The evidence for the flatness of spacetime comes from a combination of theoretical considerations and observational data. Here are some of the key lines of evidence:
Cosmic Microwave Background (CMB) Radiation: The CMB is the afterglow of the Big Bang, and its detailed measurements provide crucial information about the geometry of the universe. The CMB exhibits a nearly uniform temperature across the sky, indicating that the universe is isotropic (looks the same in all directions). It also shows small fluctuations in temperature, which can be studied to determine the overall curvature of spacetime. Observations of the CMB by missions like the Planck satellite have revealed that the universe is very close to being flat.
Large-Scale Structure of the Universe: The distribution of galaxies on large scales can be used to infer the curvature of spacetime. If the universe were significantly curved, it would affect the clustering and distribution of galaxies. Surveys of galaxy positions, such as the Sloan Digital Sky Survey (SDSS), have indicated that the large-scale structure of the universe is consistent with a flat geometry.
Baryon Acoustic Oscillations (BAO): BAO are regular patterns of galaxies imprinted in the early universe due to acoustic waves traveling through the primordial plasma. The analysis of BAO measurements from galaxy surveys provides additional evidence supporting the idea of a flat universe.
Supernovae Type Ia: Observations of distant supernovae of Type Ia, which serve as standard candles (objects with a known intrinsic brightness), have shown that the universe is undergoing accelerated expansion. This is consistent with the presence of dark energy, a component of the universe that contributes to its overall energy density and influences its geometry. The flatness of spacetime is a requirement for this accelerated expansion to be consistent with general relativity.
It's important to note that the term "flat" in the context of spacetime curvature refers to a specific type of geometry called Euclidean or flat geometry, where parallel lines never intersect and the sum of angles in a triangle is always 180 degrees. It does not mean that spacetime is devoid of gravitational effects or that it is flat in the everyday sense.
Collectively, the observations of the CMB, large-scale structure, BAO, and supernovae support the notion that the overall geometry of spacetime is very close to being flat on cosmological scales. However, it's crucial to mention that these measurements provide evidence for the flatness of the observable universe, and the possibility of a globally curved or higher-dimensional spacetime beyond our observational reach is still an area of ongoing scientific investigation.