We evaluate the one-graviton loop contribution to the vacuum polarization on de Sitter background in a 1-parameter family of exact, de Sitter invariant gauges. Our result is computed using dimensional regularization and fully renormalized with BPHZ c
ounterterms, which must include a noninvariant owing to the time-ordered interactions. Because the graviton propagator engenders a physical breaking of de Sitter invariance two structure functions are needed to express the result. In addition to its relevance for the gauge issue this is the first time a covariant gauge graviton propagator has been used to compute a noncoincident loop. A number of identities are derived which should facilitate further graviton loop computations.
We make use of the frame and gauge independent formalism for scalar and tensor cosmological perturbations developed in Ref. [1] to show that the physical cutoff for 2-to-2 tree level scatterings in Higgs inflation is above the Planck scale M_P throug
hout inflation. More precisely, we found that in the Jordan frame, the physical cutoff scale is $({Lambda}/a)_J gtrsim sqrt{M_P^2+{xi}{phi}^2}$, while in the Einstein frame it is $({Lambda}/a)_J gtrsim M_P$, where $xi$ is the nonminimal coupling and $phi$ denotes the Higgs vev during inflation. The dimensionless ratio of the physical cutoff to the relevant Planck scale is equal to one in both frames, thus demonstrating the physical equivalence of the two frames. Our analysis implies that Higgs inflation is unitary up to the Planck scale, and hence there is no naturalness problem in Higgs inflation. In this paper we only consider the graviton and scalar interactions.
We derive a noncovariant but simple representation for the self-energy of a conformally transformed graviton field on the cosmological patch of de Sitter. Our representation involves four structure functions, as opposed to the two that would be neces
sary for a manifestly de Sitter invariant representation. We work out what the four structure functions are for the one loop correction due to a massless, minimally coupled scalar. And we employ the result to work out what happens to dynamical gravitons.
We compute the third order gauge invariant action for scalar-graviton interactions in the Jordan frame. We demonstrate that the gauge invariant action for scalar and tensor perturbations on one physical hypersurface only differs from that on another
physical hypersurface via terms proportional to the equation of motion and boundary terms, such that the evolution of non-Gaussianity may be called unique. Moreover, we demonstrate that the gauge invariant curvature perturbation and graviton on uniform field hypersurfaces in the Jordan frame are equal to their counterparts in the Einstein frame. These frame independent perturbations are therefore particularly useful in relating results in different frames at the perturbative level. On the other hand, the field perturbation and graviton on uniform curvature hypersurfaces in the Jordan and Einstein frame are non-linearly related, as are their corresponding actions and $n$-point functions.
We consider phase transitions on (eternal) de Sitter in an O(N) symmetric scalar field theory. Making use of Starobinskys stochastic inflation we prove that deep infrared scalar modes cannot form a condensate -- and hence they see an effective potent
ial that allows no phase transition. We show that by proving convexity of the effective potential that governs deep infrared field fluctuations both at the origin as well as at arbitrary values of the field. Next, we present numerical plots of the scalar field probability distribution function (PDF) and the corresponding effective potential for several values of the coupling constant at the asymptotic future timelike infinity of de Sitter. For small field values the effective potential has an approximately quadratic form, corresponding to a positive mass term, such that the corresponding PDF is approximately Gaussian. However, the curvature of the effective potential shows qualitatively different (typically much softer) behavior on the coupling constant than that implied by the Starobinsky-Yokoyama procedure. For large field values, the effective potential as expected reduces to the tree level potential plus a positive correction that only weakly (logarithmically) depends on the background field. Finally, we calculate the backreaction of fluctuations on the background geometry and show that it is positive.
We consider Yukawa theory in which the fermion mass is induced by a Higgs like scalar. In our model the fermion mass exhibits a temporal dependence, which naturally occurs in the early Universe setting. Assuming that the complex fermion mass changes
as a tanh-kink, we construct an exact, helicity conserving, CP-violating solution for the positive and negative frequency fermionic mode functions, which is valid both in the case of weak and strong CP violation. Using this solution we then study the fermionic currents both in the initial vacuum and finite density/temperature setting. Our result shows that, due to a potentially large state squeezing, fermionic currents can exhibit a large oscillatory magnification. Having in mind applications to electroweak baryogenesis, we then compare our exact results with those obtained in a gradient approximation. Even though the gradient approximation does not capture the oscillatory effects of squeezing, it describes quite well the averaged current, obtained by performing a mode sum. Our main conclusion is: while the agreement with the semiclassical force is quite good in the thick wall regime, the difference is sufficiently significant to motivate a more detailed quantitative study of baryogenesis sources in the thin wall regime in more realistic settings.
In second order perturbation theory different definitions are known of gauge invariant perturbations in single field inflationary models. Consequently the corresponding gauge invariant cubic actions do not have the same form. Here we show that the cu
bic action for one choice of gauge invariant variables is unique in the following sense: the action for any other, non-linearly related variable can be brought to the same bulk action, plus additional boundary terms. These boundary terms correspond to the choice of hypersurface and generate extra, disconnected contributions to the bispectrum. We also discuss uniqueness of the action with respect to conformal frames. When expressed in terms of the gauge invariant curvature perturbation on uniform field hypersurfaces the action for cosmological perturbations has a unique form, independent of the original Einstein or Jordan frame. Crucial is that the gauge invariant comoving curvature perturbation is frame independent, which makes it extremely helpful in showing the quantum equivalence of the two frames, and therefore in calculating quantum effects in nonminimally coupled theories such as Higss inflation.
We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of th
ese correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields.
We consider an O(N) symmetric scalar field model in the mean field (Hartree) approximation and show that the symmetry can be broken in de Sitter space. We find that the phase transition can be of first order, and that its strength depends non-analyti
cally on the parameters of the model. We also show that the would-be Goldstone bosons acquire a mass, effectively becoming pseudo-Goldstone bosons, thus breaking the O(N) symmetry. Our results imply that topological defects can form during inflation.
By making a suitable generalization of the Starobinsky stochastic inflation, we propose a classical phase space formulation of stochastic inflation which may be used for a quantitative study of decoherence of cosmological perturbations during inflati
on. The precise knowledge of how much cosmological perturbations have decohered is essential to the understanding of acoustic oscillations of cosmological microwave background (CMB) photons. In order to show how the method works, we provide the relevant equations for a self-interacting inflaton field. For pedagogical reasons and to provide a link to the field theoretical case, we consider the quantum stochastic harmonic oscillator.
