Correcting the initial vacuum state in quantum gravity

Emre Kahya is a postdoc at Koc University, Turkey (he is a former graduate student of Richard Woodard). Dmitry.

Cosmology is becoming the most active area of research in theoretical physics for the last 10 years. We now understand that initial quantum fluctuations are reasons of our existence with in the context of Inflation. This brings the following question: Can we make quantum gravity calculations and expect to test them by some means? Naively one would say no. One reason is the smallness of the coupling constant:
quantum gravity effects have the order of magnitude

Since goes like , the coupling constant should go like , therefore would approximately be . Working with energy scales of LHC, 1 TeV, the biggest quantum gravitational correction is at of the order . And the fact that this series diverge at all, puzzles some of us. In any way, one might loose hope of getting any experimentally testable quantum gravity effect due to this smallness problem.

But cosmology is a unique area where the quantum gravitational effects might add up to overcome this problem. This make cosmology a very interesting area of research for theoreticians from string theorists to astrophysicists. I have been interested in quantum gravitational loop effects during the de Sitter phase of Inflation for the last five years or so. In a recent paper, arXiv:0904.4811 V. K. Onemli, R. P. Woodard and myself worked on a problem of correcting the initial vacuum state of a massless minimally coupled scalar with on non-dynamical de Sitter.

In flat space QFT one calculates the expectation value of matrix elements between true in and out vacuum states in the infinite past and future. This is very useful in scattering problems in flat space QFT but not very relevant for cosmology where the universe began with an initial singularity and particle production precludes the in vacuum from evolving to the out vacuum. The relevant thing to do would be to release the universe from a prepared state at finite time and let it evolve as it will. This can be done by using the In-In formalism or the so called Schwinger-Keldysh formalism.

Since we are doing perturbation theory, the lowest order correction can be obtained by using the free vacuum. It occasionally is the case that one obtains secular growth from higher order corrections and correcting the initial state does not affect this. For some cases corrections to the initial state might be as big as 4-volume effects. But for both cases it would certainly cause some problems related to initial value divergences. In this recent work, we showed that the divergent terms that appear in the expectation value of the stress energy tensor at two loops order in the presence of free Bunch-Davies vacuum, can be absorbed by correcting the initial vacuum state.

In short, cosmology is a natural locale for quantum gravity since gravity is a long range force and it knows about the scale factor . In-in formalism fits much better in cosmology and one would prefer to use that instead of the in-out formalism that we are used to in flat space QFT calculations. Taking the free vacuum is easier but it might result into terms which would diverge in initial value surface, and might even result into changes at the order of 4-volume effects. And this problem can be avoided by correcting the initial vacuum state.

Further detail and references can be found in our paper:

E. O. Kahya, V. K. Onemli and R. P. Woodard “A Completely Regular Quantum Stress Tensor with w < -1″” arXiv:0904.4811 [gr-qc].