Quintessence with tachyonic resonance and late-time cosmic-microwave-background and gravitational-wave signals

TL;DR

The paper investigates dynamical dark energy through a quintessence model featuring a sharp transitional feature in the equation of state $w(a)$ (TDE). Using a plateau-like potential and tachyonic resonance, the authors perform linear Floquet analysis and nonlinear lattice simulations (including matter) to show how rapid rolling triggers perturbation growth, backreaction, and a late-time transition that can mimic a dark-matter-like component. They compare the TDE realization to a smooth DSCh quintessence parameterization via MCMC analysis, finding comparable fits to current data with transition around $a_t\sim0.9$ and $w_0$ in the range $-0.3$ to $-0.5$; the SN data largely drive these results. The model predicts observable late-time signals, notably a LISW imprint on the CMB around $\ell\sim50$ and a stochastic GW background whose peak frequency depends on the decay constant $f$, with prospects for constraints from quasar astrometry and future PTAs/Theia, highlighting rich observational prospects for late-time cosmology.

Abstract

Combinations of recent cosmological observations, including Dark Energy Spectroscopic Instrument (DESI), show hints of a dynamical nature for dark energy. While the data suggest the possibility of the phantom crossing, it is worth thoroughly exploring quintessence models. Given that phenomenological parametrisations of the equation-of-state parameter $w(a)$ with a sharp transitional feature fit the data well, we study the realisation of such models in quintessence. In the late Universe, the quintessence field begins to oscillate abruptly, changing the behaviour of $w$. Naturally, such a model entails tachyonic instability, and particle production modifies $w$. We perform numerical lattice simulations to study the time dependence of $w$. In addition, the violent particle production produces significant density perturbations and the stochastic gravitational-wave background, whose characteristic scale depends on the mass scale of the quintessence around the minimum of the potential. We discuss the observability of these late-time cosmological signals through cosmic microwave background, quasar astrometry, pulsar timing arrays, and other observational probes.

Figures (18)

• Figure 1: The growth rate $\mu_k$ (equivalent to $\mu_\kappa$ in Appendix \ref{['sec: linear analysis']}) normalized by the oscillation half period $\Delta\tau$ (Eq. \ref{['eq: delta tau']}) as a function of the physical wavenumber $k$ and the oscillation amplitude $\phi_\mathrm{amp}$. White lines indicate the cosmological redshifts of $k$ and $\phi_\mathrm{amp}$ in the expanding universe for $f=10^{-3}M_\mathrm{Pl}$, $V_0/(3\Omega_\phi H_0^2M_\mathrm{Pl}^2)=1.1$, $H_0=66km/s/Mpc$, and $\Omega_\mathrm{m}=0.32$ (the quintessence density is given by $\Omega_\phi=1-\Omega_\mathrm{m}$).
• Figure 2: The evolution of the power spectrum $\mathcal{P}_\phi=\frac{k^3}{2\pi^2}\abs{\delta\phi_k}^2$ normalised by $m_\mathrm{th}^2$ from $t=0$ ($z=9$; corresponding to the initial field value, $\phi_\mathrm{i}/f=7.32$) to $t=900/(660H_*)$ with the time step $\Delta t=20/(660H_*)$ where $H_*=100km/s/Mpc$ from red to purple. The black dashed line corresponds to today, $t_0=897/(660H_*)$. The evaluated value of $t_0$ and the required initial condition $\phi_\mathrm{i}$ are slightly different in the lattice simulation, as large fluctuations even change the background expansion history.
• Figure 3: Dynamics of the simulation-box average field value $\expval{\phi} /f$ with (lattice simulation; blue solid line) and without (yellow dotted line) the backreaction from perturbations for $f = 10^{-3} M_\mathrm{Pl}$. $\tilde{t}$ is physical time normalized by $660H_* = 1000H_0$. The vertical black dotted line represents the current time $a = 1$.
• Figure 4: Time dependence of the spatially averaged energy density components of scalar field: the kinetic energy $E_{\phi, K}$ (blue), the gradient energy $E_{\phi, G}$ (orange), the potential energy $E_{\phi, V}$ (purple), and the total energy $\rho_{\text{tot}}$ (pink) for $f=10^{-3}M_\mathrm{Pl}$ (left) and $f=10^{-4}M_\mathrm{Pl}$ (right). $\tilde{t}$ is physical time normalized by $660H_* = 1000H_0$. $\tilde{\rho}$ is energy density normalized by $(f\times660H_*)^2$. The vertical black dotted line represents the current time $a = 1$. The output cosmological parameters are found as $H_0/(\mathrm{km/s/Mpc}) = 66.3$ and $\Omega_\mathrm{m} = 0.316$ for $f=10^{-3}M_\mathrm{Pl}$, while $H_0/(\mathrm{km/s/Mpc}) = 65.1$ and $\Omega_\mathrm{m} = 0.327$ for $f=10^{-4}M_\mathrm{Pl}$.
• Figure 5: Time dependence of the EoS parameter of the scalar field $\phi$ (solid blue line) for $f=10^{-3}M_\mathrm{Pl}$ (left) and $10^{-4}M_\mathrm{Pl}$ (right). $\tilde{t}$ is physical time normalized by $660H_* = 1000H_0$. The dashed orange line is the result of the time average. The vertical black dotted line represents the current time $a = 1$.