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We consider holomorphic Poisson-BF theory on twistor space. Classically, this describes self-dual Einstein gravity on space-time, but at the quantum level it is plagued by an anomaly. The anomaly corresponds to the fact that integrability…
The generalisation of proper time, as an alternative to models with extra dimensions of space, has been proposed as the source of the elementary structures of matter. Direct connections with the Standard Model of particle physics together…
Spontaneous collapse models aim to resolve the measurement problem in quantum mechanics by considering wave-function collapse as a physical process. We analyze how these models affect a decaying flavor-oscillating system whose evolution is…
The observed baryon asymmetry of the universe (BAU) cannot be explained by the known sources of charge-parity (CP)-violation in the Standard Model (SM). A non-zero permanent electric-dipole-moment (EDM) for fundamental particles, nuclei or…
In this thesis, we discuss some of the applications of cosmological perturbation theory in the late universe. We begin by reviewing the tools used to understand the standard model of cosmology theoretically and to compute its observational…
It is shown that nonlinear terms in equations of gravitons on the background of curved space-time of the expanding Universe can solve the problem of the negative square of the effective mass formally arising in linear approximation for…
In Ho\v{r}ava-Lifshitz gravity a scaling isotropic in space but anisotropic in spacetime, often called anisotropic scaling with the dynamical critical exponent z=3, lies at the base of its renormalizability. This scaling also leads to a…
We present a predictive framework for neutrino mass generation based on the spontaneous breaking of a leptonic $U(1)_{L_\mu-L_\tau}$ symmetry within a supersymmetric setting. The breaking of the global symmetry gives rise to a Majoron-like…
Recent papers by Gavela et al. and Huet et al. claim to have shown that incluion of higher order interactions between quasiparticles dramatically decreases the baryon asymmetry of the universe which can arise in the Minimal Standard Model.…
It seems to be generally accepted that apparently anomalous cosmological observations, such as accelerating expansion, etc., necessarily are inconsistent with standard general relativity and standard matter sources. Following the…
We establish Sobolev type inequalities in the noncommutative settings by generalizing monotone metrics in the space of quantum states, such as matrix-valued Beckner inequalities. We also discuss examples such as random transpositions and…
We study a rotating and expanding, Godel type metric, originally considered by Korotkii and Obukhov, showing that, in the limit of large times and nearby distances, it reduces to the open metric of Friedmann. In the epochs when radiation or…
Motivated by the recent SuperKamiokande results on atmospheric neutrinos, we incorporate massive neutrinos, with large angle oscillation between the second and third generations, in a theory with R-parity violating supersymmetry. The…
In the standard cosmological model the dark energy (DE) and nonrelativistic (NR) matter densities are observationally determined to be comparable at the present time, in spite of their greatly different evolution histories. This `cosmic…
We present a framework to describe completely general first-order perturbations of static, spatially compact, and locally rotationally symmetric class II spacetimes within the theory of general relativity. The perturbation variables are by…
A manifestly covariant equation is derived to describe the second order perturbations in topological defects and membranes on arbitrary curved background spacetimes. This, on one hand, generalizes work on macroscopic strings in Minkowski…
In recent times, one of the strongest hints of Physics Beyond the Standard Model (BSM) has been the anomaly in the ratios $R_D$ and $R_{D^\ast}$ measured in the charged current decays of $B$-mesons. In this work, we perform a comprehensive…
It is known that the overlap of two energy eigenstates in a decaying quantum system is bounded from above by a function of the energy detuning and the individual decay rates. This is usually traced back to the positive definiteness of an…
The highly successful Standard Model is not complete. It does not explain the baryonic asymmetry in the Universe, the existence of dark matter or the non-zero masses of the neutrinos. Extensions of the Standard Model that propose the…
A general theory of preparational uncertainty relations for a quantum particle in one spatial dimension is developed. We derive conditions which determine whether a given smooth function of the particle's variances and its covariance is…