Extended Temporal Relativity: A Relativistic Framework for Re-evaluating Cosmic Age under Gravitational Time Dilation

In this paper, I introduce Extended Temporal Relativity (ETR), a novel relativistic framework that re-evaluates the age of the universe by incorporating gravitational time dilation effects during early high-density epochs. Standard cosmological models, including ΛCDM, estimate the universe’s age as 13.8 billion years based on comoving frames that neglect proper time distortions caused by extreme curvature in the early universe. By integrating coordinate time from a frame external to those gravitational wells, ETR suggests that the "true" age of the universe may approach 38 billion years. This approach modifies the temporal metric by applying a density-dependent time dilation integral, offering potential resolutions to cosmological anomalies such as the horizon problem and the apparent maturity of early cosmic structures. ETR remains within the four-dimensional general relativity framework, refining age estimation without invoking additional dimensions or exotic physics. Future work includes numerical integration using real cosmic density parameters and simulation-based comparison with ΛCDM predictions.