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As a rule in General Relativity the spacetime metric fixes the Einsteintensor and through the Field Equations (FE) the energy-momentum tensor. Howeverone cannot write the FE explicitly until a class of observers has beenconsidered. Every class of observers defines a decomposition of theenergy-momentum tensor in terms of the dynamical variables energy density($\mu$), the isotropic pressure ($p$), the heat flux $q^a$ and the tracelessanisotropic pressure tensor $\pi_{ab}$. The solution of the FE requiresadditional assumptions among the dynamical variables known with the genericname equations of state. These imply that the properties of the matter for agiven class of observers depends not only on the energy-momentum tensor but onextra a priori assumptions which are relevant to that particular class ofobservers. This makes difficult the comparison of the Physics observed bydifferent classes of observers for the {\it same} spacetime metric. One way toovercome this unsatisfactory situation is to define the extra conditionrequired among the dynamical variables by a geometric condition, which will bebased on the metric and not to the observers. Among the possible and multipleconditions one could use the consideration of collineations. We examine thispossibility for the Friedmann-Lema\^{i}tre-Robertson-Walker models admittingmatter and Ricci collineations and determine the equations of state for thecomoving observers. We find linear and non-linear equations of state, whichlead to solutions satisfying the energy conditions, therefore describingphysically viable cosmological models.Comment: 14 pages, Latex; to appear in General Relativity and Gravitatio

Geometric Equations of State in Friedmann-Lemaître Universes Admitting Matter and Ricci Collineations