The recently introduced swampland criterion for de Sitter [17] can be viewed as a (hierarchically large) bound on the smallness of the slow roll parameter V. This leads us to consider the other slow roll parameter η V more closely, and we are lead to conjecture that the bound is not necessarily on V , but on slow roll itself. A natural refinement of the de Sitter swampland conjecture is therefore that slow roll is violated at O(1) in Planck units in any UV complete theory. A corollary is that V need not necesarily be O(1), if η V −O(1) holds. We consider various tachyonic tree level constructions of de Sitter in IIA/IIB string theory (as well as closely related models of inflation), which superficially violate [17], and show that they are consistent with this refined version of the bound. The phrasing in terms of slow roll makes it plausible why both versions of the conjecture run into trouble when the number of e-folds during inflation is high. We speculate that one way to evade the bound could be to have a large number of fields, like in N-flation.

By a systematic survey of the parameter space we confirm our surmise[1] that the Minimal Supersymmetric GUT(MSGUT) based on the 210 ⊕ 126 ⊕ 126 ⊕ 10 Higgs system is incompatible with the generic Type I and Type II seesaw mechanisms. The incompatibility of the Type II seesaw mechanism with this MSGUT is due to its generic extreme sub-dominance with respect to the Type I contribution. The Type I mechanism although dominant over Type II is itself unable to provide Neutrino masses larger than ∼ 10 −3 eV anywhere in the parameter space. Our Renormalization Group based analysis shows the origin of these difficulties to lie in a conflict between baryon stability and neutrino oscillation. The MSGUT completed with a 120-plet Higgs is the natural next to minimal candidate. We propose a scenario where the 120-plet collaborates with the 10-plet to fit the charged fermion masses. The freed 126-plet couplings can then give sub-dominant contributions to charged fermion masses and enhance the Type I seesaw masses sufficiently to provide a viable seesaw mechanism. We give formulae required to verify this scenario.

The supersymmetric SO(10) GUT based on the 210 ⊕ 10 ⊕ 120 ⊕ 126 ⊕ 126 Higgs system provides a minimal framework for the emergence of the R-parity exact MSSM at low energies and a viable supersymmetric seesaw explanation for the observed neutrino masses and mixing angles. We present formulae for MSSM decomposition of the superpotential invariants, tree level light charged fermion effective Yukawa couplings, Weinberg neutrino mass generation operator, and the d = 5, ∆B = ∆L = 0 effective superpotential in terms of GUT parameters. We use them to determine fits of the 18 available fermion mass-mixing data in terms of the superpotential parameters of the NMSGUT and SUGRY(NUHM) type soft supersymmetry breaking parameters ({mf , m 1/2 , A 0 , M 2 H,H }) specified at the MSSM one loop unification scale M 0 X = 10 16.33 GeV. Our fits are compatible with electroweak symmetry breaking and Unification constraints and yield right-handed neutrino masses in the leptogenesis relevant range : 10 8 − 10 13 GeV. Matching the SM data requires lowering the strange and down quark Yukawas in the MSSM via large tan β driven threshold corrections and characteristic soft Susy breaking spectra. The Susy spectra have light pure Bino LSP, heavy exotic Higgs(inos) and large µ, A 0 , M H,H parameters ∼ 100 TeV. Typically third generation sfermions are much heavier than the first two generations. The smuon is often the lightest charged sfermion thus offering a Bino-CDM co-annihilation channel. The parameter sets obtained are used to calculate B violation rates which are found to be generically much faster(∼ 10 −28 yr −1 ) than the current experimental limits. Improvements which may allow acceptable B violation rates are identified.

We present strong evidence that the tree level slow roll bounds of arXiv:1807.05193 and arXiv:1810.05506 are valid, even when the tachyon has overlap with the volume of the cycle wrapped by the orientifold. This extends our previous results in the volume-dilaton subspace to a semi-universal modulus. Emboldened by this and other observations, we investigate what it means to have a bound on (generalized) slow roll in a multi-field landscape. We argue that for any point φ 0 in an N -dimensional field space with V (φ 0 ) > 0, there exists a path of monotonically decreasing potential energy to a point φ 1 within a path length O(1), such that−O(1). The previous de Sitter swampland bounds are specific ways to realize this stringent non-local constraint on field space, but we show that it also incorporates (for example) the scenario where both slow roll parameters are intermediate-valued and the Universe undergoes a small number of e-folds, as in the Type IIA set up of arXiv:1310.8300. Our observations are in the context of tree level constructions, so we take the conservative viewpoint that it is a characterization of the classical "boundary" of the string landscape. To emphasize this, we argue that these bounds can be viewed as a type of Dine-Seiberg