This post is a critique of Can rotation solve the Hubble Puzzle? found here: https://academic.oup.com/mnras/article/538/4/3038/8090496
We’re going to specifically focus on how cosmic rotation would manifest (or fail to manifest) in cosmic microwave background (CMB) polarization data. While the idea of a mild global rotation is not new, modern CMB observations (particularly polarization patterns) place very tight constraints on any large-scale anisotropy or vorticity in the universe.
1. The Essence of Gödel-Type Rotation in Cosmology
- Gödel Universe: A famous exact solution to Einstein’s field equations that includes rotation and allows closed time-like curves (CTCs). Realistic cosmologies inspired by Gödel geometry typically dilute (or cap) the rotation rate to avoid blatant causal paradoxes.
- Proposed Model: The new theory suggests a tiny angular velocity (on the order of a few × 10^−18 s^−1, or 1 Gyr^−1) in the dark fluid, presumably below the threshold for generating closed time-like loops at the current horizon.
- Hubble Tension: In principle, a small rotation might alter the path of light or the expansion history enough to reconcile the high- and low-redshift measurements of the Hubble constant.
2. Why CMB Polarization Is Crucial
- Sensitive to Anisotropies: The CMB’s polarization (particularly the E-mode and B-mode power spectra) is extremely sensitive to any global anisotropy or preferred directions in the universe.
- Scalar, Vector, Tensor Modes:
- Scalar perturbations lead to the usual density/temperature fluctuations.
- Vector (vorticity) perturbations – such as those from rotation or shear – can leave signatures in B-mode polarization on certain angular scales.
- Tensor modes (gravitational waves) also produce B-mode patterns, but typically at different scales/frequency ranges.
- High-Precision Measurements: Planck (and subsequent experiments like BICEP/Keck, SPT, ACT) have measured or tightly constrained polarization patterns across wide angular scales. Any large-scale vorticity in the cosmic fluid typically would imprint additional power in the B-mode spectrum or produce unusual correlations between E and B modes.
3. Existing Observational Limits on Cosmic Rotation
WMAP and Planck Constraints: Analyses have placed upper bounds on anisotropic expansion and “universal vorticity” of the cosmic fluid. These constraints are derived from temperature and polarization maps. Typical results suggest that any global rotation is many orders of magnitude below what would be needed to cause an observable effect.
Directional Variations: Rotation introduces a preferred axis and can generate off-diagonal correlations in the CMB anisotropies/polarization. Observational data so far do not show these patterns at a significant level; they generally remain consistent with isotropy to high precision.
Order-of-Magnitude Estimates: Although the new theory proposes an angular velocity near the edge of avoiding closed time-like curves, one must ensure it does not exceed observational bounds—often quoted in the range (sorry, need latex here):
ω≲10−17 s−1\omega \lesssim 10^{-17} \; \mathrm{s}^{-1}
Or even tighter, depending on the exact model. If a “slow rotation” is slightly larger than that bound, it would contradict the CMB’s near-isotropy.
4. Potential Polarization Signals from a Rotating Fluid
- Vector Mode (Vorticity) Contributions:
- A rotating cosmology could manifest as residual vector modes in the primordial plasma, generating small-scale B-modes beyond the standard lensing or inflationary gravitational-wave contributions.
- While the effect might be subtle, Planck and ground-based polarimeters have not detected any significant “excess” B-mode signal at the relevant angular scales.
- Dipole/Quadrupole Alignments:
- Some papers note possible “anomalies” in the CMB, like alignments of quadrupole/octopole phases. However, these are typically borderline statistical curiosities and are not widely accepted as evidence for rotation.
- If universal rotation was stronger, we’d expect more robust, large-scale directional correlations that should appear clearly in polarization data. They haven’t.
5. Reconciling the Hubble Tension vs. CMB Polarization Constraints
Even if a slow rotation can tweak the late-time expansion rate to reconcile the local (e.g., SH0ES) and early (Planck) measurements of H0H_0, that same rotation:
- Must remain small enough not to conflict with the tight upper limits from CMB polarization.
- Cannot create large anisotropies in temperature or polarization maps that Planck would have spotted.
Hence, any claim that a rotation rate near ω∼1 Gyr−1\omega \sim 1 \, \text{Gyr}^{-1} resolves the Hubble discrepancy must demonstrate that the implied anisotropy:
- Does not exceed the current non-detection threshold for vector-mode (vorticity) signals in the B-mode power spectrum.
- Does not produce unacceptable shifts in the CMB temperature anisotropy or other observables.
In many published analyses, these dual requirements (help the Hubble tension and remain invisible to precise CMB data) prove challenging, because the magnitude of rotation needed to affect the Hubble tension often outstrips the tiny upper bound from CMB anisotropy data.
Concluding Critique
- Pros: The idea of a slowly rotating, Gödel-like universe is theoretically intriguing and historically well-known as a potential source of global anisotropy that could affect cosmic measurements. If it’s extremely small, it may avoid the typical pathologies (like closed time-like loops) and remain consistent with many isotropy tests.
- Main Issue – CMB Polarization: Modern polarization constraints (Planck, BICEP, etc.) strongly limit any large-scale cosmic vorticity. Even a “slow” rotation can be too large if it noticeably alters the expansion history or the geometry. Hence, any claim that such rotation solves the Hubble tension must rigorously show how it avoids overproducing vector-mode B-modes or directional anomalies in polarization.
- Overall Feasibility: While it might be mathematically consistent, in practice the amplitude of rotation required to shift H0H_0 is likely to conflict with the very tight observational upper bounds on cosmic anisotropy—especially from the CMB polarization data. A small enough rotation to pass current polarization tests might not be sufficient to reconcile the Hubble tension in a meaningful way.
Thus, from a CMB-polarization perspective, the theory faces an uphill battle: it must carefully demonstrate that the rotational rate needed to fix the Hubble discrepancy does not contradict the observed isotropy of the early universe to extremely high precision.