Cosmological Consequences of Extended Bose-Einstein Condensate Dark Matter in Specific Modified Gravity

Abstract

In thismanuscript,weconsiderthenewlyproposedmodi¯edtheoryin whichtopologicalinvariantGauss-Bonnet G is coupledwiththeenergy- momentumsquared(¿ 2 = ¿¹º¿ ¹º). Forthismatter-geometriccoupling,we consider f(G; ¿ 2) = f(G) + g(¿ 2) modelfor°atFRWuniverse.Thedy- namics ofbouncingcosmologyarethoroughlyexaminedwithintheframe- workofunderlyingviablemodel,canovercomethesingularity'schallengein standard Big-Bangcosmology.Westudypowerlawscalefactorandsome cosmological bouncingscalefactorssuchasthefourtypesofbouncesare matter, oscillatory,super,andsymmetric.Inthisscenario,theequationof state parameteriscomputed ! and thesquaredsoundspeedparameter.We also checkthedynamicsof !¡!0 plane forunderlyingframework.Interest- ingly,itshouldbenotedthateveryoutcomefavortherecentobservational data.