Constructing the Potential of a Noncanonical Scalar Field for Dark Energy and Analyzing Its Effects on Cosmic Inhomogeneity Abu Ala An-Nadwi (a*), Fargiza Abdan Malikul Mulki (bcd), Muchammad Najmi Syarif Al Baihaqi (a), Hesti Retno Tri Wulandari (bcd)
a) Astronomy Study Program, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung, Indonesia
*abuannadwi[at]gmail.com
b) Astronomy Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung, Indonesia
c) Bosscha Observatory, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Peneropongan Bintang No. 45 Lembang, Indonesia
d) University Center of Excellence for Space Science, Technology and Innovation, Institut Teknologi Bandung, Jl. Ganesha No. 10 Bandung, Indonesia
Abstract
We investigate a cosmological model in which dark energy is represented by a noncanonical scalar field, characterized by a Lagrangian with a nonlinearity index \( n \) in its kinetic term (a.k.a. noncanonical Lagrangian). The potential function is semi-analytically constructed and optimized under the assumption of a constant equation of state to describe the cosmological dynamics for various values of \( n \). Using Type Ia Supernova data, the cosmological parameters \( \Omega_{m,0} \) and \( H_0 \) are constrained to determine the value of \( n \) that fits the observations. The resulting potential exhibits a negative exponential form, indicating a weakening of its strength as the universe evolves. A perturbation analysis is subsequently performed in the conformal Newtonian gauge to investigate the dynamics of cosmic inhomogeneities. Based on this analysis, the structure growth rate \( f(z) \) at \( z \approx 1 \) is found to be approximately 0.74-0.78, which is lower than the corresponding value in the \(\Lambda \)CDM model, estimated at around 0.87-0.88. Furthermore, the model predicts a future loitering phase around \( a \sim 3.2 \), during which the growth of structure slows down due to the interplay between the repulsive nature of the scalar field and the gravitational attraction of matter.
Keywords: Dark energy- Noncanonical scalar field- Potential construction
