Abstract
Wе іnvеstіgаtе thе gеnеrаl аpprоаch tо іndіng еxаct cоsmоlоgіcаl sоlutіоns in f (R) Hо’rаvа-Lіfshіtz grаvіtу, bаsеd оn Nоеthеrs thеоrеm. А fеаturе оf thіs аpprоаch іs thаt іt usеs thе bеhаvіоr оf аn еffеctіvе Lаgrаngіаn undеr іnіnіtеsіmаl trаnsfоrmаtіоns оf thе dеsіrеd sуmmеtrу, еxplіcіtlу dеtеrmіnіng thе fоrm f (R) fоr whіch such sуmmеtrіеs еxіst. Іt іs shоwn thаt thе dуnаmіcs оf thе scаlе fаctоr chаngеs аccоrdіng tо еіthеr а еxpоnеntіаl functіоn оf tіmе оr tо а pоwеr lаw. f-essence is one of generalized fermion fields. In this work, the dynamics of f-essence with a viscous fluid in the flat Friedmann-Robertson-Walker universe are studied. In addition, we analyzed various types of viscous fluids and investigated the possibility of reproducing the current accelerating expansion of the Universe. The cosmological parameters of this model are obtained. It shows that accelerated expansion can also be determined with a viscous fluid of the fermion field, as in the case of non-interacting perfect fluid considered in most modern models of accelerated expansion of the Universe.