We develop the calculation of the divergent part of one-loop covariant effective action for scalar fields minimally and non-minimally coupled to gravity using the generalized Schwinger-DeWitt technique. We derive the field-space metric using Vilkovisky's prescription and obtain new terms in the one-loop corrections which are absent in past literature with trivial choices of field-space metric. We further calculate the covariant versions of past results, obtained using the standard approach, by applying Barvinsky and Vilkovisky's extension to the ordinary Schwinger-DeWitt approach. For completeness, we study the one-loop gravitational corrections for a dilaton-extended two-field Starobinsky model and compare with known results.

We investigate the quantum stability of generalised Proca theories in curved spacetime treating gravity as a dynamical field. To compute the quantum gravitational corrections, we evaluate the divergent part of the effective action at one-loop level using Vilkovisky-DeWitt formalism, which gives us a gauge invariant and gauge condition independent effective action. It is shown that the quantum corrections are suppressed by a UV cutoff parametrically higher than the Proca mass, if the coupling constants are restricted to lie in a certain range. Furthermore, it is shown that the quantum corrections remain suppressed even at scales where classical non-linearities dominate over kinetic terms, allowing Vainshtein mechanism to work.

We perform the calculation for tree-level ultraviolet unitarity violation scales for scalar-R 2 inflation models by including an additional R 2|Φ|2-type term. Due to certain constraints, we resort to the Einstein frame for our calculations, where we separate our analysis between metric and Palatini formulations. We follow recent works in this line that debunk the naive predictions for unitarity violations in Higgs' inflation models to determine how to accurately estimate the behaviour of scattering amplitudes in the UV limit. Later, we work out different cases by assuming potentials corresponding to known inflation scenarios so we could predict the range of coupling parameters for which the theories would remain unitary up to the Planckian regime. We also try to find the behaviour of the scattering amplitudes for these theories during the transition from inflationary to reheating epoch.

We use the local momentum space technique to obtain an expansion of the Feynman propagators for scalar field and graviton up to first order in curvature. The expressions for propagators are cross-checked with the past literature as well as with the expressions for the traced heat kernel coefficients. The propagators so obtained are used to compute one loop divergences in Vilkovisky-Dewitt's effective action for a scalar field minimally coupled with gravity for arbitrary space-time background.

We propose an algebraic analysis using a 3+1 decomposition to identify conditions for a clever cancellation of the higher derivatives, which plagued the theory with Ostrogradsky ghosts, by exploiting some existing degeneracy in the Lagrangian. We obtain these conditions as linear equations (in terms of coefficients of the higher derivative terms) and demand that they vanish, such that the existence of nontrivial solutions implies that the theory is degenerate. We find that, for the theory under consideration, no such solutions exist for a general inhomogeneous scalar field, but that the theory is degenerate in the unitary gauge. We, then, find modified FLRW equations and narrow down conditions for which there could exist a de Sitter inflationary epoch. We further find constraints on the coefficients of the remaining higher-derivative interaction terms, based on power-counting renormalizability and tree-level unitarity up to the Planck scale.