Renormalized Stress Tensor for trans-Planckian Cosmology

Finite expressions for the mean value of the stress tensor corresponding to a scalar field with a generalized dispersion relation in a Friedman--Robertson--Walker universe are obtained using adiabatic renormalization. Formally divergent integrals are evaluated by means of dimensional regularization. The renormalization procedure is shown to be equivalent to a redefinition of the cosmological constant and the Newton constant in the semiclassical Einstein equations.Comment: 14 pages. Minor changes; version published in Physical Review

Failures of homogeneous and isotropic cosmologies in extended quasidilaton massive gravity

We analyze the extended quasidilaton massive gravity model around a Friedmann-Lemaître-Robertson- Walker cosmological background. We present a careful stability analysis of asymptotic fixed points. We find that the traditional fixed point cannot be approached dynamically, except from a perfectly fine-tuned initial condition involving both the quasidilaton and the Hubble parameter. A less-well examined fixed- point solution, where the time derivative of the zeroth Stückelberg field vanishes φ_ 0 1⁄4 0, encounters no such difficulty, and the fixed point is an attractor in some finite region of initial conditions. We examine the question of the presence of a Boulware-Deser ghost in the theory. We show that the additional constraint that generically allows for the elimination of the Boulware-Deser mode is only present under special initial conditions. We find that the only possibility corresponds to the traditional fixed point and the initial conditions are the same fine-tuned conditions that allow the fixed point to be approached dynamically.Fil: Anselmi, Stefano. Université Paris Diderot - Paris 7; Francia. Institut d’Astrophysique de Paris; Francia. Case Western Reserve University; Estados UnidosFil: Kumar, Saurabh. Case Western Reserve University; Estados UnidosFil: Lopez Nacir, Diana Laura. Cern - European Organization For Nuclear Research; Suiza. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Starkman, Glenn D.. Case Western Reserve University; Estados Unido

Counterterms in semiclassical Horava-Lifshitz gravity

We analyze the semiclassical Ho\v{r}ava-Lifshitz gravity for quantum scalar fields in 3+1 dimensions. The renormalizability of the theory requires that the action of the scalar field contains terms with six spatial derivatives of the field, i.e. in the UV, the classical action of the scalar field should preserve the anisotropic scaling symmetry ($t \to L^{2z}t,$ $\vec{x} \to L^2 \vec{x}$, with $z=3$) of the gravitational action. We discuss the renormalization procedure based on adiabatic subtraction and dimensional regularization in the weak field approximation. We verify that the divergent terms in the adiabatic expansion of the expectation value of the energy-momentum tensor of the scalar field contain up to six spatial derivatives, but do not contain more than two time derivatives. We compute explicitly the counterterms needed for the renormalization of the theory up to second adiabatic order and evaluate the associated $\beta$ functions in the minimal subtraction scheme.Comment: 8 page

On Loops in Inflation II: IR Effects in Single Clock Inflation

In single clock models of inflation the coupling between modes of very different scales does not have any significant dynamical effect during inflation. It leads to interesting projection effects. Larger and smaller modes change the relation between the scale a mode of interest will appear in the post-inflationary universe and will also change the time of horizon crossing of that mode. We argue that there are no infrared projection effects in physical questions, that there are no effects from modes of longer wavelength than the one of interest. These potential effects cancel when computing fluctuations as a function of physically measurable scales. Modes on scales smaller than the one of interest change the mapping between horizon crossing time and scale. The correction to the mapping computed in the absence of fluctuations is enhanced by a factor N_e, the number of e-folds of inflation between horizon crossing and reheating. The new mapping is stochastic in nature but its variance is not enhanced by N_e.Comment: 13 pages, 1 figure; v2: JHEP published version, added minor comments and reference

Anomalous Dimensions and Non-Gaussianity

We analyze the signatures of inflationary models that are coupled to strongly interacting field theories, a basic class of multifield models also motivated by their role in providing dynamically small scales. Near the squeezed limit of the bispectrum, we find a simple scaling behavior determined by operator dimensions, which are constrained by the appropriate unitarity bounds. Specifically, we analyze two simple and calculable classes of examples: conformal field theories (CFTs), and large-N CFTs deformed by relevant time-dependent double-trace operators. Together these two classes of examples exhibit a wide range of scalings and shapes of the bispectrum, including nearly equilateral, orthogonal and local non-Gaussianity in different regimes. Along the way, we compare and contrast the shape and amplitude with previous results on weakly coupled fields coupled to inflation. This signature provides a precision test for strongly coupled sectors coupled to inflation via irrelevant operators suppressed by a high mass scale up to 1000 times the inflationary Hubble scale.Comment: 40 pages, 10 figure

The Volume of the Past Light-Cone and the Paneitz Operator

We study a conjecture involving the invariant volume of the past light-cone from an arbitrary observation point back to a fixed initial value surface. The conjecture is that a 4th order differential operator which occurs in the theory of conformal anomalies gives $8\pi$ when acted upon the invariant volume of the past light-cone. We show that an extended version of the conjecture is valid for an arbitrary homogeneous and isotropic geometry. First order perturbation theory about flat spacetime reveals a violation of the conjecture which, however, vanishes for any vacuum solution of the Einstein equation. These results may be significant for constructing quantum gravitational observables, for quantifying the back-reaction on spacetime expansion and for alternate gravity models which feature a timelike vector field.Comment: 22 pages, no figures, 5 tables. Version 2 substantially extended to cover nonzero spatial curvature, and with simplified derivation

EFT beyond the horizon: stochastic inflation and how primordial quantum fluctuations go classical

We identify the effective theory describing inflationary super-Hubble scales and show it to be a special case of effective field theories appropriate to open systems. Open systems allow information to be exchanged between the degrees of freedom of interest and those that are integrated out, such as for particles moving through a fluid. Strictly speaking they cannot in general be described by an effective lagrangian; rather the appropriate `low-energy' limit is instead a Lindblad equation describing the evolution of the density matrix of the slow degrees of freedom. We derive the equation relevant to super-Hubble modes of quantum fields in near-de Sitter spacetimes and derive two implications. We show the evolution of the diagonal density-matrix elements quickly approaches the Fokker-Planck equation of Starobinsky's stochastic inflationary picture. This provides an alternative first-principles derivation of this picture's stochastic noise and drift, as well as its leading corrections. (An application computes the noise for systems with a sub-luminal sound speed.) We argue that the presence of interactions drives the off-diagonal density-matrix elements to zero in the field basis. This shows why the field basis is the `pointer basis' for the decoherence of primordial quantum fluctuations while they are outside the horizon, thus allowing them to re-enter as classical fluctuations, as assumed when analyzing CMB data. The decoherence process is efficient, occurring after several Hubble times even for interactions as weak as gravitational-strength. Crucially, the details of the interactions largely control only the decoherence time and not the nature of the final late-time stochastic state, much as interactions can control the equilibration time for thermal systems but are largely irrelevant to the properties of the resulting equilibrium state

On Loops in Inflation III: Time Independence of zeta in Single Clock Inflation

Studying loop corrections to inflationary perturbations, with particular emphasis on infrared factors, is important to understand the consistency of the inflationary theory, its predictivity and to establish the existence of the slow-roll eternal inflation phenomena and its recently found volume bound. In this paper we prove that the zeta correlation function is time-independent at one-loop level in single clock inflation. While many of the one-loop diagrams lead to a time-dependence when considered individually, the time-dependence beautifully cancels out in the overall sum. We identify two subsets of diagrams that cancel separately due to different physical reasons. The first cancellation is related to the change of the background cosmology due to the renormalization of the stress tensor. It results in a cancellation between the non-1PI diagrams and some of the diagrams made with quartic vertices. The second subset of diagrams that cancel is made up of cubic operators, plus the remaining quartic ones. We are able to write the sum of these diagrams as the integral over a specific three-point function between two very short wavelengths and one very long one. We then apply the consistency condition for this three-point function in the squeezed limit to show that the sum of these diagrams cannot give rise to a time dependence. This second cancellation is thus a consequence of the fact that in single clock inflation the attractor nature of the solution implies that a long wavelength zeta perturbation is indistinguishable from a trivial rescaling of the background, and so results in no physical effect on short wavelength modes.Comment: 47 pages, 7 figures; v2: JHEP published version, typos and minor correction