Extracting New Physics from the CMB

We review how initial state effects generically yield an oscillatory component in the primordial power spectrum of inflationary density perturbations. These oscillatory corrections parametrize unknown new physics at a scale $M$ and are potentially observable if the ratio $H_{infl}/M$ is sufficiently large. We clarify to what extent present and future CMB data analysis can distinguish between the different proposals for initial state corrections.Comment: Invited talk by B. Greene at the XXII Texas Symposium on Relativistic Astrophysics, Stanford University, 13-17 December 2004, (TSRA04-0001), 8 pages, LaTeX, some references added, added paragraph at the end of section 2 and an extra note added after the conclusions regarding modifications to the large k power spectra deduced from galaxy survey

Boundary Effective Field Theory and Trans-Planckian Perturbations: Astrophysical Implications

We contrast two approaches to calculating trans-Planckian corrections to the inflationary perturbation spectrum: the New Physics Hypersurface [NPH] model, in which modes are normalized when their physical wavelength first exceeds a critical value, and the Boundary Effective Field Theory [BEFT] approach, where the initial conditions for all modes are set at the same time, and modified by higher dimensional operators enumerated via an effective field theory calculation. We show that these two approaches -- as currently implemented -- lead to radically different expectations for the trans-Planckian corrections to the CMB and emphasize that in the BEFT formalism we expect the perturbation spectrum to be dominated by quantum gravity corrections for all scales shorter than some critical value. Conversely, in the NPH case the quantum effects only dominate the longest modes that are typically much larger than the present horizon size. Furthermore, the onset of the breakdown in the standard inflationary perturbation calculation predicted by the BEFT formalism is likely to be associated with a feature in the perturbation spectrum, and we discuss the observational signatures of this feature in both CMB and large scale structure observations. Finally, we discuss possible modifications to both calculational frameworks that would resolve the contradictions identified here.Comment: Reworded commentary, reference added (v2) References added (v3

Oscillations in the bispectrum

There exist several models of inflation that produce primordial bispectra that contain a large number of oscillations. In this paper we discuss these models, and aim at finding a method of detecting such bispectra in the data. We explain how the recently proposed method of mode expansion of bispectra might be able to reconstruct these spectra from separable basis functions. Extracting these basis functions from the data might then lead to observational constraints on these models.Comment: 6 pages, 2 figures, submitted to JOP: Conference Series, PASCOS 201

Where does Cosmological Perturbation Theory Break Down?

We apply the effective field theory approach to the coupled metric-inflaton system, in order to investigate the impact of higher dimension operators on the spectrum of scalar and tensor perturbations in the short-wavelength regime. In both cases, effective corrections at tree-level become important when the Hubble parameter is of the order of the Planck mass, or when the physical wave number of a cosmological perturbation mode approaches the square of the Planck mass divided by the Hubble constant. Thus, the cut-off length below which conventional cosmological perturbation theory does not apply is likely to be much smaller than the Planck length. This has implications for the observability of "trans-Planckian" effects in the spectrum of primordial perturbations.Comment: 25 pages, uses FeynM

Exact spectrum of scalar field perturbations in a radiation deformed closed de Sitter universe

We observe that the equation of motion for a free scalar field in a closed universe with radiation and a positive cosmological constant is given by Lam\'e's equation. Computing the exact power spectrum of scalar field perturbations, the presence of both curvature and radiation produces a red tilt weakly dependent on the amount of radiation.Comment: 16 pages, 2 figure

Observational Signatures and Non-Gaussianities of General Single Field Inflation

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.Comment: 53 pages, 5 figures; v3, minor revision, JCAP version; v4, numerical coefficients corrected in Appendix B, discussion on consistency condition revise

Observational Signatures and Non-Gaussianities of General Single Field Inflation

We perform a general study of primordial scalar non-Gaussianities in single field inflationary models in Einstein gravity. We consider models where the inflaton Lagrangian is an arbitrary function of the scalar field and its first derivative, and the sound speed is arbitrary. We find that under reasonable assumptions, the non-Gaussianity is completely determined by 5 parameters. In special limits of the parameter space, one finds distinctive ``shapes'' of the non-Gaussianity. In models with a small sound speed, several of these shapes would become potentially observable in the near future. Different limits of our formulae recover various previously known results.Comment: 53 pages, 5 figures; v3, minor revision, JCAP version; v4, numerical coefficients corrected in Appendix B, discussion on consistency condition revise

Enhanced Non-Gaussianity from Excited Initial States

We use the techniques of effective field theory in an expanding universe to examine the effect of choosing an excited inflationary initial state built over the Bunch-Davies state on the CMB bi-spectrum. We find that even for Hadamard states, there are unexpected enhancements in the bi-spectrum for certain configurations in momentum space due to interactions of modes in the early stages of inflation. These enhancements can be parametrically larger than the standard ones and are potentially observable in current and future data. These initial state effects have a characteristic signature in $l$-space which distinguishes them from the usual contributions, with the enhancement being most pronounced for configurations corresponding to flattened triangles for which two momenta are collinear.Comment: 33 pages, 1 figure. Refs added and minor addition

Decoupling in an expanding universe: backreaction barely constrains short distance effects in the cosmic microwave background

We clarify the status of transplanckian effects on the cosmic microwave background (CMB) anisotropy. We do so using the boundary effective action formalism of hep-th/0401164 which accounts quantitatively for the cosmological vacuum ambiguity. In this formalism we can clearly 1) delineate the validity of cosmological effective actions in an expanding universe. The corollary of the initial state ambiguity is the existence of an earliest time. The inability of an effective action to describe physics before this time demands that one sets initial conditions on the earliest time hypersurface. A calculation then shows that CMB anisotropy measurements are generically sensitive to high energy corrections to the initial conditions. 2) We compute the one-loop contribution to the stress-tensor due to high-energy physics corrections to an arbitrary cosmological initial state. We find that phenomenological bounds on the backreaction do not lead to strong constraints on the coefficient of the leading boundary irrelevant operator. Rather, we find that the power spectrum itself is the quantity most sensitive to initial state corrections. 3) The computation of the one-loop backreaction confirms arguments that irrelevant corrections to the Bunch-Davies initial state yield non-adiabatic vacua characterized by an energy excess at some earlier time. However, this excess only dominates over the classical background at times before the `earliest time' at which the effective action is valid. We conclude that the cosmological effective action with boundaries is a fully self-consistent and quantitative approach to transplanckian corrections to the CMB