No, the finite speed of light is not evidence that the universe is hyperbolic. The finiteness of the speed of light is a fundamental principle of physics that arises from Einstein's theory of relativity, which describes how objects and information behave in the presence of gravity. It states that the speed of light in a vacuum is a constant, denoted by "c," and is approximately 299,792,458 meters per second.
The notion of a hyperbolic universe refers to a specific geometric shape of space, where the geometry is curved in a particular way. In a hyperbolic universe, the sum of the angles of a triangle is less than 180 degrees, and parallel lines eventually diverge away from each other.
The finite speed of light does not directly provide evidence for the curvature or shape of the universe. Instead, it has implications for causality and the transmission of information. It means that the information cannot travel faster than the speed of light, and it sets a cosmic speed limit for cause and effect relationships.
To determine the curvature of the universe, scientists rely on various observations and measurements, such as the cosmic microwave background radiation, the distribution of galaxies, and the behavior of light from distant objects. Currently, the most widely accepted cosmological model based on observations suggests that the universe is nearly flat on large scales. This model is consistent with the observations made by cosmic microwave background experiments like the Planck satellite and large-scale galaxy surveys like the Sloan Digital Sky Survey.