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Perpetual motion and Big Bang theory seem to allude that the universe can’t last forever because matter and energy are dispensed.

Is it plausible the Universe has infinite matter?

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Yes. Currently it is at least plausible that the universe is spatially flat. If that is the case then, barring global topological weirdness, it is also spatially infinite. That would mean it contains an infinite amount of matter.

Disclaimer. I don't know how large the uncertainties on spatial flatness currently are: if Wikipedia is to be trusted $\Omega = 1.00 \pm 0.02$ ($1$ being flat) based on data from WMAP and Planck.

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    $\begingroup$ Combining the latest results from Planck Collab. (2020) with lensing data and baryonic acoustic oscillation data constrain the curvature to be $\Omega_k = 0.0007 \pm 0.0019$ (where $\Omega_k$ is the deviation of your $\Omega$ from $1$). So yeah, pretty flat. But remember, that's only the observable Universe; we don't really have any idea what goes on beyond that. $\endgroup$
    – pela
    May 27, 2021 at 22:18

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