The new Spectrum Roentgen Gamma (SRG)/eROSITA X-ray telescope has a superiorresponse to extended soft X-rays in terms of effective area, energy resolution,and field-of-view (FoV). This makes SRG/eROSITA ideal for studying low X-raysurface brightness emission of cosmic filaments. We search for extended X-rayemission between the two nearby galaxy clusters Abell 3667 and Abell 3651 thatare separated by a projected transverse distance of ${\sim} 13\,\mathrm{Mpc}$,using data from the SRG/eROSITA All-Sky Survey. Detailed X-ray image analysisof the region between the two galaxy clusters and redshift analysis of sourcesbetween them is performed. We carried out thorough surface brightness analysisbetween the clusters and in their outskirts studying enhanced emission indifferent directions. The analysis is complemented with an X-ray pointedobservation from XMM-Newton, infrared 2MASS data and redshift information fromNED. We discover an emission filament beyond the known radio relic in thenorthwest of A3667 and even beyond three times its virial radius, smoothlyconnecting to A3651. The X-ray emission in the direction of the filament showsa $30\pm3\,\%$ enhancement with a significance of $11\,\sigma$. The 2MASS mapand redshift analysis show an alignment of sources along the filament and makea projection effect unlikely. Taking the redshift progression of sources withinthe filament into account, its three-dimensional length is estimated to be inthe range of $25\,\mathrm{Mpc} - 32\,\mathrm{Mpc}$. Surface brightness analysisin combination with assumptions for ranges of plausible temperatures andmetallicities leads to estimates of total flux, gas mass and central baryonoverdensity of $F_\mathrm{X}= (7.1^{+2.1}_{-1.0})\times 10^{-12}\,\mathrm{ergs^{-1} cm^{-2}}$, $M_\mathrm{g}=(2.8^{+5.4}_{-1.0})\times10^{14}\,\mathrm{M_\odot}$ and $\delta_0=220^{+390}_{-65}$, respectively.

We estimate how the mean density of dust in the universe varies withredshift, using submillimetre continuum observations and a method designed tominimise the effect of dust temperature. We have used the Herschel-ATLAS toshow that the median temperature of dust in galaxies is ~22 K and does not varysignificantly with redshift out to z=1. With this as our estimate of themass-weighted dust temperature, we have used an 850-micron survey of the COSMOSfield to estimate the mean density of dust in 10 redshift bins over the range 0< z < 5.5. We find that the mean density of dust increased by a factor of ~10from z=5 to z=2, declined slightly to z=1, and then steeply to the present day.The relationship between the mean density of dust and redshift is similar tothe relationship between the mean star-formation rate and redshift, althoughthe increase for the former is steeper from z=5 to z=2. We have also used thesubmillimetre measurements to estimate the mean density of gas over the sameredshift range. The values we estimate for the dust-traced gas are much lowerand with a different redshift dependence than estimates of the mean density ofatomic gas but similar to estimates of the mean density of the CO-traced gas.We find that the depletion time for the dust-traced gas in the universe as awhole declines with redshift in the same way seen for individual galaxies.