Talks

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.

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.

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

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.

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.

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.

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.

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.

The stability of spacetime has been related to the production of particles and also to the imaginary parts of the perturbative series. The unitarity relations of the quantum theory impose relations between these two phenomena.

An ultraviolet complete quantum gravity theory is formulated in which vertex functions in Feynman graphs are entire functions and the propagating graviton is described by a local, causal propagator. A scalar-tensor action describes classical gravity theory. The cosmological constant problem is investigated in the context of the ultraviolet complete quantum gravity. Also investigated are black holes and cosmology.

I will start with a brief qualitative discussion of the construction of a dS-invariant state for interacting theories using Euclidean methods and its real-time evolution within the closed-time-path formalism, as well as of the closely related in-in formalism. Next, I will focus on the two-point quantum correlation function for the Riemann tensor of the metric perturbations around dS including the one-loop correction from matter fields. A key object is the stress tensor two-point function, from which the one-loop Ricci correlator follows straightforwardly. We have obtained the exact result for minimally coupled fields with arbitrary mass in terms of maximally symmetric bitensors, which makes dS invariance manifest. Long range correlations are present for sufficiently small (but nonvanishing) masses, and the discontinuity of the massless limit can be understood in a simple way. Finally, I will comment on the implications for the tensorial power spectrum and on the calculation of the Weyl correlations.