Henry George Liddell, Robert Scott, A Greek-English Lexicon, κόσμος
With the change in the understanding of the universe over the past 2,000+ years, it's very difficult to come up with a 1:1 correspondence between κόσμος and our modern scientific "definition" of cosmos (Carl Sagan's and Neil de Grasse Tyson's TV series notwithstanding).
To the Greeks, κόσμος encompassed the Earth at the center with our sun orbiting around us with the stars embedded in or as holes in the surrounding sphere. So taking that route, κόσμος to us, is the visible universe. However, it would seem to be that, to the ancients, each planet (other Earths) would have its own sun. When Epicurus/Lucretius says there are other worlds, he's using κόσμοι (plural) which implies that arrangement. The "gods" supposedly live "between" kosmoi, so by definition, they don't seem to be "living" IN a world-system. They are said to live *between* world-systems. BUT each κόσμος has its own home planet at its center.
That LSJ definition includes:
Philos., world-order, universe, first in Pythag., acc.to Placit.2.1.1, D.L.8.48 (cf. [Philol.]21), or Parm., acc. to Thphr. ap. D.L.l.c.; “κόσμον τόνδε οὔτε τις θεῶν οὔτε ἀνθρώπων ἐποίησεν, ἀλλ᾽ ἦν ἀεὶ καὶ ἔστιν καὶ ἔσται πῦρ” Heraclit.30; “ὁ καλούμενος ὑπὸ τῶν σοφιστῶν κ.” X.Mem.1.1.11: freq. in Pl., Grg.508a, Ti.27a, al.; “ἡ τοῦ ὅλου σύστασίς ἐστι κ. καὶ οὐρανός” Arist.Cael.280a21, cf. Epicur.Ep. 2p.37U., Chrysipp.Stoic.2.168, etc.; “ὁ κ. ζῷον ἔμψυχον καὶ λογικόν” Posidon. ap. D.L.7.139, cf. Pl.Ti.30b: sts. of the firmament, “γῆς ἁπάσης τῆς ὑπὸ τῷ κόσμῳ κειμένης” Isoc.4.179; “ὁ περὶ τὴν γῆν ὅλος κ.” Arist. Mete.339a20; μετελθεῖν εἰς τὸν ἀέναον κ., of death, OGI56.48 (Canopus, iii B. C.); but also, of earth, as opp. heaven, “ὁ ἐπιχθόνιος κ.” Herm. ap. Stob.1.49.44; or as opp. the underworld, “ὁ ἄνω κ.” Iamb.VP27.123; of any region of the universe, “ὁ μετάρσιος κ.” Herm. ap. Stob.1.49.44; of the sphere whose centre is the earth's centre and radius the straight line joining earth and sun, Archim.Aren.4; of the sphere containing the fixed stars, Pl.Epin.987b: in pl., worlds, coexistent or successive, Anaximand. et alii ap.Placit.2.1.3, cf. Epicur.l.c.; also, of stars, “Νὺξ μεγάλων κ. κτεάτειρα” A.Ag.356 (anap.), cf. Heraclid.et Pythagorei ap.Placit.2.13.15 (= Orph.Fr.22); οἱ ἑπτὰ κ. the Seven planets, Corp.Herm.11.7.
So, even that is a somewhat vague, wide-ranging definition.
So sum up, neither Martin nor Eikadistes are wrong in their modern analogies, but it could also be said that neither are quite correct either.