We consider General Relativity (GR) on a space-time whose spatial slices are compact manifolds M with non-empty boundary ∂M . We argue that this theory has a nontrivial space of 'vacua', consisting of spatial metrics obtained by an action on a reference flat metric by diffeomorpisms that are non-trivial at the boundary. In an adiabatic limit the Einstein equations reduce to geodesic motion on this space of vacua with respect to a particular pseudo-Riemannian metric that we identify. We show how the momentum constraint implies that this metric is fully determined by data on the boundary ∂M only, while the Hamiltonian constraint forces the geodesics to be null. We comment on how the conserved momenta of the geodesic motion correspond to an infinite set of conserved boundary charges of GR in this setup.

It is known that in single scalar field inflationary models the standard curvature perturbation ζ, which is supposedly conserved at superhorizon scales, diverges during reheating at times 0ϕ̇=, i.e. when the time derivative of the background inflaton field vanishes. This happens because the comoving gauge 0φ=, where φ denotes the inflaton perturbation, breaks down when 0ϕ̇=. The issue is usually bypassed by averaging out the inflaton oscillations but strictly speaking the evolution of ζ is ill posed mathematically. We solve this problem in the free theory by introducing a family of smooth gauges that still eliminates the inflaton fluctuation φ in the Hamiltonian formalism and gives a well behaved curvature perturbation ζ, which is now rigorously conserved at superhorizon scales. At the linearized level, this conserved variable can be used to unambiguously propagate the inflationary perturbations from the end of inflation to subsequent epochs. We discuss the implications of our results for the inflationary predictions.

Recently, it has been shown that during preheating the entropy modes circulating in the loops, which correspond to the inflaton decay products, meaningfully modify the cosmological correlation functions at superhorizon scales. In this paper, we determine the significance of the same effect when reheating occurs in the perturbative regime. In a typical two scalar field model, the magnitude of the loop corrections are shown to depend on several parameters like the background inflaton amplitude in the beginning of reheating, the inflaton decay rate and the inflaton mass. Although the loop contributions turn out to be small as compared to the preheating case, they still come out larger than the loop effects during inflation.

We express the in-in functional determinant giving the one-loop effective potential for a scalar field propagating in a cosmological spacetime in terms of the mode functions specifying the vacuum of the theory and then apply adiabatic regularization to make this bare potential finite. In this setup, the adiabatic regularization offers a particular renormalization prescription that isolates the effects of the cosmic expansion. We apply our findings to determine the radiative corrections to the classical inflaton potentials in scalar field inflationary models and also we derive an effective potential for the superhorizon curvature perturbation ζ encoding its scatterings with the subhorizon modes. Although the resulting modifications to the cosmological observables like nongaussianity turn out to be small, they distinctively appear after horizon crossing. I. INTRODUCTIONFunctional determinants arise in various instances in quantum field theory like in the calculations of the effective actions, gauge fixing Faddeev-Popov terms, semiclassical tunneling amplitudes and Jacobian factors (for a review see e.g. [1]). In general, they appear as results of Gaussian path integrals and there are different methods in evaluating them such as the heat-kernel expansion, zeta function regularization and Gel'fand-Yaglom theorem.The functional determinants also appear in quantum cosmology since Gaussian in-in/Schwinger-Keldysh path integrals are often encountered. For example, in certain models of preheating one assumes the existence of a reheating scalar that interacts with the inflaton, yet the action may still be quadratic in the reheating scalar yielding a Gaussian path integral in quantum theory (see [2,3]). Similarly, in single scalar field models one may consider integrating out the quadratic inflaton fluctuations about the inflating background to determine the quantum backreaction effects (see e.g. [4][5][6][7][8][9]). Obviously, the functional determinants in a cosmological setting are time dependent and they can naturally be interpreted as effective actions.

No abstract