How can we tell the difference between matter and antimatter by observation in space?

Tl;DR

• Detection via polarized light - Antimatter interaction with polarized light could be detected by vector rotation;


• We're mostly sure, because absence of gamma rays and characteristic Faraday polarization indicates absence of observable antimatter in meaningful amounts.

Long answer

I do believe @userLTK to be correct on his comment.

To my limited knowledge, the absence of gamma-ray bursts that characterizes matter-antimatter interactions hints of baryonic matter prevalence throughout the visible universe; an anti-galaxy near a baryonic galaxy would show a healthy amount of gamma rays originating from boundary particle collisions.

This effect would be observable between structures of any scale - e.g. star/anti-star, galaxy/anti-galaxy or supercluster/anti-supercluster.

"Light from the Depths of Time", by Rudolph Kippenhahn, mentions that

[...] Even when, like a star, it is radiation, its spectrum remains
exactly the same, quite independent of whether atoms or anti-atoms are
responsible for the light.

So the light originating from anti-galaxies would look the same as ordinary galaxies. But what about gravity?

A quote from "Isodual Theory of Antimatter: with applications to Antigravity, Grand Unification and Cosmology" may help us further:

[...] However, the photons is invariant under charge conjugation and
travel at the maximal causal speed in vacuum, c. Therefore, the
photon could well result to be a superposition of positive and
negative energies, perhaps as a condition to travel at the speed c,
in which case the photon would be an isoselfdual state, thus
experiencing attraction in both fields of matter and antimatter.

Meaning that antimatter would also cause gravitational effects, such as lensing.

That would make remote detection of anti-matter quite hard - it would emit and bend light in exactly the same fashion as common matter.

Faraday polarization rotation could give us some hope:

Polarized light, e.g., from non-thermal synchrotron sources, that
passes through gas with a non-zero magnetic field will have its
polarization vector rotated by the process of Faraday rotation. [...]
Note that regions dominated by antimatter (positrons) cause a rotation
opposite to that caused by regions dominated by matter (electrons).

(SLAC Summer Institute on Particle Physics (SSI04), Aug. 2-13, 2004)

But the same source mentions that

The effect has been measured many times and the amount of rotation,
usually expressed in terms of the so-called “rotation measure” is
given by the line-of-sight integral [...] The fact that we observe an
effect at all means that on average, we can’t have equal amounts of
antimatter and matter along our various lines of sight.

So it seems that the visible universe is missing some antimatter after all.