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Rapidly rotating turbulent flow is characterized by the emergence of columnarstructures that are representative of quasi-two dimensional behavior of theflow. It is known that when energy is injected into the fluid at anintermediate scale $L_f$, it cascades towards smaller as well as larger scales.In this paper we analyze the flow in the \textit{inverse cascade} range at asmall but fixed Rossby number, {$\mathcal{R}o_f \approx 0.05$}. Several{numerical simulations with} helical and non-helical forcing functions areconsidered in periodic boxes with unit aspect ratio. In order to resolve theinverse cascade range with {reasonably} large Reynolds number, the analysis isbased on large eddy simulations which include the effect of helicity on eddyviscosity and eddy noise. Thus, we model the small scales and resolveexplicitly the large scales. We show that the large-scale energy spectrum hasat least two solutions: one that is consistent withKolmogorov-Kraichnan-Batchelor-Leith phenomenology for the inverse cascade ofenergy in two-dimensional (2D) turbulence with a {$\sim k_{\perp}^{-5/3}$}scaling, and the other that corresponds to a steeper {$\sim k_{\perp}^{-3}$}spectrum in which the three-dimensional (3D) modes release a substantialfraction of their energy per unit time to 2D modes. {The spectrum that} emerges{depends on} the anisotropy of the forcing function{,} the former solutionprevailing for forcings in which more energy is injected into 2D modes whilethe latter prevails for isotropic forcing. {In the case of anisotropic forcing,whence the energy} goes from the 2D to the 3D modes at low wavenumbers,large-scale shear is created resulting in another time scale $\tau_{sh}$,associated with shear, {thereby producing} a $\sim k^{-1}$ spectrum for the{total energy} with the 2D modes still following a {$\sim k_{\perp}^{-5/3}$}scaling.

Anisotropy and non-universality in scaling laws of the large scale energy spectrum in rotating turbulence