rarus.

Uncertain. Possibly related to Lithuanian i̇̀rti (“to dissolve, fall into ruin”) and Proto-Slavic *oriti. It has also been compared to Ancient Greek ἐρῆμος (erêmos, “lonely”), but this may be phonetically difficult if certain sound laws involving laryngeals and *r are accepted. More information *Beekes 2010 and Schrijver 1991 assume Greek ἐρῆμος (erêmos) must be from a root of the form *h₁reh₁-. Schrijver 1991 therefore denies that ἐρῆμος (erêmos) and rārus are cognates, because per Schrijver's sound laws, no gradation of *h₁reh₁- can regularly give rise to Latin rār-: *h₁r̥h₁rós would give Latin *rarus with short -a- (compare ratus from *h₂rh₁tós), whereas *h₁reh₁rós would give Latin *rērus with long -ē-. Schrijver is uncertain whether i̇̀rti and *oriti are cognate with Greek ἐρῆμος (erêmos) or with Latin rārus: in the latter case, Schrijver assumes Latin rā- came from *Hreh₂-, with schwebeablaut. Beekes treats derivation of rārus from zero-grade *h₁r̥h₁-ro- as possible, without explicitly addressing Schrijver's argument that this should be expected to yield *rar-. *Woodhouse 2011 postulates different sound laws, assuming that Greek initial ἐρ- (er-) can come either from PIE *h₁r- or PIE *r- and that PIE *rHC- became Latin ra- with short -a-, whereas PIE *HrHC- became Latin rā- with long -ā-. Based on these assumptions, Woodhouse derives ratus from a root starting with *r- (instead of *h₁r as postulated by Schrijver) and assumes that Latin rārus might show rā- as the regular outcome of earlier *h₂rH-, from the zero-grade of a root *h₂erH- shared with i̇̀rti. De Vaan 2008 mentions *h₂erH- (“to disappear, perish”) as a possible root of rārus but dismisses it as semantically unlikely.