  Verifying the fully kinematic nature of the cosmic microwave background (CMB)
dipole is of fundamental importance in cosmology. In the standard cosmological
model with the Friedman-Lemaitre-Robertson-Walker (FLRW) metric from the
inflationary expansion the CMB dipole should be entirely kinematic. Any
non-kinematic CMB dipole component would thus reflect the preinflationary
structure of spacetime probing the extent of the FLRW applicability. Cosmic
backgrounds from galaxies after the matter-radiation decoupling, should have
kinematic dipole component identical in velocity with the CMB kinematic dipole.
Comparing the two can lead to isolating the CMB non-kinematic dipole. It was
recently proposed that such measurement can be done using the near-IR cosmic
infrared background (CIB) measured with the currently operating Euclid
telescope, and later with Roman. The proposed method reconstructs the resolved
CIB, the Integrated Galaxy Light (IGL), from Euclid's Wide Survey and probes
its dipole, with a kinematic component amplified over that of the CMB by the
Compton-Getting effect. The amplification coupled with the extensive galaxy
samples forming the IGL would determine the CIB dipole with an overwhelming
signal/noise, isolating its direction to sub-degree accuracy. We develop
details of the method for Euclid's Wide Survey in 4 bands spanning 0.6 to 2
mic. We isolate the systematic and other uncertainties and present
methodologies to minimize them, after confining the sample to the magnitude
range with negligible IGL/CIB dipole from galaxy clustering. These include the
required star-galaxy separation, accounting for the extinction correction
dipole using the method newly developed here achieving total separation,
accounting for the Earth's orbital motion and other systematic effects.
(Abridged)
