Nonperturbative infrared effects for light scalar fields in de Sitter space

We study the phi^4 scalar field theory in de Sitter space using the 2PI effective action formalism. This formalism enables us to investigate the nonperturbative quantum effects. We use the mean field and gap equations and calculate the physical mass and effective potential. We find that nonperturbative infrared effects on de Sitter space produce a curvature-induced mass and work to restore the broken Z_2 symmetry.Comment: 14 pages, 3 figures, section 2 revised, discussion in section 4 changed, results not change

Solving the Effective Field Equations for the Newtonian Potential

Loop corrections to the gravitational potential are usually inferred from scattering amplitudes, which seems quite different from how the linearized Einstein equations are solved with a static, point mass to give the classical potential. In this study we show how the Schwinger-Keldysh effective field equations can be used to compute loop corrections to the potential in a way which parallels the classical treatment. We derive explicit results for the one loop correction from the graviton self-energy induced by a massless, minimally coupled scalar.Comment: 15 pages, uses LaTeX2

Stress Tensor Correlators in the Schwinger-Keldysh Formalism

We express stress tensor correlators using the Schwinger-Keldysh formalism. The absence of off-diagonal counterterms in this formalism ensures that the +- and -+ correlators are free of primitive divergences. We use dimensional regularization in position space to explicitly check this at one loop order for a massless scalar on a flat space background. We use the same procedure to show that the ++ correlator contains the divergences first computed by `t Hooft and Veltman for the scalar contribution to the graviton self-energy.Comment: 14 pages, LaTeX 2epsilon, no figures, revised for publicatio

Dominance of gauge artifact in the consistency relation for the primordial bispectrum

The conventional cosmological perturbation theory has been performed under the assumption that we know the whole spatial region of the universe with infinite volume. This is, however, not the case in the actual observations because observable portion of the universe is limited. To give a theoretical prediction to the observable fluctuations, gauge-invariant observables should be composed of the information in our local observable universe with finite volume. From this point of view, we reexamine the primordial non-Gaussianity in single field models, focusing on the bispectrum in the squeezed limit. A conventional prediction states that the bispectrum in this limit is related to the power spectrum through the so-called consistency relation. However, it turns out that, if we adopt a genuine gauge invariant variable which is naturally composed purely of the information in our local universe, the leading term for the bispectrum in the squeezed limit predicted by the consistency relation vanishes.Comment: 12 pages; v2: accepted version in JCA

A Simple Operator Check of the Effective Fermion Mode Function during Inflation

We present a relatively simple operator formalism which reproduces the leading infrared logarithm of the one loop quantum gravitational correction to the fermion mode function on a locally de Sitter background. This rule may serve as the basis for an eventual stochastic formulation of quantum gravity during inflation. Such a formalism would not only effect a vast simplification in obtaining the leading powers of $\ln(a)$ at fixed loop orders, it would also permit us to sum the series of leading logarithms. A potentially important point is that our rule does not seem to be consistent with any simple infrared truncation of the fields. Our analysis also highlights the importance of spin as a gravitational interaction that persists even when kinetic energy has redshifted to zero.Comment: 39 pages, no figuire.(1) New version has clarified the ultimate motivation by adding sentences to the abstract and to the penultimate paragraph of the introduction. (2) By combining a number of references and equations we have managed to reduce the length by 2 page

A new diagrammatic representation for correlation functions in the in-in formalism

In this paper we provide an alternative method to compute correlation functions in the in-in formalism, with a modified set of Feynman rules to compute loop corrections. The diagrammatic expansion is based on an iterative solution of the equation of motion for the quantum operators with only retarded propagators, which makes each diagram intrinsically local (whereas in the standard case locality is the result of several cancellations) and endowed with a straightforward physical interpretation. While the final result is strictly equivalent, as a bonus the formulation presented here also contains less graphs than other diagrammatic approaches to in-in correlation functions. Our method is particularly suitable for applications to cosmology.Comment: 14 pages, matches the published version. includes a modified version of axodraw.sty that works with the Revtex4 clas

Possible Enhancement of High Frequency Gravitational Waves

We study the tensor perturbations in a class of non-local, purely gravitational models which naturally end inflation in a distinctive phase of oscillations with slight and short violations of the weak energy condition. We find the usual generic form for the tensor power spectrum. The presence of the oscillatory phase leads to an enhancement of gravitational waves with frequencies somewhat less than 10^{10} Hz.Comment: 27 pages, 11 figures, LaTeX.2

Dimensionally Regulated Graviton 1-Point Function in de Sitter

We use dimensional regularization to compute the 1PI 1-point function of quantum gravity at one loop order in a locally de Sitter background. As with other computations, the result is a finite constant at this order. It corresponds to a small positive renormalization of the cosmological constant.Comment: 25 pages, LaTeX 2epsilon, uses Axodraw for one figure, revised to add some reference

Two Loop Scalar Bilinears for Inflationary SQED

We evaluate the one and two loop contributions to the expectation values of two coincident and gauge invariant scalar bilinears in the theory of massless, minimally coupled scalar quantum electrodynamics on a locally de Sitter background. One of these bilinears is the product of two covariantly differentiated scalars, the other is the product of two undifferentiated scalars. The computations are done using dimensional regularization and the Schwinger-Keldysh formalism. Our results are in perfect agreement with the stochastic predictions at this order.Comment: 43 pages, LaTeX 2epsilon, 5 figures (using axodraw.sty) Version 2 has updated references and important corrections to Tables 3-5 and to eqns (139-141), (145-146), (153-155), (158) and (160