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We use VANDELS spectroscopic data overlapping with the $\simeq$7 Ms ChandraDeep Field South survey to extend studies of high-mass X-ray binary systems(XRBs) in 301 normal star-forming galaxies in the redshift range $3 < z < 5.5$.Our analysis evaluates correlations between X-ray luminosities ($L_X$), starformation rates (SFR) and stellar metallicities ($Z_\star$) to higher redshiftsand over a wider range in galaxy properties than hitherto. Using a stackinganalysis performed in bins of both redshift and SFR for sources with robustspectroscopic redshifts without AGN signatures, we find convincing evolutionarytrends in the ratio $L_X$/SFR to the highest redshifts probed, with a strongertrend for galaxies with lower SFRs. Combining our data with published samplesat lower redshift, the evolution of $L_X$/SFR to $z\simeq5$ proceeds as $(1 +z)^{1.03 \pm 0.02}$. Using stellar metallicities derived from photosphericabsorption features in our spectroscopic data, we confirm indications at lowerredshifts that $L_X$/SFR is stronger for metal-poor galaxies. We usesemi-analytic models to show that metallicity dependence of $L_X$/SFR alone maynot be sufficient to fully explain the observed redshift evolution of X-rayemission from high-mass XRBs, particularly for galaxies with SFR $<30$$M_\odot$ yr$^{-1}$. We speculate that the discrepancy may arise due to reducedoverall stellar ages in the early Universe leading to higher $L_X$/SFR for thesame metallicity. We use our data to define the redshift-dependent contributionof XRBs to the integrated X-ray luminosity density and, in comparison withmodels, find that the contribution of high-mass XRBs to the cosmic X-raybackground at $z>6$ may be $\gtrsim 0.25$ dex higher than previously estimated.

The VANDELS Survey: New constraints on the high-mass X-ray binary populations in normal star-forming galaxies at 3 < z < 5.5