Constraints on dark energy from the gravitational wave background

Abstract

Current observational data indicate that dark energy (DE) is a cosmological constant without considering its conclusiveness evidence. Considering the dynamic nature of $$\Lambda $$ Λ individually as a function of time and the scale factor, we review their effects on the gravitational waves. This article is a continuation of the previous work (Khodagholizadeh in JHEAp 36:48–54, 2022), in which DE only was based on Hubble’s parameter and/or its derivatives. For the DE model based on the scale factor ($$a^{-m}$$ a - m ), the results showed that the parameter m is more limited as $$ 2 < m \leqslant 3$$ 2 < m ⩽ 3 compared with the other models and due to the small value of DE density at the early universe. It is only in the mode $$m=3$$ m = 3 that DE affects the low-frequency gravitational waves when its frequency is less than the $$10^{-3}$$ 10 - 3 Hz in a matter-dominated epoch. The broad bound on reducing the amplitude and the B-B polarization multipole coefficients, from maximum to minimum, is for the models developed based on the Hubble parameter function. There are primary sources of low- and very low-frequency GWs, such as the coalescence of massive black hole binaries with $$M_{bh} > 10^{3} M_{sun}$$ M bh > 10 3 M sun , to determine the type of DE by mHz frequency space experiments (e.g., LISA) and by nHz-range NANOGrav 15-year data.