Science with the space-based interferometer LISA. IV: Probing inflation with gravitational waves

TL;DR

This paper evaluates LISA's capability to detect stochastic gravitational-wave backgrounds produced during inflation beyond the irreducible vacuum signal. It analyzes four well-motivated mechanisms—particle production during inflation, inflationary spectator fields, EFTs with broken spatial reparametrizations, and PBH-induced mergers—using LISA sensitivity curves and cross-checks with CMB and PBH/N_eff constraints. By developing local and global parametrizations that connect microphysical parameters (e.g., ξ, c_s, s, m_h, H) to observable spectra, the authors map viable regions where LISA could detect or constrain these signals. The findings underscore LISA's potential to illuminate inflationary physics, test symmetry-breaking patterns, and probe PBH-related GW backgrounds, while highlighting caveats from high-frequency extrapolations and backreaction effects.

Abstract

We investigate the potential for the LISA space-based interferometer to detect the stochastic gravitational wave background produced from different mechanisms during inflation. Focusing on well-motivated scenarios, we study the resulting contributions from particle production during inflation, inflationary spectator fields with varying speed of sound, effective field theories of inflation with specific patterns of symmetry breaking and models leading to the formation of primordial black holes. The projected sensitivities of LISA are used in a model-independent way for various detector designs and configurations. We demonstrate that LISA is able to probe these well-motivated inflationary scenarios beyond the irreducible vacuum tensor modes expected from any inflationary background.

Figures (18)

• Figure 1: Power law sensitivity curves for the six LISA configurations considered in this work: red A5M5, red dashed A5M2, blue A2M5, blue dashed A2M2, green A1M5, green dashed A1M2.
• Figure 2: For a power-law stochastic background of the form $\Omega_{\rm gw}=A(f/f_*)^{n_T}$, the shaded regions represent the detectable regions in the $(n_T\,,\,A)$ parameter space visible by the six LISA configurations under analysis: red A5M5, red dashed A5M2, blue A2M5, blue dashed A2M2, green A1M5, green dashed A1M2. We have chosen six representative pivot frequencies, $f_*=0.05\,,\,0.5\,,\,3\,,\,5\,,\,50\,,\,100$ mHz.
• Figure 3: Limits on the tensor spectral tilt $n_T$ and the tensor-to-scalar ratio $r$ for the six LISA configurations listed in table 1, assuming a power-law spectrum \ref{['eq:GWen']} (with arbitrary $n_{T}$, not \ref{['eq:CR']}) with reference scale $k_{*}=0.05\, \rm{Mpc}^{-1}$. This highlights the ability of LISA to test the $r - n_T$ relation.
• Figure 4: Spectrum of GWs today $h^2\Omega_{\rm GW}$ obtained from a numerical integration of the dynamical equations of motion (for a model of quadratic inflaton potential, with inflaton - gauge field coupling $f = M_{\rm Pl} / 35$), versus the local parametrization $h^2\Omega_{\rm GW} \propto (f/f_*)^{n_T}$, evaluated at various pivot frequencies $f_*$ and with the spectral tilt $n_T$ obtained from successive approximations to the analytic expression (\ref{['eq:nT']}).
• Figure 5: Region in the $(\xi,\epsilon-\eta)$ parameter space that LISA can probe, in the best configuration (left panel) and in the worst configuration (right panel). As a reference, we include the points corresponding to quadratic chaotic inflation for inflaton-gauge field coupling $M_{\rm Pl}/f = 35, 34, 33, 32$ and $31$. Note that the spectral index $n_T$, not shown in the figures to avoid to overcrowd them, is well approximated by the simple formula $n_T\simeq (4\pi\xi-6)\,(\epsilon-\eta)$.