We investigate two classes of models of quintessential inflation, based upon canonical as well as noncanonical scalar fields. In particular, introducing potentials steeper than the standard exponential, we construct models that can give rise to a successful inflationary phase, with signatures consistent with Planck 2015 results. Additionally, using nonminimal coupling of the scalar field with massive neutrino matter, we obtain the standard thermal history of the Universe, with late-time cosmic acceleration as the last stage of evolution. In both cases, inflation and late-time acceleration are connected by a tracker solution.

We reconstruct an explicit model of modified gravity in which a crossing of the phantom divide can be realized. It is shown that the (finite-time) Big Rip singularity appears in the model of modified gravity (i.e., in the so-called Jordan-frame), whereas that in the corresponding scalar field theory obtained through the conformal transformation (i.e., in the so-called Einstein frame) the singularity becomes the infinite-time one. Furthermore, we investigate the relations between the scalar field theories with realizing a crossing of the phantom divide and the corresponding modified gravitational theories by using the inverse conformal transformation. It is demonstrated that the scalar field theories describing the nonphantom phase (phantom one with the Big Rip) can be represented as the theories of real (complex) $F(R)$ gravity through the inverse (complex) conformal transformation. We also study a viable model of modified gravity in which the transition from the de Sitter universe to the phantom phase can occur. In addition, we explore the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction coming from conformal anomaly.

We study the semileptonic and non-leptonic charmed baryon decays with SU(3) flavor symmetry, where the charmed baryons can be B _c = (Ξ _c ⁰ , Ξ _c ⁺ , Λ _c ⁺ ), B _c ^′ = (Σ _c ^(++,+,0) , Ξ _c ^′ (+,0) , Ω _c ⁰ ), B _cc = (Ξ _cc ^+ + , Ξ _cc ⁺ , Ω _c ⁺ ) or B _cc = Ω _ccc ^+ + . With B _n ^(′) denoted as the baryon octet (decuplet), we find that the B _c → B _n ^′ ℓ ⁺ ν _ℓ decays are forbidden, while the Ω _c ⁰ → Ω⁻ ℓ ⁺ ν _ℓ , Ω _cc ⁺ → Ω _c ⁰ ℓ ⁺ ν _ℓ , and Ω _ccc ^+ + → Ω _cc ⁺ ℓ ⁺ ν _ℓ decays are the only existing Cabibbo- allowed modes for B _c ^′ → B _n ^′ ℓ ⁺ ν _ℓ , B _cc → B _c ^′ ℓ ⁺ ν _ℓ , and B _ccc → B _cc ^(′) ℓ ⁺ ν _ℓ , respectively. We predict the rarely studied B _c → B _n ^(′) M decays, such as $$ \mathrm{\mathcal{B}}\left({\Xi}_c^0\to {\Lambda}^0{\overline{K}}^0,{\Xi}_c^{+}\to {\Xi}^0{\pi}^{+}\right)=\left(8.3\pm 0.9,\ 8.0\pm 4.1\right)\times {10}^{-3}\kern0.5em \mathrm{and}\kern0.5em \mathrm{\mathcal{B}}\left({\Lambda}_c^{+}\to {\Delta}^{++}{\pi}^{-},{\Xi}_c^0\to {\Omega}^{-}{K}^{+}\right)=\left(5.5\pm 1.3,\kern0.5em 4.8\pm 0.5\right)\times {10}^{-3} $$ ℬ Ξ c 0 → Λ 0 K ¯ 0 , Ξ c + → Ξ 0 π + = 8.3 ± 0.9 , 8.0 ± 4.1 × 10 − 3 and ℬ Λ c + → Δ + + π − , Ξ c 0 → Ω − K + = 5.5 ± 1.3 , 4.8 ± 0.5 × 10 − 3 . For the observation, the doubly and triply charmed baryon decays of $$ {\Omega}_{cc}^{+}\to {\Xi}_c^{+}{\overline{K}}^0,{\Xi}_{cc}^{++}\to \left({\Xi}_c^{+}{\pi}^{+},{\varSigma}_c^{++}{\overline{K}}^0\right),\kern0.5em \mathrm{and}\kern0.5em {\Omega}_{ccc}^{++}\to \left({\Xi}_{cc}^{++}{\overline{K}}^0,{\Omega}_{cc}^{+}{\pi}^{+},{\Xi}_c^{+}{D}^{+}\right) $$ Ω cc + → Ξ c + K ¯ 0 , Ξ cc + + → Ξ c + π + , Σ c + + K ¯ 0 , and Ω c c c + + → Ξ cc + + K ¯ 0 , Ω cc + π + , Ξ c + D + are the favored Cabibbo-allowed decays, which are accessible to the BESIII and LHCb experiments.

We study the inert triplet models, in which the standard model is extended to have a new SU(2)L triplet scalar (Y=0 or 2) with an Z2 symmetry. We show that the neutral component of the triplet can be a good dark matter candidate. In particular, for the hypercharge Y=0 triplet model, the WMAP data favors the region where the dark matter mass is around 5.5~TeV, which is also consistent with the direct detection experiments. In contrast, for the Y=2 model, although dark matter with its mass around 2.8~TeV is allowed by WMAP, it is excluded by the direct detection experiments because the spin-independent cross section is enhanced by the Z-mediated tree-level scattering process.

We calculate the Higgs decay rate of $h$\rightarrow${}Z$\gamma${}$ by including the contributions from new scalars with arbitrary quantum numbers of the weak isospin ($T$) and hypercharge ($Y$) in the Standard Model. We find that our general formula for the decay rate of $h$\rightarrow${}Z$\gamma${}$ matches with that for $h$\rightarrow${}$\gamma${}$\gamma${}$ in the limit of ${m}_{Z}=0$, but it is different from those in the literature. To illustrate our result, by taking the current $2$\sigma${}$ excess of the $h$\rightarrow${}$\gamma${}$\gamma${}$ rate measured by the LHC, we examine the corresponding shift for the $Z$\gamma${}$ decay channel due to the new scalar. We show that the enhancement or reduction of the $h$\rightarrow${}Z$\gamma${}$ rate only depends on the relative size of $T$ and the absolute value of $Y$. Explicitly, we predict $0.76<{R}_{Z$\gamma${}}$\equiv${}$\Gamma${}(h$\rightarrow${}Z$\gamma${})/{$\Gamma${}}_{\mathrm{SM}}(h$\rightarrow${}Z$\gamma${})<2.05$ by imposing the observed range of $1.5<{R}_{$\gamma${}$\gamma${}}$\equiv${}$\Gamma${}(h$\rightarrow${}Z$\gamma${}$\gamma${})/\phantom{\rule{0ex}{0ex}}{$\Gamma${}}_{\mathrm{SM}}(h$\rightarrow${}$\gamma${}$\gamma${})<2$, which is independent of the number of multiplets and the couplings to the Higgs particle as long as the scalars are heavier than 200 GeV. This result provides a clear signature for the future LHC measurements to test physics beyond the Standard Model.