Regulating the infrared by mode matching: A massless scalar in expanding spaces with constant deceleration

In this paper we consider a massless scalar field, with a possible coupling $\xi$ to the Ricci scalar in a $D$ dimensional FLRW spacetime with a constant deceleration parameter $q=\epsilon-1$, $\epsilon=-{\dot{H}}/{H^2}$. Correlation functions for the Bunch-Davies vacuum of such a theory have long been known to be infrared divergent for a wide range of values of $\epsilon$. We resolve these divergences by explicitly matching the spacetime under consideration to a spacetime without infrared divergencies. Such a procedure ensures that all correlation functions with respect to the vacuum in the spacetime of interest are infrared finite. In this newly defined vacuum we construct the coincidence limit of the propagator and as an example calculate the expectation value of the stress energy tensor. We find that this approach gives both in the ultraviolet and in the infrared satisfactory results. Moreover, we find that, unless the effective mass due to the coupling to the Ricci scalar $\xi R$ is negative, quantum contributions to the energy density always dilute away faster, or just as fast, as the background energy density. Therefore, quantum backreaction is insignificant at the one loop order, unless $\xi R$ is negative. Finally we compare this approach with known results where the infrared is regulated by placing the Universe in a finite box. In an accelerating universe, the results are qualitatively the same, provided one identifies the size of the Universe with the physical Hubble radius at the time of the matching. In a decelerating universe however, the two schemes give different late time behavior for the quantum stress energy tensor. This happens because in this case the length scale at which one regulates the infrared becomes sub-Hubble at late times.Comment: 55 pages, 6 figure

Baryogenesis from `electrogenesis' in a scalar field dominated epoch

Scalar fields can play a dominant role in the dynamics of the Universe until shortly before nucleosynthesis. Examples are provided by domination by a kinetic mode of a scalar field, which may be both the inflaton and the late time `quintessence', and also by more conventional models of reheating. The resultant modification to the pre-nucleosynthesis expansion rate can allow solely an asymmetry in right handed electrons to produce a net baryon asymmetry when reprocessed by the anomalous B+L violating processes of the standard model. The production of such a source asymmetry - what we term `electrogenesis' - requires no additional B or L violation beyond that in the standard model. We consider a specific model for its generation, by a simple perturbative out of equilibrium decay of Higgs like scalar fields with CP-violating Yukawa couplings to the standard model leptons. We show that, because of the much enhanced expansion rate, such a mechanism can easily produce an adequate asymmetry from scalars with masses as low as 1 TeV. Kinetic mode domination is strongly favoured because it evades large entropy release which dilutes the asymmetry. We also discuss briefly the effect of the abelian hypercharge anomaly.Comment: 25 pages, 2 figure

Lamb Shift of Unruh Detector Levels

We argue that the energy levels of an Unruh detector experience an effect similar to the Lamb shift in Quantum Electrodynamics. As a consequence, the spectrum of energy levels in a curved background is different from that in flat space. As examples, we consider a detector in an expanding Universe and in Rindler space, and for the latter case we suggest a new expression for the local virtual energy density seen by an accelerated observer. In the ultraviolet domain, that is when the space between the energy levels is larger than the Hubble rate or the acceleration of the detector, the Lamb shift quantitatively dominates over the thermal response rate.Comment: 20 page

The Scalar Field Kernel in Cosmological Spaces

We construct the quantum mechanical evolution operator in the Functional Schrodinger picture - the kernel - for a scalar field in spatially homogeneous FLRW spacetimes when the field is a) free and b) coupled to a spacetime dependent source term. The essential element in the construction is the causal propagator, linked to the commutator of two Heisenberg picture scalar fields. We show that the kernels can be expressed solely in terms of the causal propagator and derivatives of the causal propagator. Furthermore, we show that our kernel reveals the standard light cone structure in FLRW spacetimes. We finally apply the result to Minkowski spacetime, to de Sitter spacetime and calculate the forward time evolution of the vacuum in a general FLRW spacetime.Comment: 13 pages, 1 figur

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

Problems and hopes in nonsymmetric gravity

We consider the linearized nonsymmetric theory of gravitation (NGT) within the background of an expanding universe and near a Schwarzschild mass. We show that the theory always develops instabilities unless the linearized nonsymmetric lagrangian reduces to a particular simple form. This form contains a gauge invariant kinetic term, a mass term for the antisymmetric metric-field and a coupling with the Ricci curvature scalar. This form cannot be obtained within NGT. Based on the linearized lagrangian we know to be stable, we consider the generation and evolution of quantum fluctuations of the antisymmetric gravitational field (B-field) from inflation up to the present day. We find that a B-field with a mass m ~ 0.03(H_I/10^(13)GeV)^4 eV is an excellent dark matter candidate.Comment: 9 pages, 1 figure. Based on two talks by the authors at the 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology (IRGAC) 2006, Barcelon