Smoking-gun signatures of bounce cosmology from echoes of relic gravitational waves

Abstract

We report a novel feature of relic gravitational waves (GWs) in non-singular bounce cosmologies that is testable in light of GWs astronomy. In non-singular bounce cosmologies, the effective potential $M_p^2 a^{\prime \prime}/a$ that governs the evolution of primordial GWs contains two peaks due to the existence of contraction phase prior to the standard expansion phase. Accordingly, relic GWs interference between the two peaks, resulting in a distinctive oscillatory feature in the spectrum, analog to the resonant tunneling effect in quantum mechanics. As a result, the GWs spectrum exhibits an oscillatory patterns on high frequecy regime, distinctive to other cosmological scenarios such as inflation. We show that the amplitude of GWs spectrum is high enough to reach the sensitivity of current and forthcoming GWs instruments, making our predictions falsifiable. Hence, our finding offers a promising way to experimentally test the non-singular bounce scenarios and search for new physics in early universe cosmologies.

Figures (4)

• Figure 1: Left panel: the effective potential $M_p^2V(\tau)$ in inflationary (blue line) and bounce (green line) cosmologies. Middle panel: propogation of primordial GWs with different structure of effective potential (one-peak structure in the upper panel and two-peak structure in the lower panel). Right panel: the energy density spectrum in inflationary (blue line) and bounce (green line) cosmologies. Conformal time $\tau$ is rescaled such that $\tau = -\tau_{\ast}$($\tau = 0$) represents the location of negative(positive) peak in bounce scenario. $f_{\rm IM}$ is the frequency of GWs that cross the horizon at the end of inflationary epoch/contraction phase, respectively.
• Figure 2: Illustration of the bouncing scenarios.
• Figure 3: GWs signals (solid lines) versus experimental sensitivity curves as a function of $f$ (dashed lines). Left panel: GWs spectrum in the frequency band $10^{-5}$-$1$ Hz, with sensitivity curve of Taiji (green), TianQin (orange), LISA (light blue), BBO (cyan) and DECIGO (gray). Right panel: GWs spectrum in the frequency band $1$-$10^3$ Hz, with sensitivity curve of CE (green) and ET (gray). The GWs signals are evaluated with $w_c = 1.2$, $w_{\rm rh} = 0$ so the spectra index is $n_{\rm IM} = 0.87$ at intermediate regimes $f \leq f_{\rm IM}$. This is different from the scalar-induced GWs in inflation Domenech:2021ztg where the spectrum has a log-dependence slope $n_{\rm GW}(f) = 3 - 2 \ln(f/f_c)$ in the IR regime $f \ll f_c$Yuan:2019wwo. Other values of model parameters can be found in Sec. IV of supp.
• Figure 4: Left: The energy spectrum $\Omega_{\rm GW}$ (Green solid line) versus power-law function $f^{n_{\rm IR}}$ (Red dashed line) and $f^{n_{\rm UM}}$ (Blue dashed line). Right: $\Omega_{\rm GW}$ on high frequencies (Green solid line) versus the approximation $1 - 4k^2 a_s^2$ and the function $f^4e^{-\mu f}$ (Blue dashed line).