Dense retrieval relies on aligning document and query embeddings; however, its performance is often constrained by the scarcity of labeled queries. Although prior work has attempted to model the many-to-one relationship between documents and queries using Gaussian Mixture Models (GMMs), such Euclidean-based approaches induce norm shrinkage (‖𝜇‖ < 1) in normalized semantic spaces, resulting in distorted similarity scores. To address this fundamental geometric inconsistency, we propose vMF-HSE, a training-free hyperspherical semantic expansion framework that models the latent query space using a von Mises-Fisher (vMF) mixture distribution on the unit hypersphere 𝕊^d-1. We leverage Sra’s Newton-based optimization within the Expectation-Maximization (EM) algorithm to ensure robust parameter estimation even in high-dimensional semantic spaces. Building upon this stable estimation, we propose a novel adaptive stopping mechanism (𝜅-Stop) that adaptively determines the optimal number of synthetic queries per document by monitoring the convergence of marginal information gain. Experimental results on the BEIR benchmark demonstrate that vMF-HSE consistently outperforms conventional Euclidean-based methods in zero-shot retrieval settings, establishing the necessity of geometrically consistent modeling for normalized semantic spaces.