Using techniques from loop quantum gravity, the standard theory of cosmological perturbations was recently generalized to encompass the Planck era. We now apply this framework to explore pre-inflationary dynamics. The framework enables us to isolate and resolve the true trans-Planckian difficulties, with interesting lessons both for theory and observations. Specifically, for a large class of initial conditions at the bounce, we are led to a self consistent extension of the inflationary paradigm over the 11 orders of magnitude in density and curvature, from the big bounce to the onset of slow roll. In addition, for a narrow window of initial conditions, there are departures from the standard paradigm, with novel effects -such as a modification of the consistency relation between the ratio of the tensor to scalar power spectrum and the tensor spectral index, as well as a new source for non-Gaussianities-which could extend the reach of cosmological observations to the deep Planck regime of the early universe.

Cosmological perturbations are generally described by quantum fields on (curved but) classical space-times. While this strategy has a large domain of validity, it can not be justified in the quantum gravity era where curvature and matter densities are of Planck scale. Using techniques from loop quantum gravity, the standard theory of cosmological perturbations is extended to overcome this limitation. The new framework sharpens conceptual issues by distinguishing between the true and apparent trans-Planckian difficulties and provides sufficient conditions under which the true difficulties can be overcome within a quantum gravity theory. In a companion paper, this framework is applied to the standard inflationary model, with interesting implications to theory as well as observations.

Since the standard inflationary paradigm is based on quantum field theory on classical space-times, it excludes the Planck era. Using techniques from loop quantum gravity, the paradigm is extended to a self-consistent theory from the Planck scale to the onset of slow roll inflation, covering some 11 orders of magnitude in energy density and curvature. This pre-inflationary dynamics also opens a small window for novel effects, e.g. a source for non-Gaussianities, which could extend the reach of cosmological observations to the deep Planck regime of the early universe. PACS numbers: 98.80.Qc, 04.60.Pp, 04.60.Kz The inflationary paradigm has had remarkable success in accounting for the inhomogeneities in the cosmic microwave background (CMB) that serve as seeds for the large scale structure of the universe. However it has certain conceptual limitations from particle physics as well as quantum gravity perspectives. For example: i) The physical origin of the inflaton and its properties remains unclear; ii) Since the background geometry and matter satisfy Einstein's equations, the big bang singu-larity persists [1]; iii) One ignores pre-inflationary dynamics and simply requires that perturbations be in the Bunch Davies (BD) vacuum at the onset of the slow roll; and, iv) When evolved back in time these perturbative modes acquire trans-Planckian frequencies and the underlying framework of quantum field theory on classical space-times becomes unreliable. Here we will not address any of the particle physics issues. Rather, we focus on the incompleteness related to quantum gravity and show that this limitation can be overcome. In addition, we find that pre-inflationary dynamics can produce certain deviations from the BD vacuum at the onset of inflation, leading to novel effects which could be seen, e.g., in non-Gaussianities through future measurements of the halo bias and the 'µ-type distortions' in the CMB [2]. Loop quantum gravity (LQG) offers a natural framework to address these issues because effects of its underlying quantum geometry dominate at the Planck scale, leading to singularity resolution in a variety of cosmolog-ical models, including some that admit anisotropies and inhomogeneities [3]. Even though LQG is still incomplete , notable advances have occurred-e.g., in cosmol-ogy, analysis of black holes, and a derivation of the gravi-ton propagator-by using the following strategy: First carry out a truncation of the classical theory geared to the given physical problem and then use LQG techniques to construct the quantum theory [4]. For inflation, then, we are led to focus just on first order perturbations off the spatially flat Friedman backgrounds with a scalar field φ. In numerical simulations we will use the quadratic potential V = (1/2)m 2 φ 2 with m = 1.21 × 10 −6 m Pl , the value that comes from the 7 year WMAP data [5, 6]. Throughout we use natural Planck units. The truncated phase space: We have Γ Trun = Γ o × Γ 1 where Γ o is the 4-dimensional phase space of homogeneous fields, and Γ 1 , of the first o...

Cosmological inflation generates a spectrum of density perturbations that can seed the cosmic structures we observe today. These perturbations are usually computed as the result of the gravitationally-induced spontaneous creation of perturbations from an initial vacuum state. In this paper, we compute the perturbations arising from gravitationally-induced stimulated creation when perturbations are already present in the initial state. The effect of these initial perturbations is not diluted by inflation and survives to its end, and beyond. We consider a generic statistical density operator ρ describing an initial mixed state that includes probabilities for nonzero numbers of scalar perturbations to be present at early times during inflation. We analyze the primordial bispectrum for general configurations of the three different momentum vectors in its arguments. We find that the initial presence of quanta can significantly enhance non-gaussianities in the so-called squeezed limit. Our results show that an observation of non-gaussianities in the squeezed limit can occur for single-field inflation when the state in the very early inflationary universe is not the vacuum, but instead contains early-time perturbations. Valuable information about the initial state can then be obtained from observations of those non-gaussianities.

We provide an exhaustive numerical exploration of the predictions of loop quantum cosmology (LQC) with a post-bounce phase of inflation for the primordial power spectrum of scalar and tensor perturbations. We extend previous analysis by characterizing the phenomenologically relevant parameter space and by constraining it using observations. Furthermore, we characterize the shape of LQC-corrections to observable quantities across this parameter space. Our analysis provides a framework to contrast more accurately the theory with forthcoming polarization data, and it also paves the road for the computation of other observables beyond the power spectra, such as non-Gaussianity.

We give an efficient method, combining number-theoretic and combinatorial ideas, to exactly compute black hole entropy in the framework of loop quantum gravity. Along the way we provide a complete characterization of the relevant sector of the spectrum of the area operator, including degeneracies, and explicitly determine the number of solutions to the projection constraint. We use a computer implementation of the proposed algorithm to confirm and extend previous results on the detailed structure of the black hole degeneracy spectrum.

We give a complete and detailed description of the computation of black hole entropy in loop quantum gravity by employing the most recently introduced numbertheoretic and combinatorial methods. The use of these techniques allows us to perform a detailed analysis of the precise structure of the entropy spectrum for small black holes, showing some relevant features that were not discernible in previous computations. The ability to manipulate and understand the spectrum up to the level of detail that we describe in the paper is a crucial step towards obtaining the behavior of entropy in the asymptotic (large horizon area) regime.

We argue that the anomalous power asymmetry observed in the cosmic microwave background (CMB) may have originated in a cosmic bounce preceding inflation. In loop quantum cosmology (LQC) the big bang singularity is generically replaced by a bounce due to quantum gravitational effects. We compute the spectrum of inflationary non-Gaussianity and show that strong correlation between observable scales and modes with longer (super-horizon) wavelength arise as a consequence of the evolution of perturbations across the LQC bounce. These correlations are strongly scale dependent and induce a dipole-dominated modulation on large angular scales in the CMB, in agreement with observations.