Dense Retrieval Models (DRMs) estimate the semantic similarity between queries and documents based on their embeddings. Prior studies highlight the importance of embedding contextualization in enhancing retrieval performance. To this aim, existing approaches primarily leverage token-level information derived from query/document interactions. In this paper, we introduce a novel DRM, namely DenseC3, which leverages query/document interactions based on the full embedding representations generated by a Transformer-based model. To enhance similarity estimation, DenseC3 integrates external linguistic information about the Cognitive Complexity of texts, enriching the contextualization of embeddings. We empirically evaluate our approach across seven benchmarks and three different IR tasks to assess the impact of Cognitive Complexity-aware query and document embeddings for contextualization in dense retrieval. Results show that our approach consistently outperforms standard fine-tuning techniques on lightweight bi-encoders (e.g., BERT-based) and traditional late-interaction models (i.e., ColBERT) across all benchmarks. On larger retrieval-optimized bi-encoders like Contriever, our model achieves comparable or higher performance on four of the considered evaluation benchmarks. Our findings suggest that Cognitive Complexity-aware embeddings enhance query and document representations, improving retrieval effectiveness in DRMs. Our code is available online at: https://github.com/FaySokli/DenseC3.