Dynamical and Parameter Constraints of Dark Energy Dynamics Model with \(\alpha\)-Attractor Potential Scalar Field Aulia Taqiaturrahmah, Hesti Retno Tri Wulandari, Fargiza Abdul Malikul Mulki
Institut Teknologi Bandung
Abstract
Observations of type Ia supernovae have shown that the expansion of the universe is accelerating. Since generic matters can not induce acceleration, dark energy as an additional component with negative pressure has been proposed. Cosmological constant is the simplest dark energy model, however, it suffers from energy scale and coincidence problems. Aiming at alleviating cosmological constant problems, various models of dynamical dark energy in the form of scalar fields have been put forward, such as quintessence, k-essence, and phantom field. A model is considered more successful if it accommodates a broader range of initial values (basins of attractions) and evolves convergently to the late time conditions. Unfortunately, the proposed scalar fields still have relatively narrow basins of attractions. Therefore, -\alpha--attractors have been proposed, and are predicted to have vast basins of attractions with their attractor property.
The dynamical behavior of \(\alpha\)-attractors is governed by its potential parameters. The parameter \(\alpha\) is responsible for the scaling, while the two power parameters, \(p\) and \(n\), dictate the shape of the potential model. Additionally, the initial value of the field determine the evolutionary track and how it meets observational constraints for a given set of parameters. Another feature of this model is the \(c\) parameter determined by the closure relation in fulfilling the energy density budget of the universe. A stability test was performed using an autonomous method, describing the behaviors around critical points. Physically interpreted, the \(\alpha\)-attractor evolves following the equation of cosmic dynamics, which goes through generic matter- and dark energy-dominated eras. The results for Starobinsky potential, i.e., the \(\alpha\)-attractor potential model with \(\alpha=1\), \(p=2\), and \(n=1\), shows that there exists a stable cosmic acceleration solution. We used supernovae Ia and BAO data to perform a statistical analysis employing Markov Chain Monte Carlo. We found that the data support a solution with \(\alpha=2.848\), \(p=3.077\), and \(n=4.929\) for the initial value of \(\phi_{ini}=2.59\).
Keywords: basin of attraction, dark energy, scalar field, \(\alpha\)-attractor
