We examine the constraints on the two Higgs doublet model (2HDM) due to the stability of the scalar potential and absence of Landau poles at energy scales below the Planck scale. We employ the most general 2HDM that incorporates an approximately Standard Model (SM) Higgs boson with a flavor-aligned Yukawa sector to eliminate potential tree-level Higgs-mediated flavor-changing neutral currents. Using basis independent techniques, we exhibit regimes of the 2HDM parameter space with a 125 GeV SM-like Higgs boson that is stable and perturbative up to the Planck scale. Implications for the heavy scalar spectrum are exhibited.

The most general 2HDM contains an extended Yukawa sector that includes new sources of flavor-changing neutral currents (FCNCs), which must be suppressed due to experimental bounds. The flavor-alignment ansatz asserts a proportionality between the Yukawa matrices that couple the up-type (down-type) fermions to the two respective Higgs doublet fields of the 2HDM, thereby eliminating FCNCs at tree-level. If flavor-alignment is imposed at a high energy scale, such as the Planck scale, tree-level FCNCs can be generated at the electroweak scale via renormalization group running. We determine the size of FCNCs that can be generated at the electroweak scale via Planck scale flavor-alignment, and use experimental bounds on flavor-changing observables to place constraints on the flavor-aligned 2HDM parameter space.