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We study a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) space-time in thetheory of $f(Q)$-gravity, where $Q$ denotes the non-metricity scalar. It hasbeen previously shown in the literature, that there exist four distinctfamilies of connections, which are compatible with the isometries of the FLRWmetric; three for the spatially flat case and one when the spatial curvature ispresent. In the spatially flat case, one connection is dynamically irrelevantand yields the dynamics of the coincident gauge in the Cartesian coordinates.For this, we obtain the general solution of an arbitrary $f(Q)$ theory with aperfect fluid matter content, and present various examples for specific choicesof the $f(Q)$ function. We proceed by studying the effect of the rest of theconnections, which are dynamical and affect the equations of the motion. Weconcentrate in scenarios that depart from the $Q=$const. case, which justreproduces General Relativity with a cosmological constant, and derive novelvacuum solutions for a power-law $f(Q)$ function.

FLRW solutions in $f(Q)$ theory: the effect of using different connections