This paper examines the allowed amount of IG ( intergalactic ) dust , which is constrained by extinction and reddening of distant SNe Ia and thermal history of IGM ( intergalactic medium ) affected by dust photoelectric heating .
Based on the observational cosmic star formation history , we find an upper bound of \chi , the mass ratio of the IG dust to the total metal in the Universe , as \chi \la 0.1 for 10 { \AA } \la a \la 0.1 \micron and \chi \la 0.1 ( a / 0.1 \micron ) for 0.1 \micron \la a \la 1 \micron , where a is a characteristic grain size of the IG dust .
This upper bound of \chi \sim 0.1 suggests that the dust-to-metal ratio in the IGM is smaller than the current Galactic value .
The corresponding allowed density of the IG dust increases from \sim 10 ^ { -34 } g cm ^ { -3 } at z = 0 to \sim 10 ^ { -33 } g cm ^ { -3 } at z \sim 1 , and keeps almost the value toward higher redshift .
This causes IG extinction of \la 0.2 mag at the observer ’ s B -band for z \sim 1 sources and that of \la 1 mag for higher redshift sources .
Furthermore , if E ( B - V ) \sim 0.1 mag at the observer ’ s frame against z \ga 1 sources is detected , we can conclude that a typical size of the IG dust is \la 100 Å .
The signature of the 2175 Å feature of small graphite may be found as a local minimum at z \sim 2.5 in a plot of the observed E ( B - V ) as a function of the source redshift .
Finally , the IGM mean temperature at z \la 1 can be still higher than 10 ^ { 4 } K , provided the size of the IG dust is \la 100 Å .