LISA as a probe of pre-big-bang physics: a nested sampling analysis

TL;DR

The paper addresses how to constrain the GWB predicted by pre-big-bang cosmology using LISA by performing Bayesian inference with nested sampling on an eight-parameter model, considering both minimal and non-minimal scenarios and including foregrounds. It showcases how the GWB can appear as a flat or broken power law within LISA's band and delineates the mapping between fundamental theory parameters ($H_1$, $m$, $σ_i$, $β$) and observable spectral features. The authors quantify recoverability under favorable conditions, finding, for example, ~18% 68% CL uncertainties for $H_1$ or $m$ when the corresponding bends lie in the LISA window, and tight constraints on $β$ for left-bend cases. If a compatible signal is detected, LISA could provide empirical hints of string-inspired early-universe physics; non-detections would still constrain the viable parameter space and motivate multi-band approaches for future progress.

Abstract

Using a nested sampling analysis, we study the gravitational-wave background (GWB) predicted by pre-big-bang cosmology, both in its minimal and non-minimal version. Within the LISA sensitivity range, the GWB signal is a flat or a broken power law, parametrized by four fundamental quantities: the Hubble parameter at the curvature bounce $H_1$, the axion mass $m$, the initial amplitude of the axion field $σ_i$ and the exponent $β$ governing the high-energy growth of the dilaton and the dynamics of the internal dimensions. We determine the posterior distributions of these parameters based on how LISA would detect such signal. Including the galactic and extra-galactic foregrounds in the analysis, the most stringent constraints on $H_1$, $σ_i$ and $β$ are obtained when the signal exhibits a left-bend feature, while for $m$ this happens for a right-bend feature. Relative uncertainties reach $ΔH_1/H_1 ,\,Δm/m \sim 18\%$ at $68\%$ confidence level under favourable conditions. LISA will thus be capable of placing significant constraints on the pre-big-bang model, potentially providing empirical hints of string theory in the case of detection.

Figures (6)

• Figure 1: Dependence of GWB test curves on the parameters $\beta$, $H_1$, $m$ and $\sigma_i$.
• Figure 2: The four test curves of the injected signals: a plateau with high SNR (top left); a plateau with low SNR (top right); a left-bend broken power law (bottom left); a right-bend broken power law (bottom right). The LISA sensitivity curve is shown in black and the injected signal in light blue.
• Figure 3: Top right: injected test signal of the pre-big-bang scenario (yellow curve) and reconstructed signal (red curve), compared with the LISA sensitivity curve (solid black); shaded regions in light (dark) blue correspond to the 68% (respectively, 95%) CL uncertainty in the reconstructed signal. Triangle plot: Two- and one-dimensional posterior probability distributions of the test-curve parameters. In the marginalized plot, the true and reconstructed value are marked by, respectively, a dashed yellow and a solid red line. The injected values are $\beta = 0$, $H_1 = 10^{-3.4}$, $m = 10^{-5.0}$ and $\sigma_i = 0.80$. Galactic and extra-galactic foregrounds are included.
• Figure 4: Top right: injected test signal of the minimal pre-big-bang scenario (yellow curve) and reconstructed signal (red curve), compared with the LISA sensitivity curve (solid black); shaded regions in light (dark) blue correspond to the 68% (respectively, 95%) CL uncertainty in the reconstructed signal. Triangle plot: Two- and one-dimensional posterior probability distributions of the test-curve parameters. In the marginalized plots, the true and reconstructed values are marked by, respectively, a dashed yellow and a solid red line. The injected values are $\beta = 0$, $H_1 = 10^{-3.9}$, $m = 10^{-8.0}$ and $\sigma_i = 0.20$. Galactic and extra-galactic foregrounds are included.
• Figure 5: Top right: injected test signal of the minimal pre-big-bang scenario (yellow curve) and reconstructed signal (red curve), compared with the LISA sensitivity curve (solid black); shaded regions in light (dark) blue correspond to the 68% (respectively, 95%) CL uncertainty in the reconstructed signal. Triangle plot: Two- and one-dimensional posterior probability distributions of the test-curve parameters. In the marginalized plots, the true and reconstructed values are marked by, respectively, a dashed yellow and a solid red line. The injected values are $\beta = 0$, $H_1 = 10^{-3.5}$, $m = 10^{-3.3}$ and $\sigma_i = 0.95$. Galactic and extra-galactic foregrounds are included.