i>Φ</i>, hypothesized to be time–varying dark energy, that have been proposed.

In the cyclic phantom model, the universe is dominated sequentially by radiation, matter, and a phantom dark energy field, followed by a standard inflationary phase. Since this cycle repeats endlessly, the universe spends a substantial portion of its lifetime in a state for which the matter and dark energy densities have comparable magnitudes, thus ameliorating the coincidence problem.

In inflection point quintessence, a cosmology invented by the author and her advisor, the accelerated expansion of the universe is driven by a scalar field rolling near an inflection point in the potential. For the simplest such models, in which the potential is of the form <i>V(Φ) = V₀ + V₃ (Φ – Φ₀)³</i>, the scalar field can yield an eternal or a transient acceleration. The cases that imitate the ΛCDM can be consistent with either outcome.

Finally, a quintessence model with a modified exponential potential given by <i>V(Φ) = V₀ (1 + e^–λΦ)</i> can produce an acceptable accelerated expansion at late times. The strongest constraints on the model from Cosmic Microwave Background observations give the limit <i>λ</i> > 13. This cosmology provides a partial solution to the coincidence problem. The above three models of the universe contain scalar fields. The goal of this dissertation is to further the revelation of dark energy by providing ideas for more accurate models of the universe.