The hypothetical massive dark photon ($gamma$) which has kinetic mixing with the SM photon can decay electromagnetically to $e^+e^-$ pairs if its mass $m$ exceeds $2m_e$ and otherwise into three SM photons. These decays yield cosmological and superno
vae associated signatures. We briefly discuss these signatures, particularly in connection with the supernova SN1987A and delineate the extra constraints that may then arise on the mass and mixing parameter of the dark photon. In particular, we find that for dark photon mass $m_{gamma}$ in the 5-20 MeV range, arguments based on supernova 1987A observations lead to a bound on $epsilon$ which is about 300 times stronger than the presently existing bounds based on energy loss arguments.
We discuss the issue of vacuum stability of standard model by embedding it within the TeV scale left-right universal seesaw model (called SLRM in the text). This model has only two coupling parameters $(lambda_1, lambda_2)$ in the Higgs potential and
only two physical neutral Higgs bosons $(h, H)$. We explore the range of values for $(lambda_1, lambda_2)$ for which the light Higgs boson mass $M_h=126$ GeV and the vacuum is stable for all values of the Higgs fields. Combining with the further requirement that the scalar self couplings remain perturbative till typical GUT scales of order $10^{16}$ GeV, we find (i) an upper and lower limit on the second Higgs $(H)$ mass to be within the range: $0.4 leq frac{M_H}{v_R}leq 0.7$, where the $v_R$ is the parity breaking scale and (ii) that the heavy vector-like top, bottom and $tau$ partner fermions ($P_3, N_3, E_3$) mass have an upper bound $M_{P_3, N_3, E_3} leq v_R$. We discuss some phenomenological aspects of the model pertaining to LHC.
