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We study the effects of pre-recombination physics on the StochasticGravitational Wave Background (SGWB) anisotropies induced by the propagation ofgravitons through the large-scale density perturbations and theircross-correlation with Cosmic Microwave Background (CMB) temperature and E-modepolarization ones. As examples of Early Universe extensions to the $\Lambda$CDMmodel, we consider popular models featuring extra relativistic degrees offreedom, a massless non-minimally coupled scalar field, and an Early DarkEnergy component. Assuming the detection of a SGWB, we perform a Fisheranalysis to assess in a quantitative way the capability of future gravitationalwave interferometers (GWIs) in conjunction with a future large-scale CMBpolarization experiment to constrain such variations. Our results show that thecross-correlation of CMB and SGWB anisotropies will help tighten theconstraints obtained with CMB alone, with an improvement that significantlydepends on the specific model as well as the maximum angular resolution$\ell_{\rm max}^{\rm GW}$ of the GWIs, their designed sensitivity, and theamplitude $A_*$ of the monopole of the SGWB.

Probing pre-Recombination Physics by the Cross-Correlation of Stochastic Gravitational Waves and CMB Anisotropies