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Recently, an interesting inflationary scenario, named Gauss-Bonnet inflation, is proposed by Kanti et al. [1,2]. In the model, there is no inflaton potential but the inflaton couples to the Guass-Bonnet term. In the case of quadratic coupling, they find inflation occurs with graceful exit. The scenario is attractive because of the natural set-up. However, we show there exists the gradient instability in the tensor perturbations in this inflationary model. We further prove the no-go theorem for the Gauss-Bonnet inflation without an inflaton potential.

The symmetry breaking of 5-dimensional SU(6) GUT is realized by Scherk-Schwarz mechanisms through trivial and pseudo non-trivial orbifold S 1 /Z 2 breakings to produce dimensional deconstruction 5D SU(6)→4D SU(6). The latter also induces near-brane weakly-coupled SU(6) Baby Higgs to further break the symmetry into SU(3) C ⊗SU(3) H ⊗U(1) C . The model successfully provides a scenario of the origin of (Little) Higgs from GUT scale, produces the (intermediate and light) Higgs boson with the most preferred range and establishes coupling unification and compactification scale correctly.October 18, 2018 1:15 WSPC/INSTRUCTION FILE Near-brane˙SU6˙IJMP 2 October 18, 2018 1:15 WSPC/INSTRUCTION FILE Near-brane˙SU6˙IJMP 3Higgses produce SM-like Higgses and become the topic of discussion in this paper. The second symmetry breaking of 4D SU(6)→ 4D SU(3)⊗SU(3)⊗U(1) is performed by SU (6) Little-like Higgs through orbifold-based field re-definition and the broken shift symmetry induced by the properties of VEV in lower-near-brane [15,16]. The VEV s are obtained from two Scherk-Schwarz parameters [4][5][6][7].One can immediately predict the birth of SU(3) Little Higgses from the SU(6)origin Little Higgses. This derivation is indeed workable and quite successful.The paper is organized as follows, first special conditions of Scherk-Schwarz breaking, the trivial and pseudo non-trivial orbifold S 1 /Z 2 breaking [15,22,24] are revealed in the next Section, then 5D model of SU(6) with 2 branes and the bulk [32,33] where gauge bosons and scalar bosons live in near-brane area (y ∼ 0) which will provide SU(6)-origin Little Higgs, and SU(6) Baby Higgs which is basically weakly-coupled. The two have been well reconciled within the model as well as SU(6) GUT and Baby Higgs.The pseudo non-trivial symmetry breaking to SU(3)⊗SU(3)⊗U(1) is explained in the next section. Subsequently it is shown that the emerging gauge bosons from broken 5-dimensional SU(6) could be considered as scalar boson [6,7,20] which provides the Coleman Weinberg potential for radiative symmetry breaking of 4D SU(6). Before summarizing the results, a brief discussion on the order estimations of relevant physical observables within the model is given.

We investigate the Kerr-Newman-NUT black hole solution obtained from Plebański-Demiański solutions with several assumptions. The origin of the microscopic entropy of this black hole is studied using the conjectured Kerr/CFT correspondence which is first proposed for extremal Kerr black holes. The isometry of the near-horizon extremal Kerr-Newman-NUT black hole shows that the asymptotic symmetry group may be applied to compute the central charge of the Virasoro algebra. Furthermore, by assuming Frolov-Thorne vacuum, the temperatures can be obtained which then using Cardy formula, the microscopic entropy is obtained and agrees with the Bekenstein-Hawking entropy. We also assume the case when the lowest eigenvalue of the conformal operator L 0 is non-zero to find the logarithmic correction of the entropy of NHEKNUT black hole. At the limit J → 0, the extremal Reissner-Nordström-NUT solution is produced and by adding the fibered coordinate we find the 5D solution. The second dual CFT is used to find the entropy and it still produces the area law of 5D black hole solution. So, the extremal Reissner-Nordström-NUT solution is also holographically dual to the CFT.

In this article, we consider a special case of Metric-Affine f (R)-gravity for f (R) = R, i.e. the Metric-Affine General Relativity (MAGR). As a companion to the first article in the series, we perform the (3+1) decomposition to the hypermomentum equation, obtained from the minimization of the MAGR action S [g, ω] with respect to the connection ω. Moreover, we show that the hypermomentum tensor H could be constructed completely from 10 hypersurfaces variables that arise from its dilation, shear, and rotational (spin) parts. The (3+1) hypermomentum equations consists of 1 scalar, 3 vector, 3 matrix, and 1 tensor equation of order -21 . Together with the (3+1) decomposition of the traceless torsion constraint, consisting of 1 scalar and 1 vector equation, we obtain 10 hypersurface equations, which are the main result in this article. Finally, we consider some special cases of MAGR, namely, the zero hypermomentum, metric, and torsionless cases. For vanishing hypermomentum, we could retrieve the metric compatibility and torsionless condition in the (3+1) framework, hence forcing the affine connection to be Levi-Civita as in the standard General Relativity.withn * ∈ T * p M is the covariant vector ton, satisfyingn * = g (n, •) = g (n) (the label p is omitted for simplicity).The Adapted Coordinate, Lapse Function, and Shift Vector Let x µ = x 0 , x i be a local coordinate on M, with x 0 and x i are, respectively, the temporal and spatial part of x µ . The corresponding coordinate vector basis on T p M is ∂ µ = {∂ 0 , ∂ i }. Any vector V ∈ T p M could be decomposed as follows: