Unique gravitational wave signatures of GLPV scalar-tensor theories

Abstract

We study gravitational waves induced by scalar primordial fluctuations in Gleyzes-Langlois-Piazza-Vernizzi (GLPV), beyond Horndeski, scalar-tensor theories. We uncover, at the level of the action, a new scalar-scalar-tensor interaction, unique to GLPV models disconnected from Horndeski via disformal transformation. The new interaction, arising in the unitary-degenerate (U-DHOST) sector of GLPV, leads to third derivatives in the source for scalar-induced tensor modes, which are absent in Horndeski-related theories. Such new higher-derivative terms lead to a further enhanced production of induced gravitational waves. We predict that for a scale-invariant primordial spectrum, the induced gravitational wave spectral density has a characteristic frequency dependence proportional to $f^5$. Such a fast-rising spectrum offers a potential unique signature of modified gravity in the early universe.

Figures (3)

• Figure 1: GLPV effects dominate for modes that become subhorizon $k\tau>1$ ($k > aH$) before the transition to GR ($\tau<\tau_t$), with $\tau_t$ occurring before BBN ($\tau_{BBN}$). Assuming the initial power spectrum peaks at $k_p$, the dominant GLPV impact is on the subhorizon modes with $k_p>k_t$, where $k_t=1/\tau_t$.
• Figure 2: Spectral density of the induced GWs normalized by $A_\zeta^2$ for $b_5=10^ {-4}$ for two different values of $\tau_t$. The left hand side is a log-normal primordial spectrum and the right hand side is a scale-invariant one. The dashed lines show the GR limit.
• Figure 3: We show the induced GW spectrum today for a log-normal (peaked at $k_p$) and a scale-invariant (with a UV cut-off at $k_{\rm UV}$) spectrum of curvature fluctuations, respectively shown in black and blue lines. Solid lines indicate the induced GWs from the GLPV model, while dashes lines indicate the Horndeski model in Domenech:2024drm (we also provide details in App. \ref{['subsubsec:Horndeski_Toy_Model']}). The dotted lines indicate the GR limit. We fix the amplitude of the scalar power spectrum to $A_\zeta = 10^{-7}$ and $A_\zeta = 10^{-9}$ for the log-normal and scale-invariant case, respectively. Further, we set $\tilde{\Gamma} = b_5= 10^{-4}$ and $k_p/k_t= 10^4$ and $k_{\rm UV}=k_t=10^{4.5}$. For the log-normal distribution we fixed $f_p=k_p/(2\pi) \simeq 1.7 \times 10^{-3}\,{\rm Hz}$ and for the scale-invariant spectrum $f_{\rm UV} \simeq 30\,{\rm Hz}$. For illustration purposes, we show the power-law integrated sensitivity curves as described in Ref. Thrane:2013oyaSchmitz:2020syl for LIGO A+ A+, Einstein Telescope (ET) (15km arms triangular configuration Branchesi:2023mws), Cosmic Explorer (CE) ce, DECIGO Yagi:2011wgKawamura:2020pcg, LISA Barke:2014lsa and $\mu$-Ares Sesana:2019vho experiments. The purple-shaded region shows the upper bounds from the LVK collaboration KAGRA:2021kbb.