1. Introduction: The Foundational Assumptions of Modern Cosmology

The standard model of cosmology, known as $\Lambda$CDM, stands as one of the triumphs of twentieth-century physics. It successfully integrates the expansion of the Universe, the synthesis of light elements, the formation of large-scale structure, and the existence of the Cosmic Microwave Background (CMB) into a coherent narrative. However, this model rests upon a foundational axiom that precedes the field equations of General Relativity themselves: the Cosmological Principle (CP). The CP asserts that, on sufficiently large scales (typically exceeding 100 Mpc), the Universe is statistically homogeneous and isotropic. This implies that there are no privileged positions and no privileged directions in the cosmos.¹

The mathematical manifestation of the CP is the Friedmann-Lemaître-Robertson-Walker (FLRW) metric, which reduces the ten independent components of the Einstein field equations to differential equations governing a single time-dependent scale factor, $a(t)$. This metric underpins our definitions of cosmic time, the Hubble parameter $H(t)$, and the interpretation of redshift as a measure of expansion.¹ Consequently, the validity of the $\Lambda$CDM model—and indeed, our understanding of dark energy, dark matter, and the age of the Universe—is inextricably linked to the validity of the FLRW metric and the CP.

While the CP was initially a philosophical necessity—introduced by Einstein and later formalized by Milne to make the equations of cosmology solvable—it has since been subjected to rigorous observational testing. The discovery of the CMB in 1965 provided strong evidence for isotropy, revealing a Universe that was remarkably uniform in its infancy. The temperature fluctuations in the CMB, $\Delta T/T$, are on the order of $10^{-5}$, consistent with a Universe that is isotropic to a high degree of precision.³

However, the CMB is not perfectly isotropic. It contains a prominent dipole anisotropy, a variation in temperature of amplitude $\Delta T/T \approx 10^{-3}$, which is two orders of magnitude larger than the primordial fluctuations. In the standard paradigm, this dipole is interpreted not as an intrinsic feature of the Universe, but as a kinematic effect arising from the peculiar motion of the Solar System relative to the cosmic rest frame.⁴ This interpretation predicts that a corresponding dipole must exist in the distribution of distant extragalactic sources. If the Solar System is moving through a sea of photons, it is also moving through the sea of galaxies and quasars that constitute the large-scale structure (LSS) of the Universe.

Over the past two decades, and intensifying in recent years with the release of large-area surveys like CatWISE and RACS, a significant tension has emerged. Measurements of the dipole in the number counts of distant radio galaxies and quasars consistently reveal an amplitude that is significantly larger—by a factor of two to three—than the kinematic prediction derived from the CMB.³ This discrepancy, now reaching statistical significance levels exceeding $5\sigma$, has been termed the “Cosmic Dipole Anomaly.” It represents one of the most severe challenges to the CP and the standard model, suggesting that the rest frame of matter and the rest frame of radiation may not coincide, or that the Universe possesses an intrinsic anisotropy that violates the fundamental assumptions of FLRW cosmology.¹

This report provides an exhaustive review of the Cosmic Dipole Anomaly. It synthesizes evidence from radio continuum surveys, infrared quasar catalogs, and redshift tomography. It examines the theoretical basis for the kinematic dipole, the statistical methodologies used to measure it, and the potential for systematic errors. Furthermore, it explores theoretical extensions to the standard model—including “tilted” Bianchi cosmologies and modified gravity theories—that seek to explain the anomaly. Finally, it forecasts the potential of next-generation facilities such as the Euclid mission, the Square Kilometre Array (SKA), and the Vera C. Rubin Observatory (LSST) to definitively resolve this cosmic puzzle.

2. The Kinematic Hypothesis and the Cosmic Microwave Background

2.1 The CMB Dipole: Observation and Interpretation

The Cosmic Microwave Background provides the ultimate reference frame for cosmology. Observations by the COBE, WMAP, and Planck satellites have mapped the CMB temperature field with exquisite precision. The dominant feature in these maps, after the monopole temperature $T_0 = 2.7255$ K, is the dipole moment.

The Planck 2018 results constrain the solar system’s peculiar velocity, under the kinematic interpretation, to be:

$$v_{\text{CMB}} = 369.82 \pm 0.11 \text{ km s}^{-1}$$

This velocity vector points towards the Galactic coordinates $(l, b) = (264.021^\circ \pm 0.011^\circ, 48.253^\circ \pm 0.005^\circ)$.3

In the standard model, this velocity is attributed to the gravitational pull of local large-scale structures. The Solar System orbits the Galactic Center; the Milky Way falls towards the Andromeda Galaxy; the Local Group falls towards the Virgo Cluster; and the Local Supercluster is influenced by the Great Attractor and the Shapley Concentration.⁹ The vector sum of these motions results in the net velocity observed as the CMB dipole.

The temperature distribution of the CMB in the presence of an observer velocity $\vec{v}$ is given by the relativistic Doppler formula:

$$T(\hat{n}) = \frac{T_0}{\gamma (1 – \vec{\beta} \cdot \hat{n})}$$where $\vec{\beta} = \vec{v}/c$, $\gamma = (1 – \beta^2)^{-1/2}$ is the Lorentz factor, and $\hat{n}$ is the direction of observation. To first order in $\beta$, this simplifies to:

$$T(\hat{n}) \approx T_0 (1 + \hat{n} \cdot \vec{\beta})$$

This dipolar modulation is kinematic in nature. It is not an intrinsic variation in the temperature of the last scattering surface, but a frame-dependent effect. Crucially, this interpretation relies on the assumption that the CMB rest frame represents the global rest frame of the Universe. If the CP holds, the distribution of matter on large scales must also be isotropic in this same frame.4

2.2 Relativistic Effects on Matter Distribution

If the CMB dipole is kinematic, an observer moving with velocity $\vec{v}$ relative to the cosmic rest frame should see a specific signature in the distribution of distant sources. This signature arises from two distinct relativistic effects: Doppler boosting and relativistic aberration.¹

2.2.1 Doppler Boosting

The flux density $S$ of a source is frame-dependent. For a source with a power-law spectrum $S \propto \nu^{-\alpha}$, the observed flux density $S_{\text{obs}}$ is related to the rest-frame flux density $S_{\text{rest}}$ by:

$$S_{\text{obs}} = S_{\text{rest}} \delta^{1+\alpha}$$

where $\delta = [\gamma (1 – \vec{\beta} \cdot \hat{n})]^{-1}$ is the Doppler factor. Since $\delta > 1$ in the direction of motion, sources appear brighter. In a flux-limited survey (which counts all sources brighter than a threshold $S_{\text{lim}}$), this brightening brings sources that would otherwise be too faint to be detected into the sample. The magnitude of this effect depends on the slope of the number counts, $x$, defined by $N(>S) \propto S^{-x}$.3

2.2.2 Relativistic Aberration

Aberration is the apparent displacement of objects toward the direction of motion. The angle of incidence $\theta$ in the observer’s frame is related to the angle $\theta’$ in the rest frame by:

$$\cos \theta = \frac{\cos \theta’ + \beta}{1 + \beta \cos \theta’}$$

This effect causes the solid angle elements to shrink in the forward direction and expand in the backward direction. Consequently, the number density of sources per unit solid angle increases in the direction of motion, even if the intrinsic spatial distribution is uniform.9

2.3 The Ellis-Baldwin Formulation

In their seminal 1984 paper, George Ellis and John Baldwin derived the combined effect of boosting and aberration on the observed number counts of sources. They showed that for a flux-limited survey of sources with spectral index $\alpha$ and count slope $x$, the observed number density $N(\hat{n})$ is modulated by a dipole of amplitude $\mathcal{D}$:

$$N(\hat{n}) = \bar{N} (1 + \mathcal{D} \cos \theta)$$where the theoretical kinematic dipole amplitude is:$$\mathcal{D}_{\text{kin}} = [2 + x(1 + \alpha)] \beta$$

The term “2” arises from aberration (and geometric dilution), while the term $x(1+\alpha)$ accounts for the Doppler boosting of flux across the survey threshold.3

This formula provides a rigorous consistency test for the standard model. Since $\beta$ is fixed by the CMB measurement ($\beta \approx 1.23 \times 10^{-3}$) and $x$ and $\alpha$ are observable properties of the galaxy population, one can predict $\mathcal{D}_{\text{kin}}$ precisely. For typical radio populations ($x \sim 1$, $\alpha \sim 0.75$), the amplification factor is roughly 4, leading to a predicted matter dipole of $\mathcal{D} \approx 0.5\%$. Any significant deviation from this prediction implies a violation of the underlying assumptions: either the velocity $\beta$ is different (implying matter and radiation frames differ), or the intrinsic universe is not isotropic.⁴

3. Observational Evidence from Radio Continuum Surveys

Radio galaxies have historically been the tracer of choice for testing the cosmic dipole. They are detectable out to high redshifts ($z \sim 1-2$), are sparse enough to avoid confusion, and are less affected by dust extinction than optical sources.

3.1 The NRAO VLA Sky Survey (NVSS)

The NVSS, conducted at 1.4 GHz with the Very Large Array, covers the entire sky north of declination $-40^\circ$. It contains nearly 2 million sources and has served as the primary dataset for dipole studies for two decades.³

Early studies, such as those by Blake and Wall (2002), detected a dipole in the NVSS number counts that was directionally consistent with the CMB. However, the amplitude was found to be somewhat larger than the kinematic prediction, though the large error bars at the time allowed for consistency. As measurement techniques refined, the tension grew. Singal (2011) performed a comprehensive analysis, applying stricter flux cuts to ensure completeness and removing local sources. This study found a dipole amplitude approximately four times larger than the CMB prediction, with a significance exceeding $3\sigma$.⁵

Subsequent re-analyses have largely confirmed this excess. Rubart and Schwarz (2013) and Tiwari et al. (2015) employed different estimators and masking strategies, consistently finding amplitudes in the range of $\mathcal{D} \sim 1.5 – 2.5 \times 10^{-2}$, compared to the expected $\sim 0.5 \times 10^{-2}$. The direction of the NVSS dipole generally aligns with the CMB dipole (within $\sim 20^\circ-30^\circ$), which is crucial; a random systematic error would not be expected to align with the Solar motion vector so well.⁵

3.2 The TIFR GMRT Sky Survey (TGSS)

The TGSS ADR1, operating at 150 MHz, offers a low-frequency counterpart to NVSS. Investigating the dipole at different frequencies is essential for checking frequency-dependent systematics. Analyses of TGSS data have reported even more extreme anomalies, with some studies finding dipole amplitudes up to ten times the kinematic expectation.⁵ However, TGSS is known to have more complex calibration issues and significant ionospheric effects compared to NVSS, leading some researchers to treat these extreme values with caution. Nevertheless, when conservative cuts are applied, TGSS still exhibits a statistically significant excess over the $\Lambda$CDM prediction.

3.3 The Rapid ASKAP Continuum Survey (RACS)

The arrival of the Rapid ASKAP Continuum Survey (RACS) has provided a vital new dataset in the Southern Hemisphere, complementing the Northern coverage of NVSS. RACS-low, centered at 887.5 MHz, covers the sky south of $\delta = +30^\circ$.

Recent studies combining NVSS and RACS provide a near-all-sky view of the radio continuum universe. Wagenveld et al. (2025) and Oayda et al. (2025) performed Bayesian analyses of the combined NVSS and RACS datasets. They found that while there are internal tensions between the catalogs (likely due to different flux scales and calibration strategies), the combined data strongly reject the purely kinematic CMB hypothesis. Specifically, RACS data alone indicates a “strong tension” with the Planck expectation, yielding a dipole amplitude consistent with the NVSS excess.³

3.4 Summary of Radio Dipole Findings

The consensus from radio surveys is clear: while the direction of the matter dipole is broadly consistent with the CMB dipole, the amplitude is persistently high. The inferred velocity of the Solar System relative to the radio galaxy frame is $v_{\text{radio}} \sim 1000 – 1500$ km s$^{-1}$, drastically higher than the $v_{\text{CMB}} \approx 370$ km s$^{-1}$. This “Radio Dipole Anomaly” suggests that radio galaxies are not at rest in the CMB frame, or that there is a surplus of sources in the direction of motion that cannot be explained by kinematics alone.⁹

4. The Quasar Dipole and the “Orthogonality” Argument

While radio surveys provided the first hints of the anomaly, they are susceptible to specific systematics, such as calibration drifts in interferometers and the complex morphology of radio lobes (which can be resolved into multiple sources, biasing counts). Quasars (Active Galactic Nuclei) observed in the infrared provide an independent and physically distinct tracer.

4.1 The Wide-field Infrared Survey Explorer (WISE) and CatWISE

The WISE mission mapped the entire sky in four infrared bands. The CatWISE2020 catalog, derived from WISE data, contains roughly 1.35 million quasars selected via their red mid-infrared colors ($W1 – W2 \ge 0.8$). This selection effectively isolates AGNs at redshifts $0.5 < z < 2.0$ (mean $z \sim 1.2$) from stars and normal galaxies.²

Secrest et al. (2021) performed a landmark analysis of the CatWISE quasar distribution. After masking the Galactic plane and correcting for extinction, they measured a dipole with an amplitude of $\mathcal{D}_{\text{obs}} = 0.01554 \pm 0.00079$. The kinematic expectation, derived from the specific $x$ and $\alpha$ of the quasar population, was $\mathcal{D}_{\text{kin}} \approx 0.007$.

• Significance: The observed dipole is more than double the expected value. The statistical significance of the discrepancy is $4.9\sigma$ (one-sided normal distribution), meaning the probability of this result occurring by chance in a $\Lambda$CDM universe is less than one in a million.⁷
• Direction: The CatWISE dipole points towards $(l, b) \approx (238^\circ, 29^\circ)$. While this is offset from the CMB dipole by about $27^\circ$, it is statistically consistent with alignment given the uncertainties and the potential influence of the “Clustering Dipole” (discussed in Section 6).

4.2 The Argument for Orthogonality

The confirmation of the dipole anomaly with quasars is a pivotal moment in this field because of the orthogonality of the datasets:

1. Physical Mechanism: Radio galaxies are detected via synchrotron radiation from relativistic jets and lobes. CatWISE quasars are detected via thermal emission from hot dust in the accretion torus. These are distinct physical processes involving different particle populations.
2. Instrumental Systematics: Radio surveys use ground-based interferometers (VLA, ASKAP) subject to atmospheric and ionospheric noise, RFI, and UV-coverage limitations. CatWISE uses a space-based photometer (WISE) subject to scan-pattern artifacts and zodiacal light. The systematics are uncorrelated.
3. Sample Overlap: There is very little overlap between the NVSS and CatWISE catalogs (less than 10% of sources are common to both). They essentially probe two independent populations of the Universe.¹⁵

The fact that two completely independent surveys, using different wavelengths and instruments, both find a dipole that is aligned with the CMB but has an amplitude excess of factor $\sim 2-3$ makes it extremely difficult to attribute the anomaly to a specific instrument error. It points strongly towards a genuine cosmological signal.²

5. Statistical Methodologies and Tension Quantification

The measurement of the cosmic dipole is a subtle statistical problem. The signal ($\sim 1\%$) is small, and the noise (Poissonian and systematic) can be significant.

5.1 Estimators: Linear vs. Quadratic

Early studies often used linear estimators, summing the direction vectors of all sources. While intuitive, linear estimators are biased by non-uniform sky coverage (masks). Modern analyses, such as those by Secrest et al. and Wagenveld et al., employ quadratic or maximum likelihood estimators (MLE). These methods fit a model of the number density field (monopole + dipole + quadrupole) to the data, properly accounting for the mask and the covariance between multipoles.¹⁶

5.2 Bayesian Frameworks

Recent work has moved towards Bayesian analysis to rigorously quantify the tension. Oayda et al. (2025) presented a Bayesian hierarchical model that jointly analyzes Planck, NVSS, RACS, and CatWISE.

• Evidence Ratios: They computed the Bayesian evidence for models where the dipole is fixed to the CMB kinematics versus models where the dipole parameters are free.
• Results: The “free dipole” model is strongly favored by the data. The analysis indicates “severe tension” ($>5\sigma$) between the Planck kinematic prior and the CatWISE likelihood.
• Concordance: Crucially, the Bayesian analysis reveals a “strong concordance” between CatWISE and NVSS. Their posteriors for the dipole amplitude and direction overlap, suggesting they are observing the same underlying phenomenon, even though it disagrees with the CMB.³

5.3 The Look-Elsewhere Effect

Critics might argue that searching for anomalies in multiple catalogs incurs a “look-elsewhere” penalty. However, the dipole test is a specific, a priori prediction of the standard model. The direction is fixed by the CMB, and the amplitude is fixed by the source counts. There are no free parameters to tune. Therefore, the high significance levels reported are robust against look-elsewhere criticisms.¹⁷

6. Systematic Effects and Counter-Arguments

Before accepting the conclusion that the Universe violates the CP, one must exhaustively explore all possible systematic errors.

6.1 Masking and Mode Coupling

The Galaxy obscures a significant portion of the sky (roughly 20-40% depending on the wavelength). This missing data destroys the orthogonality of spherical harmonics, causing “mode coupling.” Power from the monopole and quadrupole can leak into the dipole.

• Critique: Abghari et al. (2024) suggested that when the mode coupling matrix is properly accounted for, the uncertainty on the dipole increases significantly, potentially reducing the tension to $<3\sigma$. They argued that the intrinsic quadrupole of the quasar distribution is unknown and degenerate with the dipole.⁷
• Rebuttal: Secrest et al. (2025) and Bashir et al. (2025) countered this with extensive forward modeling using FLASK simulations. They generated mock catalogs with standard $\Lambda$CDM clustering and applied the exact survey masks. Their results show that while mode coupling does increase variance, it does not induce a systematic bias in the amplitude. The observed signal in CatWISE is far outside the distribution of mock dipoles, even with severe masking. They conclude that mode coupling cannot explain the factor of $\sim 2$ excess.⁷

6.2 The Clustering Dipole

The measured dipole is the vector sum of the kinematic dipole (our motion) and the clustering dipole (actual large-scale structure).

$$\vec{D}_{\text{obs}} = \vec{D}_{\text{kin}} + \vec{D}_{\text{clus}}$$

In a homogeneous universe, $\vec{D}_{\text{clus}}$ should converge to zero as the survey volume increases. However, for finite surveys, “cosmic variance” persists.

• Local Structure: Structures like the Shapley Concentration could mimic a dipole. However, quasars and radio galaxies are at high redshift ($z \sim 1$). The contribution of local ($z < 0.1$) structure to the projected dipole of such distant sources is negligible.³
• Random Alignment: For the clustering dipole to explain the anomaly, it would have to be (a) large (comparable to the kinematic term) and (b) aligned with the kinematic dipole. The probability of a random LSS vector aligning with the solar motion vector to within $\sim 20^\circ$ is roughly $1\%$. The fact that this alignment is seen in multiple independent surveys makes the “random clustering” hypothesis highly unlikely.⁵

6.3 Star-Galaxy Separation

In infrared surveys, stars can mimic quasars. Stars have a dipole due to solar motion and galactic rotation, but this dipole is distinct from the cosmic one.

• Directionality: The stellar dipole is dominated by the gradient of the Milky Way, pointing towards the Galactic Center $(0^\circ, 0^\circ)$.
• Effect: If the CatWISE sample were contaminated by stars, the measured dipole vector would be pulled towards the Galactic Center. The observed CatWISE dipole points to $(238^\circ, 29^\circ)$, which is nearly orthogonal to the Galactic Center. Therefore, stellar contamination would likely dilute the anomaly rather than create it. Removing stars more aggressively would likely increase the tension.¹⁵

6.4 Redshift Evolution and Tomography

One subtle theoretical systematic involves the evolution of source populations. The standard Ellis-Baldwin formula assumes a static population.

• The Dalang-Bonvin Correction: Dalang and Bonvin (2022) showed that if the number density or luminosity function of sources evolves with redshift, additional terms enter the dipole equation. These terms arise because the Doppler shift changes the observed redshift, and if the selection function depends on redshift, this creates a secondary dipole.²⁰
• Impact: While theoretically important, applying these corrections to current datasets has not resolved the tension. In some cases, the evolution terms can actually increase the predicted kinematic dipole, making the observed excess slightly smaller but still significant.
• Tomography Results: Preliminary tomographic analyses (splitting sources into redshift bins) suggest that the dipole amplitude may be redshift-dependent. If the derived velocity $v(z)$ increases with redshift, this would effectively rule out a simple kinematic origin (which requires a constant $v$) and point towards bulk flows or intrinsic anisotropy.²⁰

7. Theoretical Interpretations: Beyond $\Lambda$CDM

If systematics cannot explain the $5\sigma$ tension, we are forced to consider physical mechanisms that violate the standard FLRW assumptions.

7.1 Large-Scale Bulk Flows and “Dark Flow”

The most direct physical interpretation of the excess dipole is that the matter rest frame is moving relative to the CMB frame. This is known as a “bulk flow.”

• Scale: The standard model predicts bulk flows should decay on scales $> 100$ Mpc. The dipole anomaly implies a coherent flow extending to $z \sim 1$ (billions of light years).
• Kashlinsky’s Dark Flow: In 2008, Kashlinsky et al. claimed to detect a bulk flow of $\sim 600-1000$ km s$^{-1}$ using the kinetic Sunyaev-Zel’dovich (kSZ) effect in galaxy clusters. While controversial and challenged by Planck kSZ results, the magnitude of the “Dark Flow” is remarkably similar to the velocity implied by the radio/quasar dipole anomaly.²²
• Implication: A flow on this scale suggests the influence of super-horizon fluctuations—gravitational gradients originating from beyond the observable Universe. This could imply that our Hubble patch is sliding towards a massive inhomogeneity outside our horizon.²⁴

7.2 Dipole Cosmology and Tilted Bianchi Models

The FLRW metric assumes zero shear and zero tilt. However, the Einstein equations allow for homogeneous but anisotropic solutions, known as Bianchi models.

• The “Tilt”: In a “tilted” Bianchi universe (specifically Type V or VII$_h$), the cosmic fluid has a global velocity field relative to the geometric expansion.
• Krishnan et al. (2023): Proposed a “Dipole Cosmology” framework. They showed that in these models, the relative velocity between the matter fluid and the radiation fluid can grow over cosmic time. This would naturally explain why the CMB dipole (radiation frame) and the quasar dipole (matter frame) differ in amplitude. They share a direction (the axis of the tilt) but decouple dynamically.²⁵
• Observables: These models predict specific signatures in the Hubble diagram (a dipole in $H_0$) and parity-violating modes in the CMB polarization, which are currently being searched for.

7.3 Modified Gravity and Dark Energy

The cosmic dipole tension may also signal a breakdown of General Relativity on large scales.

• Horndeski Theories: Certain classes of scalar-tensor theories (like Horndeski gravity) allow for effective gravitational couplings that vary with scale or direction. If dark energy is not a cosmological constant but a dynamic field (quintessence) with a gradient, it could induce an anisotropic expansion.²⁷
• Early Dark Energy (EDE): Models of EDE, proposed to solve the Hubble Tension, might also leave imprints on large-scale anisotropy. If the scalar field associated with EDE had spatial fluctuations, it could generate a large-scale mode that resembles a dipole.²⁸

7.4 Connections to Other Anomalies

The Dipole Anomaly is likely connected to other tensions in cosmology:

• The Hubble Tension: A large local bulk flow would bias local measurements of $H_0$. If we are in a bulk flow of $\sim 1000$ km s$^{-1}$, this could account for a significant fraction of the difference between Supernova ($H_0 \sim 73$) and CMB ($H_0 \sim 67$) measurements.³
• Hemispherical Asymmetry: The CMB exhibits a power asymmetry (one hemisphere is “smoother” than the other). The axis of this asymmetry aligns closely with the dipole. A single physical mechanism—such as a modulation of the primordial power spectrum by a super-horizon mode—could generate both the power asymmetry and the enhanced kinematic dipole.³⁰

8. Future Prospects: Resolving the Anomaly

The next decade will see a definitive resolution to the Cosmic Dipole Anomaly, driven by three flagship observatories.

8.1 The Euclid Mission (ESA)

Launched in 2023, Euclid will survey 15,000 square degrees of the sky in the visible and near-infrared.

• Cosmic Infrared Background (CIB): Euclid will measure the dipole of the CIB by integrating the light of all resolved galaxies. This method is independent of the number-count thresholding used in CatWISE. Forecasts suggest Euclid will measure the CIB dipole direction to sub-degree accuracy and the amplitude with extremely high signal-to-noise ($>50\sigma$).³²
• Tomography: Euclid‘s spectroscopic redshifts will allow for precise measurement of the dipole as a function of redshift ($0.9 < z < 1.8$). Observing a variation in $\mathcal{D}(z)$ would be the “smoking gun” for non-kinematic physics.³³

8.2 The Square Kilometre Array (SKA)

The SKA will be the ultimate radio survey machine.

• Source Counts: SKA will detect hundreds of millions of radio sources (compared to NVSS’s 2 million). This will reduce Poisson noise to negligible levels.
• Precision: Forecasts indicate that SKA will constrain the dipole direction to within $\sim 4^\circ$ and the amplitude to within $10\%$. This precision is sufficient to distinguish between the kinematic prediction ($\mathcal{D} \sim 0.005$) and the anomalous value ($\mathcal{D} \sim 0.015$) at $>10\sigma$.³⁴
• HI Intensity Mapping: SKA will also measure the dipole using 21cm intensity mapping, a completely different tracer than continuum counts, providing an internal cross-check.³⁶

8.3 The Vera C. Rubin Observatory (LSST)

The LSST will conduct the Legacy Survey of Space and Time, mapping the Southern sky every few nights.

• Systematics Control: LSST’s unique “dithering” strategy and rapid revisit rate allow for exquisite control over calibration systematics, which are the main counter-argument against the current dipole results.
• Third Orthogonal Probe: LSST will provide a deep optical galaxy sample. Comparing the optical dipole (LSST) with the radio (SKA) and IR (Euclid) dipoles will provide a rigorous “triangulation” of the anomaly. If all three agree on an excess, the case for new physics will be irrefutable.³⁷

9. Conclusion

The Cosmic Dipole Anomaly has graduated from a statistical curiosity to a central crisis in modern cosmology. The convergence of evidence from radio galaxies and infrared quasars points to a persistent, high-significance ($>5\sigma$) discrepancy between the Universe’s matter frame and its radiation frame.

The standard kinematic interpretation—that the CMB dipole is due solely to our motion of 370 km s$^{-1}$—is increasingly untenable in the face of matter dipoles that imply velocities of $\sim 1000$ km s$^{-1}$. The “orthogonality” of the radio and quasar datasets makes instrumental systematics an unlikely explanation. While theoretical refinements like redshift evolution and LSS clustering must be accounted for, they have so far failed to close the gap.

We are left with two profound possibilities. Either we have identified a subtle, pervasive systematic error that affects all flux-limited surveys across the electromagnetic spectrum, or the Cosmological Principle is violated. If the latter is true, we may inhabit a “tilted” Universe, flowing through the cosmos relative to the light of the Big Bang, or a Universe influenced by the gravitational ghosts of pre-inflationary structure.

The resolution is imminent. With Euclid taking data and SKA and Rubin on the horizon, the next few years will determine whether the Cosmic Dipole Anomaly is the final crack that shatters the FLRW metric, or a subtle lesson in the complexities of observing the cosmos. Until then, the “lopsided universe” remains one of the most compelling clues that our standard model of cosmology is incomplete.

Comparison of Cosmic Dipole Measurements

Dataset	Type	Frequency/Band	Source Count	Dipole Amplitude (×10−2)	Kinematic Exp. (×10−2)	Tension	Reference
CMB (Planck)	Radiation	Microwave	N/A	$0.123$ (velocity)	N/A	N/A	3
NVSS	Radio Galaxies	1.4 GHz	$1.8 \times 10^6$	$1.5 – 2.5$	$\sim 0.5$	$>2\sigma$	3
TGSS	Radio Galaxies	150 MHz	$0.6 \times 10^6$	$2.0 – 6.0$	$\sim 0.5$	$>3\sigma$	5
RACS	Radio Galaxies	887 MHz	$2.1 \times 10^6$	$\sim 1.5 – 2.0$	$\sim 0.5$	Strong	6
CatWISE	Quasars	Mid-IR (W1/W2)	$1.35 \times 10^6$	$1.55 \pm 0.16$	$0.70$	$4.9\sigma$	2
Combined	Multi-tracer	All	$>4 \times 10^6$	$1.5 – 2.0$	$\sim 0.6$	$>5\sigma$	8

Table 1: Summary of major dipole measurements compared to the kinematic expectation.

Works cited

1. Colloquium: The Cosmic Dipole Anomaly – arXiv, accessed on January 9, 2026, https://arxiv.org/html/2505.23526v1
2. (PDF) Colloquium: The Cosmic Dipole Anomaly – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/392204608_Colloquium_The_Cosmic_Dipole_Anomaly
3. Cosmic dipole tensions: confronting the cosmic microwave background with infrared and radio populations of cosmological sources – Oxford Academic, accessed on January 9, 2026, https://academic.oup.com/mnras/article/543/4/3229/8266509
4. The kinematic contribution to the cosmic number count dipole – arXiv, accessed on January 9, 2026, https://arxiv.org/html/2503.02470v1
5. Resolution of the incongruency of dipole asymmetries within various large radio surveys – implications for the Cosmological Principle – Oxford Academic, accessed on January 9, 2026, https://academic.oup.com/mnras/article/528/4/5679/7604001
6. Overdispersed radio source counts and excess radio dipole detection – arXiv, accessed on January 9, 2026, https://arxiv.org/html/2509.16732v1
7. The CatWISE2020 Quasar dipole: A Reassessment of the Cosmic Dipole Anomaly – arXiv, accessed on January 9, 2026, https://arxiv.org/html/2511.00822v1
8. [2505.23526] Colloquium: The Cosmic Dipole Anomaly – arXiv, accessed on January 9, 2026, https://arxiv.org/abs/2505.23526
9. Are radio surveys showing us that the Cosmological Principle doesn’t hold up? – Astrobites, accessed on January 9, 2026, https://astrobites.org/2024/02/14/ur-template-post-title-2/
10. The Rotating Universe: Radio Galaxies and the Cosmic Dipole Anomaly, accessed on January 9, 2026, https://spacefed.com/astronomy/the-rotating-universe-radio-galaxies-and-the-cosmic-dipole-anomaly/
11. Kinematically Induced Dipole Anisotropy in Line-Emitting Galaxy Number Counts and Line Intensity Maps – arXiv, accessed on January 9, 2026, https://arxiv.org/pdf/2501.09800
12. Resolution of the incongruency of dipole asymmetries within various large radio surveys – implications for the Cosmological Principle – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/378315283_Resolution_of_the_incongruency_of_dipole_asymmetries_within_various_large_radio_surveys_-_implications_for_the_Cosmological_Principle
13. Cosmic dipole tensions: confronting the Cosmic Microwave Background with infrared and radio populations of cosmological sources – arXiv, accessed on January 9, 2026, https://arxiv.org/html/2509.18689v1
14. [2511.00822] The CatWISE2020 Quasar dipole: A Reassessment of the Cosmic Dipole Anomaly – arXiv, accessed on January 9, 2026, https://arxiv.org/abs/2511.00822
15. The Dipole Problem in Cosmology – Indico Global, accessed on January 9, 2026, https://indico.global/event/1728/contributions/30544/attachments/15592/24877/The%20Dipole%20Problem%20in%20Cosmology.pdf
16. Cosmic Multipoles in Galaxy Surveys II: Comparing Different Methods in Assessing the Cosmic Dipole | Published in The Open Journal of Astrophysics, accessed on January 9, 2026, https://astro.theoj.org/article/144907-cosmic-multipoles-in-galaxy-surveys-ii-comparing-different-methods-in-assessing-the-cosmic-dipole
17. Reassessment of the dipole in the distribution of quasars on the sky – arXiv, accessed on January 9, 2026, https://arxiv.org/html/2405.09762v2
18. The CatWISE2020 Quasar dipole: A Reassessment of the Cosmic Dipole Anomaly, accessed on January 9, 2026, https://www.researchgate.net/publication/397232239_The_CatWISE2020_Quasar_dipole_A_Reassessment_of_the_Cosmic_Dipole_Anomaly
19. Clustering properties of the CatWISE2020 quasar catalogue and their impact on the cosmic dipole anomaly – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/397006102_Clustering_properties_of_the_CatWISE2020_quasar_catalogue_and_their_impact_on_the_cosmic_dipole_anomaly
20. Redshift tomography of the kinematic matter dipole – University of Portsmouth, accessed on January 9, 2026, https://pure.port.ac.uk/ws/portalfiles/portal/106493259/Redshift_tomography_of_the_kinematic_matter_dipole.pdf
21. On the kinematic cosmic dipole tension | Request PDF – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/359307883_On_the_kinematic_cosmic_dipole_tension
22. [1411.4180] Probing the Dark Flow signal in WMAP 9 yr and PLANCK cosmic microwave background maps – arXiv, accessed on January 9, 2026, https://arxiv.org/abs/1411.4180
23. Scientists Detect Cosmic ‘Dark Flow’ Across Billions of Light Years – NASA, accessed on January 9, 2026, https://www.nasa.gov/news-release/nasa-scientists-detect-cosmic-dark-flow-across-billions-of-light-years/
24. Dark flow – Wikipedia, accessed on January 9, 2026, https://en.wikipedia.org/wiki/Dark_flow
25. Dipole cosmology: the Copernican paradigm beyond FLRW | Request PDF – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/372211883_Dipole_cosmology_the_Copernican_paradigm_beyond_FLRW
26. Towards a realistic dipole cosmology: the dipole ΛCDM model – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/381707155_Towards_a_realistic_dipole_cosmology_the_dipole_LCDM_model
27. Observations by DESI Open the Door to Modified Gravity Models – Universe Today, accessed on January 9, 2026, https://www.universetoday.com/articles/observations-by-desi-open-the-door-to-modified-gravity-models
28. The “Hubble tension”: A growing crisis in cosmology – Math Scholar, accessed on January 9, 2026, https://mathscholar.org/2024/10/the-hubble-tension-a-growing-crisis-in-cosmology/
29. Cosmic dipoles from large-scale structure surveys – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/398345183_Cosmic_dipoles_from_large-scale_structure_surveys
30. CMB-S4 and the hemispherical variance anomaly – Oxford Academic, accessed on January 9, 2026, https://academic.oup.com/mnras/article/470/1/372/3828090
31. (PDF) Resolution to the CMB Hemispherical Asymmetry, Cold Spot, Quadrupole-Octupole, and Missing Large-Angle Correlations: Cosmological Coda III of the Principia Cybernetica – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/399488032_Resolution_to_the_CMB_Hemispherical_Asymmetry_Cold_Spot_Quadrupole-Octupole_and_Missing_Large-Angle_Correlations_Cosmological_Coda_III_of_the_Principia_Cybernetica
32. Euclid preparation XLVI. The near-infrared background dipole experiment with Euclid, accessed on January 9, 2026, https://aaltodoc.aalto.fi/items/e1aa01b4-bed9-4847-9bdf-ac24ca24ac33
33. Euclid: Cosmological forecasts from the void size function – the University of Groningen research portal, accessed on January 9, 2026, https://research.rug.nl/files/603418851/aa44095_22.pdf
34. PoS(AASKA14)032, accessed on January 9, 2026, https://pos.sissa.it/215/032/pdf
35. Testing the standard model of cosmology with the SKA: the cosmic radio dipole | Request PDF – ResearchGate, accessed on January 9, 2026, https://www.researchgate.net/publication/345465646_Testing_the_standard_model_of_cosmology_with_the_SKA_the_cosmic_radio_dipole
36. Testing the standard model of cosmology with the SKA: the cosmic radio dipole – CORE, accessed on January 9, 2026, https://core.ac.uk/download/pdf/195277694.pdf
37. Examples of LSST Science Projects | Rubin Observatory, accessed on January 9, 2026, https://www.lsst.org/science/science_portfolio
38. The Rubin Observatory Legacy Survey of Space and Time (LSST), accessed on January 9, 2026, https://lsstdesc.org/pages/rubin.html