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There are features in the CMB, the distance and size of which can be derived from cosmological models (6-parameter Lambda CDM model). The expected size of the features can be predicted in terms of angles in the sky, depending on how curved large-scale space-time is. (The features are a statistical property of tiny temperature fluctuations in the CMB indicating the largest scale of causal connection - kind of sound waves - in the baryon-photon plasma before recombination 380,000 years after the Big Bang, called first acoustic peak of the CMB power spectrum. The angle should be about 1 degree for a flat space-time, in accordance with observation.) Things aren't quite straightforward, e.g. due to the way the universe has been expanding, therefore it's done with simulations.

Angles look larger in a positively curved space-time (e.g. a sphere) than in a flat space-time (e.g. a plane) than in a negatively curved space-time (e.g. a saddle).

The curvature of space-time follows the same principles as curvature of 2-dimensional surfaces. A triangle in an Euclidean plane has an angle sum of 180 degrees, while a triangle on a sphere has an angle sum of more than 180 degrees. Hence an object of a fixed size and a fixed distance looks larger (takes a larger angle) on a sphere than on a plane.

Here a sketch of a triangle on a sphere (may be interpreted as an observer looking to an object) and a triangle of the same size - meaning the same lengths of the sides in this case - in a plane:

(More on non-Euclidean geometry.)

There are features in the CMB, the distance and size of which can be derived from cosmological models (6-parameter Lambda CDM model). The expected size of the features can be predicted in terms of angles in the sky, depending on how curved large-scale space-time is. (The features are a statistical property of tiny temperature fluctuations in the CMB indicating the largest scale of causal connection - kind of sound waves - in the baryon-photon plasma before recombination 380,000 years after the Big Bang, called first acoustic peak of the CMB power spectrum. The angle should be about 1 degree for a flat space-time, in accordance with observation.) Things aren't quite straightforward, e.g. due to the way the universe has been expanding, therefore it's done with simulations.

Angles look larger in a positively curved space-time (e.g. a sphere) than in a flat space-time (e.g. a plane) than in a negatively curved space-time (e.g. a saddle).

The curvature of space-time follows the same principles as curvature of 2-dimensional surfaces. A triangle in an Euclidean plane has an angle sum of 180 degrees, while a triangle on a sphere has an angle sum of more than 180 degrees. Hence an object of a fixed size and a fixed distance looks larger (takes a larger angle) on a sphere than on a plane.

Here a sketch of a triangle on a sphere (may be interpreted as an observer looking to an object) and a triangle of the same size - meaning the same lengths of the sides in this case - in a plane:

(More on non-Euclidean geometry.)

If the observable universe is positively curved, it could be a fragment of the surface of a 3-sphere resp. 3+1-de Sitter space-time. A 3-sphere is finite. If the observable universe is flat (curvature 0), it could be a fragment of an infinite Euclidean space resp. 4-dimensional Minkowski space-time. That's plausible, but not the only possible extrapolation beyond the observable universe. An almost flat observable universe could e.g. be a fragment of a huge 3-spherical universe or of a huge 3-torus. Planck data don't indicate (in a significant way) that kind of structure outside the observable universe, but extrapolations become less valid the further we go beyond the observable universe.

According to the current (Lambda-CDM) model of the universe together with the best-fit parameters, the universe is flat within the limits of measurement. Hence it's plausible (by extrapolation), but not necessary, that the universe is either huge or even infinite.

There are features in the CMB cosmologists think they know their distance and size. They also think they know how large the features should look in terms of angles in the sky, depending on how curved large-scale space-time is. (The features are a statistical property of tiny temperature fluctuations in the CMB indicating the largest scale of causal connection - kind of sound waves - in the baryon-photon plasma before recombination 380,000 years after the Big Bang, called first acoustic peak of the CMB power spectrum. The angle should be about 1 degree for a flat space-time, in accordance with observation.) Things aren't quite straightforward, e.g. due to the way the universe has been expanding, therefore it's done with simulations.

Angles look larger in a positively curved space-time (e.g. a sphere) than in a flat space-time (e.g. a plane) than in a negatively curved space-time (e.g. a saddle).

The curvature of space-time follows the same principles as curvature of 2-dimensional surfaces. A triangle in an Euclidean plane has an angle sum of 180 degrees, while a triangle on a sphere has an angle sum of more than 180 degrees. Hence an object of a fixed size and a fixed distance looks larger (takes a larger angle) on a sphere than on a plane.

Here a sketch of a triangle on a sphere (may be interpreted as an observer looking to an object) and a triangle of the same size - meaning the same lengths of the sides in this case - in a plane:

(More on non-Euclidean geometry.)

There are features in the CMB, the distance and size of which can be derived from cosmological models (6-parameter Lambda CDM model). The expected size of the features can be predicted in terms of angles in the sky, depending on how curved large-scale space-time is. (The features are a statistical property of tiny temperature fluctuations in the CMB indicating the largest scale of causal connection - kind of sound waves - in the baryon-photon plasma before recombination 380,000 years after the Big Bang, called first acoustic peak of the CMB power spectrum. The angle should be about 1 degree for a flat space-time, in accordance with observation.) Things aren't quite straightforward, e.g. due to the way the universe has been expanding, therefore it's done with simulations.

Angles look larger in a positively curved space-time (e.g. a sphere) than in a flat space-time (e.g. a plane) than in a negatively curved space-time (e.g. a saddle).

The curvature of space-time follows the same principles as curvature of 2-dimensional surfaces. A triangle in an Euclidean plane has an angle sum of 180 degrees, while a triangle on a sphere has an angle sum of more than 180 degrees. Hence an object of a fixed size and a fixed distance looks larger (takes a larger angle) on a sphere than on a plane.

Here a sketch of a triangle on a sphere (may be interpreted as an observer looking to an object) and a triangle of the same size - meaning the same lengths of the sides in this case - in a plane:

(More on non-Euclidean geometry.)

There are features in the CMB cosmologists think they know their distance and size. They also think they know how large the features should look in terms of angles in the sky, depending on how curved large-scale space-time is. (The features are a statistical property of tiny temperature fluctuations in the CMB indicating the largest scale of causal connection - kind of sound waves - in the baryon-photon plasma before recombination 380,000 years after the Big Bang, called first acoustic peak of the CMB power spectrum. The angle should be 1 degree for a flat space-time, in accordance with observation.) Things aren't quite straightforward, e.g. due to the way the universe has been expanding, therefore it's done with simulations.

Angles look larger in a positively curved space-time (e.g. a sphere) than in a flat space-time (e.g. a plane) than in a negatively curved space-time (e.g. a saddle).

The curvature of space-time follows the same principles as curvature of 2-dimensional surfaces. A triangle in an Euclidean plane has an angle sum of 180 degrees, while a triangle on a sphere has an angle sum of more than 180 degrees. Hence an object of a fixed size and a fixed distance looks larger (takes a larger angle) on a sphere than on a plane.

Here a sketch of a triangle on a sphere (may be interpreted as an observer looking to an object) and a triangle of the same size - meaning the same lengths of the sides in this case - in a plane:

(More on non-Euclidean geometry.)

There are features in the CMB cosmologists think they know their distance and size. They also think they know how large the features should look in terms of angles in the sky, depending on how curved large-scale space-time is. (The features are a statistical property of tiny temperature fluctuations in the CMB indicating the largest scale of causal connection - kind of sound waves - in the baryon-photon plasma before recombination 380,000 years after the Big Bang, called first acoustic peak of the CMB power spectrum. The angle should be about 1 degree for a flat space-time, in accordance with observation.) Things aren't quite straightforward, e.g. due to the way the universe has been expanding, therefore it's done with simulations.

Angles look larger in a positively curved space-time (e.g. a sphere) than in a flat space-time (e.g. a plane) than in a negatively curved space-time (e.g. a saddle).

The curvature of space-time follows the same principles as curvature of 2-dimensional surfaces. A triangle in an Euclidean plane has an angle sum of 180 degrees, while a triangle on a sphere has an angle sum of more than 180 degrees. Hence an object of a fixed size and a fixed distance looks larger (takes a larger angle) on a sphere than on a plane.

Here a sketch of a triangle on a sphere (may be interpreted as an observer looking to an object) and a triangle of the same size - meaning the same lengths of the sides in this case - in a plane:

(More on non-Euclidean geometry.)