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We study the effects of the local environment on the molecular gas content ofa large sample of log($M_{*}$/$M_{\odot}$) $\gtrsim$ 10 star-forming andstarburst galaxies with specific star-formation rates (sSFRs) on and above themain sequence (MS) to $z$ $\sim$ 3.5. ALMA observations of the dust continuumin the COSMOS field are used to estimate molecular gas masses at $z$ $\approx$0.5-3.5. We also use a local universe sample from the ALFALFA HI survey afterconverting it into molecular masses. The molecular mass ($M_{ISM}$) scalingrelation shows a dependence on $z$, $M_{*}$, and sSFR relative to the MS, butno dependence on environmental overdensity $\Delta$ ($M_{ISM}$ $\propto$$\Delta^{0.03}$). Similarly, gas mass fraction (f$_{gas}$) and depletiontimescale ($\tau$) show no environmental dependence to $z$ $\sim$ 3.5. At$\langle z\rangle$ $\sim$ 1.8, the average $\langleM_{ISM}\rangle$,$\langle$f$_{gas}\rangle$, and $\langle \tau \rangle$ indensest regions is (1.6$\pm$0.2)$\times$10$^{11}$ $M_{\odot}$, 55$\pm$2%, and0.8$\pm$0.1 Gyr, respectively, similar to those in the lowest density bin.Independent of the environment, f$_{gas}$ decreases and $\tau$ increases withincreasing cosmic time. Cosmic molecular mass density ($\rho$) in the lowestdensity bins peaks at $z$ $\sim$ 1-2, and this peak happens at $z$ $<$ 1 indensest bins. This differential evolution of $\rho$ across environments islikely due to the growth of the large-scale structure with cosmic time. Ourresults suggest that the molecular gas content and the subsequentstar-formation activity of log($M_{*}$/$M_{\odot}$) $\gtrsim$ 10 star-formingand starburst galaxies is primarily driven by internal processes, and not bytheir local environment since $z$ $\sim$ 3.5.

Similar Scaling Relations for the Gas Content of Galaxies across Environments to z ~ 3.5