Torsion talks only to spin: the CMB temperature as a test of energy exchange in Einstein-Cartan cosmology

Abstract

The cosmic microwave background temperature at $z=0.886$ is known to $2\%$ from molecular absorption towards PKS~1830$-$211; CO absorbers and Sunyaev-Zel'dovich clusters extend the measurement to $z\simeq 3$. We use them on a question that cosmologies with torsion leave open. When the geometry exchanges energy with several matter components, which of them receives it? In Einstein-Cartan theory the Noether identities of each sector fix the answer. A sector's energy-momentum fails to be conserved only in proportion to its own spin, so minimally coupled light, which has none, is conserved whatever the torsion does. A metric-affine cosmology fitted to DESI DR2 distributes the exchange ``universally'' among all fluids, radiation included; the photons then gain almost a third of their energy. If the photons stay a blackbody, as FIRAS requires of any source set by local conditions, the model predicts a background colder than $T_0(1+z)$ by $7\%$ at $z\simeq 0.9$ and by $8.5\%$ at $z\gtrsim 3$, with no free parameter. PKS~1830$-$211 gives $5.08\pm 0.10\mathrm{K}$ against a predicted $4.78\mathrm{K}$; with the CO absorbers it favours the standard scaling by $\Delta {\chi }^2=13$, and 18 Planck cluster bins give ${\chi }^2=50.8$ versus $15.5$. Under the same reading the primary anisotropies would change their spectral shape by amounts Planck excludes. If dark matter carries the spin instead, $H(z)$ moves by less than $10^{-4}$ below $z=3$ at the fitted parameters and $T(z)$ is standard again.

arXiv comment31 pages, 1 figure