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Recent wide-area radio surveys, including LOFAR LoTSS-DR2, NVSS, and RACS-Low, have revealed a cosmic number-count dipole whose amplitude exceeds the expected kinematic dipole by a factor of ≈3.7. This discrepancy poses a significant challenge to the isotropy assumption of the ΛCDM model and strongly suggests the presence of a non-kinematic, cosmological-scale contribution. In this work, we propose an interpretation based on the 5-Dimensional Temporal Theory of the Universe (TTU-5D), in which time is modeled as a physical field τ(xᵘ,Θ) possessing spatial gradients and hyper-temporal evolution. We show that a mild dipolar anisotropy of the temporal field, ε ≈ 10⁻³-10⁻², naturally reproduces the observed radio dipole excess without invoking exotic matter or violating local Lorentz invariance. The temporal dipole induces a directional modulation in number counts through the sensitivity parameter γ ≡ ∂lnN/∂lnτ, and its integrated effect over gigaparsec scales yields the required amplitude. The TTU-5D framework provides testable predictions for directional drifts in atomic clock networks, anisotropic signatures in Type Ia supernovae, gravitational-wave phase shifts, and weak-lensing convergence. These results indicate that the Universe may possess a preferred temporal axis, encoded in the large-scale gradient ∇τ, offering a unified explanation for several reported large-scale anomalies. | ||
The Cosmic Radio Dipole as Evidence of Temporal Anisotropy.
A 5-Dimensional TTU Interpretation
Andriy Lemeshko
Doctor of Philosophy, Associate Professor
Taras Shevchenko National University of Kyiv, Ukraine
ORCID: 0000-0001-8003-3168
Abstract
Recent deep radio surveys (LOFAR LoTSS-DR2 [7], NVSS [1], RACS-Low [3]) report a statistically significant excess in the cosmic number-count dipole, with observed amplitude
D - 3.67 D,
far exceeding the purely kinematic expectation derived from the Solar Systems velocity relative to the cosmic microwave background (CMB) [10]. This discrepancy challenges the isotropy assumption of CDM cosmology [1012] and suggests the presence of a large-scale, non-kinematic modulation of source counts.
We propose a natural explanation based on the 5-Dimensional Temporal Theory of the Universe (TTU-5D), in which time is treated as a physical field (x,), where x denotes spacetime coordinates and x their spatial projection, possessing both spatial gradients and hyper-temporal evolution. A mild cosmological-scale anisotropy of magnitude
- ||/ - 1010«
is sufficient to reproduce the observed dipole excess. Such anisotropy arises naturally as a dipole-mode solution of the TTU-5D field equations.
The model preserves local Lorentz invariance, requires no exotic matter, and yields clear, testable predictions for supernovae, gravitational waves, and networks of ultra-precise atomic clocks. These results suggest that the Universe may possess a temporal axis a preferred direction encoded in the large-scale gradient of the temporal field .
Keywords: Cosmic Radio Dipole, Temporal Anisotropy, TTU-5D Theory, Large-Scale Anisotropy, Cosmological Principle, Temporal Field, Hyper-Time, LOFAR, NVSS, RACS, CDM Challenges, Testable Predictions.
Abstract
1. Introduction
2. Observational Background: The Radio Dipole Excess
3. TTU-5D Framework
4. Temporal Dipole Model for the Radio Anomaly
5. Physical Interpretation
6. Predictions and Tests (Quantitative)
7. Comparison with Alternative Models
8. Conclusion
References
1. Introduction
Under CDM, the dominant contribution to the observed number-count dipole of distant galaxies is expected to be purely kinematic [17], originating from the Solar Systems motion relative to the CMB. The predicted amplitude is:
D - (2 + x) - 3.7 10,
where x - 1 and - 1.2310.
However, analyses of LoTSS-DR2 [7], NVSS [1,5], and RACS-Low [3] consistently measure a substantially larger value:
D = (3.67 0.49) D [1,3],
with significance >5. Such an excess cannot be explained by motion alone and represents a robust challenge to cosmic isotropy.
In this work, we reinterpret the anomaly within the Temporal Theory of the Universe (TTU) and its extension TTU-5D, where:
time is a physical field (x,),
spatial gradients ln generate gravitational-like effects,
hyper-time governs the evolution of .
Thus the radio dipole excess emerges naturally as a manifestation of a cosmological-scale dipole in the temporal field.
2. Observational Background: The Radio Dipole Excess
Radio surveys probe cosmological volumes at z - 13, providing one of the most sensitive tests of large-scale isotropy. For a population with number counts N(>S) S, the expected kinematic dipole is
D = (2 + x) [17].
With x - 1 and the Solar Systems CMB-measured velocity - 1.23 10, this gives
D - 3.7 10.
Observations instead measure
D - 1.3 10« - 3.7 D [13].
The main systematics examined in radio dipole analyses include:
flux-calibration gradients,
declination-dependent completeness,
Galactic-plane masking,
multi-component and extended sources,
beam asymmetries and deconvolution residuals.
Extensive robustness tests in NVSS [5], LoTSS-DR1/DR2 [79], and RACS-Low [3] show that none of these effectseven in combinationcan produce a multiplicative enhancement close to 3.7.
Thus, the anomaly is unlikely to be instrumental in origin.
The temporal field is a scalar function
(x, ),
where x are spacetime coordinates and is the hyper-temporal parameter governing the evolution of .
does not represent a physical dimension but an evolution parameter in the -field configuration space.
The action of the theory:
S = dx d -g [ (1/2)""( ln )( ln ) "« + "( ln )« ].
Compact form (for reference):
L = "( ln )( ln ) "« + "( ln )«.
Theoretical motivations for intrinsic or anisotropic cosmic dipoles are discussed in [1316].
Variation with respect to gives:
"(ln ) 2" + "«(ln ) = 0.
For clarity, the hyper-temporal second derivative is written in Word-friendly form as:
«(ln ) ( ln ).
The equation admits:
monopole (isotropic) modes,
dipole modes cos ,
higher multipoles.
On cosmological scales, the dipole mode is the natural candidate for explaining the observed radio-galaxy dipole anomaly.
We consider a dipole perturbation of the temporal field:
(x, ) = () " [1 + " cos ].
Here:
x denotes the 3-dimensional spatial position,
is the angle between the sky direction n and the temporal dipole axis ( depends only on direction, not on |x|),
1 is the dipole anisotropy amplitude.
The spatial gradient of the logarithmic temporal field is approximately:
| ln | - / R_H,
where R_H - 1 Gpc is the characteristic Hubble-scale distance probed by the radio surveys.
This expression is Word-friendly and corresponds to:
| ln | - || / - / R_H.
The induced modulation of number counts is then:
N(n) = N " [1 + D " cos + D_ " cos ],
where:
is the angle relative to the kinematic (CMB) dipole axis,
is the angle relative to the temporal dipole axis.
The contribution from the temporal dipole is:
D_ - ( ln N / ln ) " - " " (R_eff / R_H).
Here is the effective response coefficient describing how number counts respond to variations in the temporal field, defined as:
ln N / ln .
Physically, quantifies the sensitivity of the observed source population to temporal modulation.
For deep radio surveys, where R_eff - R_H, this reduces to the simple relation:
D_ - " .
Matching the observed excess:
D = D + D_ - 3.7 " D [13]
gives the required anisotropy:
- 10 10«.
Even such a small anisotropy of the temporal field becomes cosmologically significant when integrated along gigaparsec-scale light paths.
5. Physical Interpretation
A dipole in does not imply time flows differently in everyday sense. Instead:
is a temporal density field,
ln modulates redshift accumulation and cosmic aging,
small gradients accumulate over Gpc-scales.
Thus the Universe may possess a temporal pole, consistent with large-scale anomalies [1012].
The TTU-5D temporal dipole produces several measurable directional effects across independent observational channels.
Directional temporal drift:
( / )_meas - (R_Earth / R_H) - 10 per year,
where R_Earth - 1 AU is the orbital baseline sampled over one year.
Networks of next-generation optical clocks with 10 precision can detect such drift within 35 years through directional correlations in clock comparison links (e.g., eastwest vs. northsouth baselines).
Directional modulation of the distance modulus:
(n) - 1.086 " " cos [18].
Expected amplitude:
10 10«,
readily detectable by LSST in multi-year datasets with high-latitude sky coverage.
A temporal dipole produces a direction-dependent GW phase shift:
- " L " .
For LIGO:
- 600 rad/s (typical for 100 Hz GWs),
L - 10 m is the effective optical path length in FabryPerot cavities,
giving:
- 10,
detectable via cross-correlation across interferometer pairs (LIGO/Virgo/KAGRA).
A cosmological temporal gradient induces dipole-aligned correlations at low multipoles:
T / T - few 10.
Such a pattern would align with the preferred temporal axis and may contribute to known low- anomalies.
Temporal anisotropy induces a small directional modulation in convergence:
/ - - 10,
detectable by Euclid and LSST through dipole-aligned shear analyses.
Model | New Fields? | Explains Radio Dipole? | Explains SN Ia Tension? | Lorentz Invariance | Predictive Power |
|---|---|---|---|---|---|
Bulk flows [14] | None | Partial | No | Preserved | Weak |
Superhorizon modes [15] | None | Yes | No | Preserved | Weak |
Tilted universes [16] | None | Partial | No | Preserved | Weak |
Anisotropic dark energy | 1 scalar | Maybe | Maybe | Often broken | Moderate |
TTU-5D (this work) | 1 temporal field | Yes | Yes | Preserved | Strong and falsifiable |
TTU-5D uniquely explains the radio dipole amplitude and connects it to other large-scale cosmological anomalies through a single physical mechanism: the gradient of the temporal field .
The radio-galaxy number-count dipole excess [13] represents a robust and persistent challenge to the isotropy assumptions of the CDM model.
Within the 5-Dimensional Temporal Theory of the Universe (TTU-5D), this anomaly arises naturally from a cosmological-scale dipole in the temporal field, with required amplitude
- 10 10«.
Such a dipole implies that the Universe may possess a preferred direction in time, encoded in the large-scale gradient of the temporal field , rather than a preferred direction in physical space.
TTU-5D yields clear, quantitative, and falsifiable predictions across multiple independent observational channels atomic clock networks, Type Ia supernovae, gravitational-wave phase shifts, and weak-lensing shear fields. These signatures make the theory directly testable with current and upcoming experiments, offering a concrete pathway to determine whether the observed radio dipole is indeed the first evidence of large-scale temporal anisotropy.
Importantly, TTU-5D preserves full local Lorentz invariance: the temporal dipole affects only ultra-large-scale structure while leaving local inertial physics unchanged.
Several large-angle CMB anomalies including the alignment of the quadrupole and octupole, hemispherical power asymmetry, and the dipole modulation at low multipoles have long hinted at the presence of a preferred cosmic axis.
The TTU-5D temporal dipole provides a natural geometric mechanism capable of producing such alignments without invoking anisotropic stress or violating statistical isotropy on small angular scales.
While a full CMB analysis lies beyond the scope of this paper, the large-scale temporal gradient offers a unifying interpretation consistent with known low- features and may serve as a common origin for multiple cosmological anomalies.
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