The Big Bang theory describes the early development and expansion of the universe from a highly compact and dense state. It does not specifically address the existence or nature of dimensions beyond the observable universe.
In the context of modern cosmology, the universe is often described as having three spatial dimensions (length, width, and height) and one dimension of time, which together form a four-dimensional spacetime. This is the framework within which we observe and study the universe.
However, some theories in physics, such as string theory, propose the existence of additional spatial dimensions beyond the ones we directly perceive. These extra dimensions are often considered to be "compactified" or curled up at extremely small scales, making them inaccessible to our current observations.
Regarding the concept of an infinite dimension, it is not a widely accepted idea in mainstream physics. While there are mathematical constructs that involve infinite-dimensional spaces, such as Hilbert spaces in quantum mechanics, these are typically abstract frameworks used in specific areas of physics and mathematics, and they do not directly correspond to the physical dimensions of our universe.
In summary, the Big Bang theory does not address the existence of infinite dimensions. It primarily focuses on the early expansion and evolution of our observable universe, within the framework of four-dimensional spacetime. The concepts of extra dimensions and infinite dimensions are part of speculative theories and mathematical frameworks that go beyond our current understanding of the universe.