RG-Induced Spectral Diffusion in History-Dependent Gravity: Log-Normal Gravitational Wave Signatures for LISA

Key Points

• This research aims to understand how gravitational wave signatures are affected by history-dependent gravity through the renormalization group.
• Derived the renormalization group running of the memory kernel using functional renormalization group framework.
• Analyzed spectral diffusion and its relation to kernel width and tensor spectrum.
• Utilized Fisher forecasting to assess LISA's detection capabilities.
• The kernel width relation is β_Λ = cξ, leading to spectral diffusion quantified by σ²(N) = Λ₀N + ½cξN².
• The tensor spectrum shows log-normal distortion with dn_T/d ln k = -1/σ².
• LISA can detect ξ ≳ 10⁻³ at approximately 10σ significance.