From childhood, we're used to thinking of space as infinite and isotropic. But Einstein and Lemaître were already asking: could the Universe be closed in on itself, like a Möbius strip or a 3-torus? Today, astronomers aren't just speculating — they're listening: 'auscultating' the cosmic microwave background — the echo of the Big Bang — trying to catch its topological timbre. If space is multiconnected, temperature patterns in the sky repeat, like the pattern of standing waves on a membrane whose shape is forever imprinted in its set of overtones.

This approach goes back to Mark Kac's famous question: Can one hear the shape of a drum? For most manifolds, the answer is yes. In cosmology, the membrane is the surface of last scattering (SLS), and the sound is the statistical correlations of the CMB. Two main clues are hunted. The first: matching circles on the celestial sphere — if the shortest closed loop is shorter than the SLS diameter, light from a single object reaches us from two opposite directions, and we see cosmic 'clones.' The second: off-diagonal elements of the covariance matrix of the spherical harmonic expansion; these signal a break in isotropy. This analysis requires numerical simulations — computing full eigenmode spectra for all 18 orientable Euclidean topologies.

The results so far are staggering in their inconclusiveness. WMAP and Planck found no statistically significant paired circles, pushing the distance to the nearest 'clone' beyond 98.5% of the SLS diameter. Bayesian analysis extended the limit to 1.03 diameters, but only a small fraction of possible shapes have been explored. Numerical experiments show: even if the shortest loop is 1.3 times larger than the SLS, a signal could appear in polarization maps — topology mixes E- and B-modes, and that's the prime goal of the upcoming LiteBIRD mission. Meanwhile, spectroscopy of distant galaxies and surveys like Euclid are building a 3D map of matter. Each inhomogeneity obeys Hubble's law, but topology information is spread across millions of modes — offering colossal statistical power.

Discovering non-trivial topology would mean that inflation, proposed by Alan Guth, was not eternal — its duration was limited, and thus it did not erase all traces of initial conditions. This would open a window into pre-inflationary physics, possibly linked to quantum gravity. In a multiconnected space, quantum corrections like the Casimir effect arise, affecting the spectrum of gravitational waves and CMB anisotropies. So instead of a featureless, homogeneous infinity, we might find ourselves inside an intricate, 'fluted' space-drum, whose overtones carry the memory of the quantum birth of the cosmos. And then Kac's question will get an answer pointing not just to a shape, but to the very number of 'drums' nested within each other, like a cosmic matryoshka. Future listening with LiteBIRD, Taurus, and galaxy surveys will bring us closer to that revelation.