Generic relevant deformations of Einstein's gravity theory contain additional degrees of freedom that have a multi-facetted stabilization dynamics on curved spacetimes. We show that these relevant degrees of freedom are self-protected against unitarity violations by the formation of classical field lumps that eventually merge to a new background geometry. The transition is heralded by the massive decay of the original vacuum and evolves through a strong coupling regime. This process fits in the recently proposed classicalization mechanism and extends it further to free field dynamics on curved backgrounds.
It has been suggested that a certain class of UV-incomplete quantum field theories can avoid unitarity violation above the cut-off energy scale by forming classical configurations at a length scale much larger than the cut-off length. This phenomenon has been named classicalization and is characterized by a length scale called classicalization radius $r_*$ which increases with energy. It has been argued that scalar field theories with derivative self-interactions are likely candidate for UV-completetion by classicalization and are much likely to form classicalons compared to non-classicalizing…
In the context of Effective Field Theory, the Hilbert space of states increases in an expanding universe. Hence, the time evolution cannot be unitary. The formation of structure is usually studied using effective field theory techniques. We study the constraints on effective field theory analyses of early universe models which come from demanding that the factor of the space of states corresponding to length scales where the primordial fluctuations are manifest does not suffer from the unitarity problem. For bouncing and emergent cosmologies, no constraints arise provided that the energy scale…
In this article we perform the Wheeler-DeWitt quantization for Bianchi type $I$ anisotropic cosmological model in the presence of a scalar field minimally coupled to the Einstein-Hilbert gravity theory. We also consider the cosmological (perfect) fluid to construct the matter sector of the model whose dynamics plays the role of time. After obtaining the Wheeler-DeWitt equation from the Hamiltonian formalism, we then define the self-adjointness relations properly. Doing that we proceed to get a solution for the Wheeler-DeWitt equation and construct a well behaved wave function for the universe.…
With fourth-order derivative theories leading to propagators of the generic ghost-like $1/(k^2-M_1^2)-1/(k^2-M_2^2)$ form, it would appear that such theories have negative norm ghost states and are not unitary. However on constructing the associated quantum Hilbert space for the free theory that would produce such a propagator, Bender and Mannheim found that the Hamiltonian of the free theory is not Hermitian but is instead $PT$ symmetric, and that there are in fact no negative norm ghost states, with all Hilbert space norms being both positive and preserved in time. Even though perturbative r…
Effective Field Theory technique is one of the most elegant ways to capture the impact of high scale theory, if any, at some low energy by incorporating higher mass dimensional ($\geq 5$) effective operators ($\mathcal{O}_i$). The low energy EFT is described in terms of only light degrees of freedom which can appear on-shell. An essential task while developing the EFT framework is to compute these $\mathcal{O}_i$'s. Hilbert Series is a novel and mathematically robust method to construct the complete set of gauge invariant independent, effective operators. The HS requires the knowledge of the t…
We study quantum field theory on a de Sitter spacetime dS$_{d+1}$ background. Our main tool is the Hilbert space decomposition in irreducible unitary representations of its isometry group $SO(d+1,1)$. As the first application of the Hilbert space formalism, we recover the Källen-Lehmann spectral decomposition of the scalar bulk two-point function. In the process, we exhibit a relation between poles in the corresponding spectral densities and the boundary CFT data. Moreover, we derive an inversion formula for the spectral density through analytical continuation from the sphere and use it to fin…
The problem of eliminating divergences arising in quantum gravity is generally addressed by modifying the classical Einstein-Hilbert action. These modifications might involve the introduction of local supersymmetry, the addition of terms that are higher-order in the curvature to the action, or invoking compactification of superstring theory from ten to four dimensions. An alternative to these approaches is to introduce a Lagrange multiplier field that restricts the path integral to field configurations that satisfy the classical equations of motion; this has the effect of doubling the usual on…
