Abstract: Projective invariance is a symmetry of the Palatini version of General Relativity which is not present in the metric formulation. The fact that the Riemann tensor changes nontrivially under projective transformations implies that, unlike in the usual metric approach, in the Palatini formulation this tensor is subject to a gauge freedom, which allows some ambiguities even in its scalar contractions. In this sense, we show that for the Schwarzschild solution there exists a projective gauge in which the (affine) Kretschmann scalar, K (R beta μnu R alpha beta μnu)-R-alpha, can be set to vanish everywhere. This puts forward that the divergence of curvature scalars may, in some cases, be avoided by a gauge transformation of the connection.

Abstract: We investigate the production of primordial Gravitational Waves (GWs) arising from First Order Phase Transitions (FOPTs) associated to neutrino mass generation in the context of type-I and inverse seesaw schemes. We examine both “high-scale” as well as “low-scale” variants, with either explicit or spontaneously broken lepton number symmetry U(1)(L), in the neutrino sector. In the latter case, a pseudo-Goldstone majoron-like boson may provide a candidate for cosmological dark matter. We find that schemes with softly-broken U(1)(L), and with single Higgs-doublet scalar sector lead to either no FOPTs or too weak FOPTs, precluding the detestability of GWs in present or near future measurements. Nevertheless, we found that, in the majoron-like seesaw scheme with spontaneously broken U(1)(L), at finite temperatures, one can have strong FOPTs and non-trivial primordial GW spectra which can fall well within the frequency and amplitude sensitivity of upcoming experiments, including LISA, BBO and u-DECIGO. However, GWs observability clashes with invisible Higgs decay constraints from the LHC. A simple and consistent fix is to assume the majoron-like mass to lie above the Higgs-decay kinematical threshold. We also found that the majoron-like variant of the low-scale seesaw mechanism implies a different GW spectrum than the one expected in the high-scale seesaw. This feature will be testable in future experiments. Our analysis shows that GWs can provide a new and complementary portal to test the neutrino mass generation mechanism.

Abstract: We explore the gravitational wave spectrum generated by string-wall structures in an SO (10) (Spin(10)) based scenario of pseudo-Goldstone boson dark matter (pGDM) particle. This dark matter candidate is a linear combination of the Standard Model (SM) singlets present in the 126 and 16 dimensional Higgs fields. The Higgs 126-plet vacuum expectation value (VEV) < 126(H)> leaves unbroken the Z(2) subgroup of Z(4), the center of SO (10). Among other things, this yields topologically stable cosmic strings with a string tension μsimilar to < 126(H)>(2). The subsequent (spontaneous) breaking of Z(2) at a significantly lower scale by the 16-plet VEV < 16(H)> leads to the appearance of domain walls bounded by the strings produced earlier. We display the gravitational wave spectrum for G μvalues varying between 10(-15) and 10(-9) (< 126(H)> similar to 10(11) – 10(14) GeV), and < 16(H)> similar to 0.1 – 10(2) TeV range (G denotes Newton's constant.) These predictions can be tested, as we show, by a variety of (proposed) experiments including LISA, ET, CE and others.