We investigate the possibility of inflation with models of antisymmetric tensor field having minimal and nonminimal couplings to gravity. Although the minimal model does not support inflation, the nonminimal models, through the introduction of a nonminimal coupling to gravity, can give rise to stable de-Sitter solutions with a bound on the coupling parameters. The values of field and coupling parameters are sub-planckian. Slow roll analysis is performed and slow-roll parameters are defined which can give the required number of e-folds for sufficient inflation. Stability analysis has been performed for perturbations to antisymmetric field while keeping the metric unperturbed, and it is found that only the sub-horizon modes are free of ghost instability for de-Sitter space.

Models of inflation with antisymmetric tensor studied in the past are plagued with ghost instability even in an unperturbed FRW background. We show that it is possible to avoid ghosts in an unperturbed FRW background by considering the most general kinetic term for antisymmetric tensor field. The kinetic part acquires a new gauge symmetry violating term whose effect on perturbed modes is to prevent the appearance of nondynamical modes, and thus avoid ghosts. For completeness, we perform a check for gradient instability and derive the conditions for perturbations to be free of gradient instability. * sandeepa16@iiserb.ac.in † abhilash92@iiserb.ac.in ‡ sukanta@iiserb.ac.in

We build upon the past studies of inflation with rank-2 antisymmetric tensor field, including here the tensor perturbations to metric. We perform a comprehensive analysis of the background dynamics of our model in the presence of non-minimal coupling curvature terms R and R µν . We find appropriate conditions on the nonminimal coupling parameters to satisfy the constraint of speed of propagation of gravitational waves. Including the tensor perturbations, the model is found to be free from ghost instabilities with minimal constraints on the parameters. We also study the evolution of gravitational waves, calculate the power spectrum and the tensor spectral index.

Covariant quantization of rank-2 antisymmetric fields is non-trivial due to additional symmetries of the gauge parameters. We present an intuitive way to deal with this additional symmetry of gauge parameters in terms of geometrical understanding of field space. We generalize the DeWitt-Vilkovisky covariant effective action formalism for quantization of such theories. As an application, we quantize a massive rank-2 antisymmetric field using the covariant effective action approach and reproduce previously obtained results.

We study the quantization of a simple model of antisymmetric tensor field with spontaneous Lorentz violation in curved spacetime. We evaluate the 1-loop corrections at first order of metric perturbation, using a general covariant effective action approach. We revisit the issue of quantum equivalence, and find that it holds for non-Lorentz-violating modes but breaks down for Lorentz violating modes. * sandeepa16@iiserb.ac.in † sukanta@iiserb.ac.in