IR issues and loops in de Sitter space - 2010

Vacuum expectation value of the square of the quantum field operator of massless or light scalar field is calculated in the De Sitter space-time. The suggested method of calculation is different from the standard one used in the 80th. The calculations are heavily based on the De Sitter covarinace of the relevant quantities. The found result is significanlty different for the old one for the massless field but coinsides with the classical result for light massive field. Possible explanation of the dicrepancy by a spontaneous breaking of De Sitter invariance or by finite duration of the (quasi) De Sitter stage is discussed.

It is well known that there should be a total cancellation of the IR divergences in closed systems described by interacting quantum field theories, such as QED and gravity. I am going to show that such a cancellation does not happen in de Sitter space.

Infrared logarithms are factors of the logarithm of the inflationary scale factor which arise in quantum field theoretic loop corrections that involve either massless, minimally coupled scalars or gravitons. They have been found by myself and collaborators in 1PI functions and by Steven Weinberg in the power spectrum of primordial perturbations. Because the inflationary scale factor grows so rapidly, infrared logarithms enhance loop corrections far beyond expectations based upon the coupling constant. They also inject time dependence into what are usually static results. For a very long period of inflation this enhancement can grow so large that weak field perturbation theory breaks down. In this talk I explain the physical reasons why infrared logarithms occur, I review the computations in which they have been seen and I describe Starobinskii's technique for evolving past the breakdown of perturbation theory. I also comment on the potential of infrared logarithms to change our understanding of inflationary cosmology.

Using simple semiclassical relations it is possible to show that the conventional cosmological correlation functions are affected by significant IR corrections in quasi de Sitter space-times when averaged over very large volumes (in the "large box"). The IR effects apparently imply a breakdown of perturbation theory in the large box on sufficiently long time scales, for example the time between self-reproduction and reheating in chaotic inflation. An interpretation of the apparent breakdown of the perturbative expansion of gravity will also be briefly discussed.

In theories with light or massless fields, loop diagrams can develop infrared divergences. We demonstrate how these can be resolved for a theory of massless interacting scalar fields in Euclidean de Sitter space. We also comment on applications to the in-in formalism in Lorentzian de Sitter space.

Hydrodynamics is the universal theory describing the behavior of fluids when their spacetime variation is on scales longer than any microphysical scale in the fluid. Relativistic hydro has applications in heavy ion collisions and early Universe cosmology, and has seen a surge of interest due to heavy ion experiments and theoretical developments in AdS/CFT. I will explain what second order hydrodynamics is and why it is the minimum theory to study in the relativistic case. Then I discuss some limitations of the theory, including a new bound on how small the viscosity can be and a complication in the rigorous definition of the viscous relaxation time

I will discuss the emergence of anomalous scaling dimensions for superhorizon fluctuations and the main ideas and concepts of particle decay during inflation, via the resummation of secular terms with the dynamical renormalization group. There are loops, IR effects and (lots of...) issues.

I will present our work on loop corrections to the power spectrum of curvature fluctuations in single-field inflationary models. We consider both standard slow-roll (where the interactions between gravitons and the scalar are included for the first time) and non-canonical Lagrangians. We show that the tensor modes cannot be neglected since, in some models, they produce one loop contributions with an amplitude that is comparable to the one coming from the scalar sector. Our study of loop corrections in non-canonical theories characterized by a small speed of sound (c_s) provides quantitative bounds on c_s, to be compared with similar constraints derived from CMB observations.

A method is developed for dealing with ultraviolet divergences in calculations of cosmological correlations, which does not depend on dimensional regularization. An extended version of the WKB approximation is used to analyze the divergences in these calculations, and these divergences are controlled by the introduction of Pauli--Villars regulator fields. This approach is illustrated in the theory of a scalar field with arbitrary self-interactions in a fixed flat-space Robertson--Walker metric with arbitrary scale factor $a(t)$. Explicit formulas are given for the counterterms needed to cancel all dependence on the regulator properties, and an explicit prescription is given for calculating finite correlation functions.

De Sitter space is a maximally symmetric space, and any (time dependent) backreaction necessarily breaks the symmetry. On the other hand, the backreaction in FLRW spaces (which, from the cosmological perspective, are more realistic spaces) respects the symmetries of the background space. One could therefore argue that it is more natural to study the backreaction on quasi-de Sitter spaces, and more generally on FLRW spaces. As examples, I will present our results on the one loop (Hubble) effective potential calculation, and the one loop stress energy calculation. We find that the backreaction from infrared modes can be important if a massless scalar couples nonminimally to the Ricci with a negative coupling, and if the Universe expands faster than exponentially.