In theoretical physics, discussions of dimensions beyond the standard three spatial and one temporal (4D spacetime) arise in the context of attempting to unify the fundamental forces of nature or explain phenomena not accounted for by the Standard Model. However, the notion of 15-dimensional space (15D) is not as common or standardized as other higher-dimensional theories such as 10-dimensional string theory or 11-dimensional M-theory.

*Here’s a general outline of the concepts involved and the implications of higher-dimensional theories:*

**Theoretical Frameworks**:

- Higher-dimensional theories, like string theory and M-theory, aim to provide a unified description of all fundamental forces, including gravity. They often require extra dimensions to accommodate the mathematical consistency and symmetry properties necessary for unification.

**Compactification**:

- In higher-dimensional theories, extra dimensions beyond the familiar 4D are usually compactified, meaning they are curled up into small geometrical shapes that are unobservable at macroscopic scales. This compactification can lead to a rich structure of physical phenomena.

**Particle Phenomena**:

- The geometry and topology of compactified dimensions can lead to a vast spectrum of particle phenomena. It can influence particle masses, charges, and interaction strengths.

**Gravitational Effects**:

- Higher-dimensional spacetime can provide a new perspective on gravity, potentially explaining why gravity is weaker than other forces, or even predicting the existence of large extra dimensions that gravity can propagate through.

**Kaluza-Klein Theory**:

- One of the pioneering higher-dimensional theories is Kaluza-Klein theory, which demonstrated how a 5-dimensional theory of gravity can yield 4D gravity plus electromagnetism. This theory serves as an inspiration for many higher-dimensional theories.

**15D Speculations**:

- There might be specific models or theories in the literature that employ a 15-dimensional space for particular reasons. However, these would be highly speculative and less mainstream compared to, say, 10D string theory or 11D M-theory.

**Mathematical Formalism**:

- The mathematical formalism required to describe physics in 15D would be quite complex and would demand a deep understanding of higher-dimensional geometry, topology, and algebra.

**Experimental Challenges**:

- One of the significant challenges with higher-dimensional theories is the lack of experimental evidence. It’s extremely challenging to devise experiments to test predictions made by these theories due to the extraordinarily high energy scales or tiny length scales involved.

**Implications for Cosmology**:

- If a higher-dimensional theory like a 15D theory were correct, it would have profound implications for cosmology, potentially offering new insights into the Big Bang, dark matter, dark energy, and the ultimate fate of the universe.

In summary, while a 15-dimensional framework is not standard in theoretical physics, the exploration of higher dimensions is a fundamental aspect of the quest for a more complete understanding of the universe.