Hemispherical Power Asymmetry

• Hemispherical Power Asymmetry is a CMB anomaly characterized by a dipolar modulation that produces systematic differences in temperature power between opposite hemispheres.
• Observations from WMAP to Planck consistently reveal a large-scale asymmetry with amplitude around 0.07 at low multipoles and a preferred axis near (215°, -30°).
• Methodological frameworks including local variance and harmonic-space estimators, alongside polarization studies, emphasize its scale-dependent nature and challenge standard isotropy assumptions.

Hemispherical power asymmetry (HPA) is the cosmic microwave background (CMB) anomaly in which one half of the sky carries systematically more large-scale temperature power than the opposite half. It is usually modeled as a dipolar modulation of an otherwise statistically isotropic field and is regarded as anomalous because, under the Cosmological Principle, the local power estimated in different sky regions should be consistent apart from cosmic variance. Across WMAP, Planck, and Planck PR4 analyses, the effect is typically strongest at low multipoles $\ell \lesssim 64$, with a classic quoted amplitude of about $A\approx 0.07$ and a preferred axis near $(224^\circ,-22^\circ)$ or $(227^\circ,-27^\circ)$ in Galactic coordinates (Sanyal et al., 20 Jan 2026, Chluba et al., 2014, Axelsson et al., 2013).

1. Phenomenological definition and standard parameterizations

The standard phenomenological description of HPA writes the observed temperature anisotropy as a dipole-modulated isotropic field,

$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$

or equivalently,

$$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$

Here $A$ is the modulation amplitude and $\hat\lambda$ or $\hat p$ is the preferred direction. In this picture, statistical isotropy is violated at the level of the local power spectrum rather than at the level of a fixed deterministic temperature pattern (Sanyal et al., 20 Jan 2026, Dai et al., 2013).

A closely related formulation promotes the primordial spectrum itself to a space-dependent quantity,

$$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$

with $A\approx 0.07$0 the comoving distance to last scattering. This makes explicit that the anomaly is interpreted as a spatial modulation across the observable Universe rather than a literal preferred direction in Fourier space. Several model-building papers adopt this form, or equivalent dipolar perturbations of an additional adiabatic component, to reconcile a large low-$A\approx 0.07$1 asymmetry with much smaller small-scale limits (Cai et al., 2013, McDonald, 2014, Dai et al., 2013).

The observational axis is not represented by a single immutable coordinate pair, but a compact region of the sky. Reported values include $A\approx 0.07$2, $A\approx 0.07$3, and an overall mean direction of approximately $A\approx 0.07$4 in later PR4-plus-WMAP local-variance analyses. This clustering, together with repeated recovery of a dipolar pattern, is why HPA is usually discussed as a preferred-axis anomaly rather than as an arbitrary hemispherical split (Sanyal et al., 20 Jan 2026, Axelsson et al., 2013).

2. Temperature evidence from WMAP to Planck PR4

Early low-resolution WMAP analyses established the anomaly in temperature space and framed it explicitly as a hemispherical contrast in angular power. Using WMAP 7-year low-resolution maps, one study scanned 24 directions, estimated all six CMB spectra with a quadratic maximum likelihood estimator, and found that the ILC temperature map shows a clear hemispherical asymmetry. The most anomalous direction in that scan was $A\approx 0.07$5, with the strongest asymmetry around $A\approx 0.07$6. For direction $A\approx 0.07$7, the reported significance reached $A\approx 0.07$8 for the ratio estimator $A\approx 0.07$9 and $(224^\circ,-22^\circ)$0 for the difference estimator $(224^\circ,-22^\circ)$1 at $(224^\circ,-22^\circ)$2. After including the a posteriori freedom in $(224^\circ,-22^\circ)$3, the probability of getting a temperature asymmetry at least as large as WMAP’s remained about $(224^\circ,-22^\circ)$4, summarized as a significance around $(224^\circ,-22^\circ)$5 (Paci et al., 2013).

A broader WMAP 9-year analysis using the combined V- and W-band map and the KQ85 mask extended the anomaly over $(224^\circ,-22^\circ)$6 to $(224^\circ,-22^\circ)$7. There, local power spectra were estimated in 12 equal HEALPix base-pixel regions, dipole directions were inferred for six independent multipole bins, and the alignment of those six directions was quantified by a dispersion angle. Only 7 of 10,000 Monte Carlo simulations had a lower dispersion angle than the data, corresponding to $(224^\circ,-22^\circ)$8, and the preferred asymmetry direction was reported as approximately $(224^\circ,-22^\circ)$9. The same work found that the ratio of power between the two maximally asymmetric hemispheres is exceeded in only $(227^\circ,-27^\circ)$0 of simulations (Axelsson et al., 2013).

Planck-era temperature studies retained the large-scale character of the effect while refining its scale dependence. A reassessment of Planck PR4 SEVEM maps with the local variance estimator (LVE) found a dipole-like anisotropy in the LVE maps with anomalous power for disc radii of $(227^\circ,-27^\circ)$1 and upward up to $(227^\circ,-27^\circ)$2 at $(227^\circ,-27^\circ)$3. In the range $(227^\circ,-27^\circ)$4 to $(227^\circ,-27^\circ)$5, none of the 600 SEVEM simulations had a dipole amplitude higher than the data. The same study emphasized that HPA is confined to low multipoles or large angular scales of the CMB sky (Sanyal et al., 2024).

A later PR4-plus-WMAP frequency-by-frequency reanalysis strengthened the robustness claim. Using seven cleaned maps spanning WMAP Q, V, and W bands and Planck PR4 SEVEM-cleaned 70, 100, 143, and 217 GHz maps, the dipolar modulation characteristic of HPA was found in all cases examined, with consistent estimates of preferred direction and scale-dependent variation in dipole amplitudes. For disc sizes $(227^\circ,-27^\circ)$6 to $(227^\circ,-27^\circ)$7, all seven maps show HPA at $(227^\circ,-27^\circ)$8 or better, and some disc sizes exceed $(227^\circ,-27^\circ)$9. The overall mean direction was summarized as approximately $$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$0 (Sanyal et al., 20 Jan 2026).

Taken together, these temperature analyses suggest that HPA is not restricted to a single mission, cleaning pipeline, or frequency channel, and that its observational content is a large-angle, approximately dipolar, scale-dependent modulation rather than a scale-invariant all-$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$1 effect (Sanyal et al., 20 Jan 2026, Sanyal et al., 2024).

3. Estimation frameworks and methodological caveats

Two methodological traditions dominate the HPA literature. The first is harmonic-space estimation of hemispherical spectra. In the WMAP 7-year analysis, the quadratic maximum likelihood estimator was applied to all six spectra,

$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$2

and used in conjunction with hemisphere-by-hemisphere power averages and two asymmetry statistics,

$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$3

Because 24 directions were scanned, the significance assessment explicitly incorporated the look elsewhere effect by taking the maximum asymmetry over the 24 directions in every Monte Carlo realization (Paci et al., 2013).

The second major framework is the local variance estimator. In its standard form, the sky is covered with discs of radius $$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$4, and the temperature variance inside each disc is computed,

$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$5

After subtracting and normalizing by the isotropic mean from simulations,

$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$6

a weak dipole-modulated sky yields

$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$7

The LVE dipole amplitude is then corrected for the isotropic bias through

$$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$8

Recent implementations fit the dipole with inverse-variance weights derived from the covariance of the local-variance maps, homogenize frequency maps to a common beam and pixel resolution, and impose explicit masking requirements on retained discs (Sanyal et al., 20 Jan 2026).

A central methodological result of the PR4 reassessment is that LVE reliability is not scale-free. The analysis showed that fixed $$\Delta T_{\rm mod}(\hat n)=\left(1+\vec d\cdot \hat n\right)\Delta T_{\rm iso}(\hat n) =\left(1+A\,\hat\lambda\cdot \hat n\right)\Delta T_{\rm iso}(\hat n),$$9 local-variance maps can generate strong overlap-induced correlations at some disc radii and that matching the LVE-map resolution to the disc radius reduces this problem. It also showed that the method breaks down for sufficiently large discs when tested on simulations with injected dipole modulation: for a 10% tolerated deviation between recovered and injected amplitude, the maximum usable radius is about $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$0 for $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$1, $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$2 for $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$3, and $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$4 for $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$5. This implies that the estimator’s reliable angular range depends on the modulation strength assumed in the test (Sanyal et al., 2024).

A third, more recent line of work extends HPA inference beyond local variance by using Minkowski Functionals on local patches. There the three functionals $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$6, $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$7, and $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$8 are fitted to Gaussian isotropic expectations to extract local temperature variance $$\frac{\Delta T}{T}(\hat n)= s(\hat n)\left[1 + A\,\hat n\cdot\hat p\right].$$9, gradient variance $A$0, and a goodness-of-fit statistic $A$1. This framework tests whether the anomaly is only a variance dipole or whether it also affects morphology and topology (Duque et al., 23 Mar 2026).

4. Polarization and morphological extensions

Polarization results have been more heterogeneous than temperature results. In WMAP 7-year low-resolution maps, no significant hemispherical power asymmetry was detected in $A$2, $A$3, $A$4, $A$5, or $A$6. The authors attributed this null result primarily to the low signal-to-noise ratio of WMAP polarization data and forecast that Planck sensitivity should improve the test of dipole modulation, especially as a complement to temperature (Paci et al., 2013).

Planck polarization studies altered that picture but did not eliminate ambiguity. A local-variance analysis of Planck 2015 low-resolution $A$7-mode maps from the Commander solution reported a significant hemispherical power asymmetry in polarization on large angular scales, at the level of $A$8 depending on the galactic mask and disc radius. For $A$9, the fitted dipole amplitudes were about $\hat\lambda$0 with $\hat\lambda$1-space masks and $\hat\lambda$2 with $\hat\lambda$3-space masks. The signal weakened for $\hat\lambda$4 and became consistent with isotropic fluctuations for $\hat\lambda$5. The inferred direction pointed broadly toward the CMB kinetic dipole direction $\hat\lambda$6, rather than exactly matching the classic temperature HPA axis, and the excess power in the local-variance maps was concentrated almost entirely in the $\hat\lambda$7 mode (Aluri et al., 2017).

Planck PR4 analyses of intensity and polarization reached a more cautious conclusion. In temperature, the PR4 Sevem and Commander maps retained strong HPA, with none of the simulations matching the data amplitude for several disc sizes. In $\hat\lambda$8-mode polarization, the PR4 Sevem map yielded a p-value of $\hat\lambda$9 for the reference mask and a preferred direction $\hat p$0, but the significance varied with the mask, from about $\hat p$1 for one $\hat p$2 mask to $\hat p$3 for the largest mask. The same study found a hint of a possible T–E alignment between the asymmetry axes at the level of $\hat p$4, with the PR4 Sevem T–E alignment p-value quoted as $\hat p$5. It also emphasized that inpainting of masked $\hat p$6 data improves $\hat p$7-mode recovery and reduces directional bias relative to simple masking (Gimeno-Amo et al., 2023).

The morphological analyses further broadened the anomaly. Using Minkowski Functionals on local patches of the Planck SMICA temperature map, one study confirmed a highly significant variance dipole with p-value $\hat p$8, reported a moderately significant dipole in the gradient variance with p-value $\hat p$9, and found a mild spatial variation in the goodness-of-fit to Gaussian isotropic predictions with p-value $$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$0. The dipoles for all three quantities pointed toward the same general region of the sky, and the paper concluded that the asymmetry is well described by dipoles and extends beyond local variance into local morphology, with a possible hint of non-Gaussianity (Duque et al., 23 Mar 2026).

This suggests that the phenomenology of HPA may not be exhausted by a single variance statistic. At the same time, the polarization and morphology results remain entangled with masking, noise, and residual-systematics issues, so they have been presented as suggestive rather than definitive (Aluri et al., 2017, Gimeno-Amo et al., 2023, Duque et al., 23 Mar 2026).

5. Scale dependence, small-scale null results, and parameter-level effects

A persistent theme in the literature is that HPA is strongly scale dependent. The anomaly is repeatedly reported as largest on large angular scales and as diminishing toward smaller angular scales. A frequency-specific PR4-plus-WMAP analysis made this explicit by fitting the corrected local-variance dipole amplitude to a power law,

$$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$1

with $$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$2. The average best-fit values across seven maps were

$$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$3

The nonzero $$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$4 was identified as evidence that the asymmetry is not scale invariant (Sanyal et al., 20 Jan 2026).

An important corrective result concerns claims of small-scale asymmetry. A study of the Planck SMICA temperature map over $$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$5–2048 initially found a raw high-$$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$6 asymmetry with naive significance $$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$7, but then showed that this apparent anomaly is a coincidence of relativistic power modulation, mask edge effects, and inter-scale correlations. After correcting for those effects, the significance fell to roughly $$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$8, leading to the conclusion that there is no anomalous intrinsic hemispherical power asymmetry on small angular scales. From this null result the paper derived the bound

$$P(k,\mathbf r)=P(k)\left[1+2A\,\hat p\cdot \frac{\mathbf r}{r_{ls}}\right],$$9

at 95% C.L. on $A\approx 0.07$00 scales (Flender et al., 2013).

This large-scale versus small-scale contrast constrains both phenomenology and model building. It excludes a simple scale-invariant extension of the low-$A\approx 0.07$01 anomaly to all multipoles and is consistent with quasar-based limits requiring much smaller asymmetry on smaller scales. Several theoretical papers therefore formulate HPA explicitly as a large-scale dipole modulation that must decay with increasing $A\approx 0.07$02 or $A\approx 0.07$03 (Flender et al., 2013, Li et al., 2019, Dai et al., 2013).

Parameter-level analyses indicate that the anomaly can project onto standard cosmological parameters when these are estimated on opposite hemispheres. In WMAP 9-year data, $A\approx 0.07$04, $A\approx 0.07$05, and $A\approx 0.07$06 were identified as the parameters most sensitive to the power asymmetry. For hemispheres aligned with the preferred asymmetry axis, the scalar spectral index was found to be $A\approx 0.07$07 in one hemisphere and $A\approx 0.07$08 in the opposite hemisphere. The same analysis emphasized that these differences are suggestive rather than highly significant (Axelsson et al., 2013).

A distinct model class, based on a space-dependent component of the adiabatic power spectrum, makes the parameter connection more explicit. There the total power is written as $A\approx 0.07$09 with

$A\approx 0.07$10

Matching a large-scale asymmetry $A\approx 0.07$11 to a small-scale bound $A\approx 0.07$12 requires $A\approx 0.07$13 for the scale dependence of the asymmetric component. The same framework predicts shifts toward a smaller spectral index and a more positive running, together with a hemispherical asymmetry in both $A\approx 0.07$14 and $A\approx 0.07$15 (McDonald, 2014).

6. Proposed physical mechanisms

The theoretical literature does not present a single accepted explanation of HPA, but it does define a constrained space of viable mechanisms. A broad survey argued that consistent models include a modulated scale-dependent isocurvature contribution to the matter power spectrum or a modulation of the reionization optical depth, gravitational-wave amplitude, or scalar spectral index. The same survey emphasized that models must satisfy both homogeneity constraints from the CMB low multipoles and quasar constraints on small-scale power asymmetries, and that scale-independent power modulation is strongly disfavored (Dai et al., 2013).

One prominent proposal links HPA to a spatially varying tensor-to-scalar ratio $A\approx 0.07$16. In that scenario,

$A\approx 0.07$17

and the BICEP2 field, lying about $A\approx 0.07$18 away from the asymmetry maximum, samples a local value

$A\approx 0.07$19

With $A\approx 0.07$20, the model yields $A\approx 0.07$21, consistent with the quoted BICEP2 result while remaining compatible with the Planck full-sky upper bound. However, even taking $A\approx 0.07$22 and $A\approx 0.07$23, the resulting temperature asymmetry is only $A\approx 0.07$24 for $A\approx 0.07$25, far below the observed $A\approx 0.07$26. Reproducing the full asymmetry would require $A\approx 0.07$27, implying $A\approx 0.07$28, in strong disagreement with BICEP2 at more than $A\approx 0.07$29. The model therefore survives only as a partial contributor and predicts that $A\approx 0.07$30 should be much smaller in the Northern hemisphere than toward the asymmetry maximum (Chluba et al., 2014).

Several scalar-sector mechanisms address the same scale-dependence problem more directly. A scale-dependent modulated reheating model uses a light modulating field with a spatially modulated red spectrum, generated through tachyonic growth of a complex scalar field, to produce a subdominant but non-negligible contribution to the adiabatic perturbation. In the quoted viable regime, the model can reproduce $A\approx 0.07$31 while satisfying $A\approx 0.07$32, the non-Gaussianity bound $A\approx 0.07$33, and the quadrupole constraint, with typical requirements $A\approx 0.07$34, $A\approx 0.07$35, and $A\approx 0.07$36. It also predicts modifications to the scalar spectral index and its running (McDonald, 2013).

A related class of models attributes HPA to a spatial modulation of the primordial sound speed $A\approx 0.07$37. In the multi-speed inflation picture, a light entropy field modulates $A\approx 0.07$38, and because $A\approx 0.07$39, a superhorizon perturbation in that field produces a direction-dependent primordial spectrum. One sound-speed paper emphasized that the same asymmetry should appear in $A\approx 0.07$40, $A\approx 0.07$41, and $A\approx 0.07$42 with the same scale dependence, and that equilateral-type non-Gaussianity should also become spatially modulated. A later treatment recast the mechanism in a generalized $A\approx 0.07$43 formalism, where the local number of e-folds depends not only on the inflaton value but also on a spatially varying sound speed parameter (Cai et al., 2013, Wang et al., 2015).

Other proposals push the origin of HPA into pre-inflationary or nonstandard primordial physics. A non-commutative inflation model produced a weak preferred direction near $A\approx 0.07$44, with $A\approx 0.07$45 and $A\approx 0.07$46, but only at about the $A\approx 0.07$47 level, leading to the conclusion that the simplest leading correction captures the asymmetry only partially (Groeneboom et al., 2010). Pre-inflationary topological-defect and primordial-configuration models instead use a superhorizon defect-induced gradient in a light field to generate a dipolar modulation after inflation, with scale dependence arising from the defect profile or from the field-to-curvature conversion mechanism (Yang et al., 2016, Kohri et al., 2013). A more recent calculation based on an early inhomogeneous phase of inflation derives a direction-dependent two-point function directly from a perturbed metric using in-in formalism, predicts $A\approx 0.07$48 multipole couplings, and fits PR4 Commander low-$A\approx 0.07$49 data with $A\approx 0.07$50 for $A\approx 0.07$51 (Gandhi et al., 29 Sep 2025).

The theoretical situation is therefore not one of absence of models, but of overconstrained model space. Large-angle amplitude, strong scale dependence, low-multipole homogeneity bounds, quasar and high-$A\approx 0.07$52 null results, and the tentative polarization phenomenology jointly force viable explanations to be both selective and quantitatively controlled (Dai et al., 2013, Flender et al., 2013).

7. Cross-probes and future observational tests

Because HPA is fundamentally a modulation of fluctuation power, its decisive tests need not be confined to CMB temperature maps. In the tensor-modulation scenario, the cleanest probe is direct comparison of hemispherical $A\approx 0.07$53-mode power. Experiments specifically mentioned as relevant for such tests include CLASS, SPIDER, PIXIE, LiteBIRD, and PRISM-like missions. The same framework notes that joint measurements of

$A\approx 0.07$54

can help distinguish a spatially varying tensor signal from other mechanisms, with $A\approx 0.07$55 identified as the cleanest direct probe (Chluba et al., 2014).

Large-scale structure surveys provide an independent route. A forecast based on a primordial gradient in the fluctuation amplitude found that the DESI galaxy survey would be able to detect this signal with higher than $A\approx 0.07$56 significance if the asymmetry exists. The same work concluded that DESI can probe the dipole amplitude higher than $A\approx 0.07$57, corresponding to a $A\approx 0.07$58 difference of the temperature fluctuation along and opposite the dipole direction, at least at the $A\approx 0.07$59 level. By contrast, eROSITA cluster forecasts were described as much less favorable because number density is too low and shot noise dominates (Zhai et al., 2017).

Intermediate scales can be probed by 21-cm tomography from the epoch of reionization. A scale-dependent parameterization inspired by multi-speed inflation was embedded in the 21-cm power spectrum and forecast for SKA Phase 2 and Omniscope. The main quoted result is that an optimum, multi-frequency observation by SKA Phase 2 can impose a constraint on the amplitude of the power asymmetry anomaly at the level of $A\approx 0.07$60 at $A\approx 0.07$61, while a cosmic variance limited experiment such as the Omniscope may improve this by an order of magnitude to $A\approx 0.07$62 (Li et al., 2019).

Future full-sky polarization remains especially important because the current Planck polarization evidence is modest and mask-sensitive. The PR4 polarization study explicitly argued that more sensitive all-sky CMB polarization data, such as those expected from LiteBIRD, are needed to reach a more robust conclusion on the possible existence of deviations from statistical isotropy in the form of a hemispherical power asymmetry (Gimeno-Amo et al., 2023).

The observational program implied by the literature is therefore multi-channel: low-$A\approx 0.07$63 temperature consistency checks, polarization dipoles, hemispherical $A\approx 0.07$64-mode comparisons, galaxy-clustering contrasts, and intermediate-scale 21-cm measurements. This suggests that the long-term status of HPA will be decided less by further remeasurement of a single anomaly statistic than by whether the same preferred-axis, scale-dependent phenomenology reappears across independent observables (Zhai et al., 2017, Li et al., 2019, Gimeno-Amo et al., 2023).