Cosmology

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.

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.

We study the relation between two sets of correlators in interacting quantum field theory on de Sitter space. The first are correlators computed using in-in perturbation theory in the region of de Sitter space to the future of a cosmological horizon (also known as the expanding cosmological patch, the conformal patch, or the Poincare patch), and for which the free propagators are taken to be those of the free Euclidean vacuum. The second are correlators obtained by analytic continuation from interacting QFT on Euclidean de Sitter; i.e., they are correlators in the Hartle-Hawking vacuum. We give an analytic argument that these correlators coincide for interacting massive scalar fields with any positive mass. We also verify this result via direct analytical and numerical calculation in two simple examples. The correspondence holds diagram by diagram, and at any finite value of a Pauli-Villars regulator mass M. Along the way, we note interesting connections between various prescriptions for perturbation theory in general static spacetimes with bifurcate Killing horizons.

We study particle decay in the de Sitter spacetime as given by first order perturbation theory in an interacting quantum field theory. We discuss first a general construction of bosonic two-point functions, including a recently discovered class of tachyonic theories that do exist in the de Sitter spacetime at discrete negative values of the squared mass parameter and have no Minkowskian counterpart. We show then that for fields with masses above a critical mass $m_c$ there is no such thing as particle stability, so that decays forbidden in flat space-time do occur there. The lifetime of such a particle also turns out to be independent of its velocity when that lifetime is comparable with de Sitter radius. For particles with lower mass is yet not completely solved. We show however that the masses of their decay products should obey quantification rules.

There has been a long-running discussion as to whether free gravitons on dS have a dS-invariant state. On the one hand, de Sitter invariant states are clearly singular in gauges favored by cosmologists; e.g. transverse traceless synchronous gauge associated with the k=0 slicing of dS. However, Higuchi has constructed a dS-invariant state using a different gauge. We resolve this tension by showing that the above “cosmologists gauge” is in fact singular on global de Sitter space. This observation may prove useful in understanding the physics of calculations indicating large IR effects involving gravity in dS.