The pre-inflationary dynamics of loop quantum cosmology: confronting quantum gravity with observations (original) (raw)
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Loop quantum cosmology: from pre-inflationary dynamics to observations
Classical and Quantum Gravity, 2015
The Planck collaboration has provided us rich information about the early universe, and a host of new observational missions will soon shed further light on the 'anomalies' that appear to exist on the largest angular scales. From a quantum gravity perspective, it is natural to inquire if one can trace back the origin of such puzzling features to Planck scale physics. Loop quantum cosmology provides a promising avenue to explore this issue because of its natural resolution of the big bang singularity. Thanks to advances over the last decade, the theory has matured sufficiently to allow concrete calculations of the phenomenological consequences of its pre-inflationary dynamics. In this article we summarize the current status of the ensuing two-way dialog between quantum gravity and observations.
Loop Quantum Gravity and the Planck Regime of Cosmology
General Relativity, Cosmology and Astrophysics, 2014
The very early universe provides the best arena we currently have to test quantum gravity theories. The success of the inflationary paradigm in accounting for the observed inhomogeneities in the cosmic microwave background already illustrates this point to a certain extent because the paradigm is based on quantum field theory on the curved cosmological space-times. However, this analysis excludes the Planck era because the background space-time satisfies Einstein's equations all the way back to the big bang singularity. Using techniques from loop quantum gravity, the paradigm has now been extended to a self-consistent theory from the Planck regime to the onset of inflation, covering some 11 orders of magnitude in curvature. 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 involving the scalar and tensor power spectra and a new source for non-Gaussianities. Thus, the genesis of the large scale structure of the universe can be traced back to quantum gravity fluctuations in the Planck regime. This report provides a bird's eye view of these developments for the general relativity community.
We study the evolution of spatially flat Friedmann-Lemaître-Robertson-Walker universe for chaotic and Starobinsky potentials in the framework of modified loop quantum cosmologies. These models result in a non-singular bounce as in loop quantum cosmology, but with far more complex modified Friedmann dynamics with higher order than quadratic terms in energy density. For the kinetic energy dominated bounce, we obtain analytical solutions using different approximations and compare with numerical evolution for various physical variables. The relative error turns out to be less than 0.3% in the bounce regime for both of the potentials. Generic features of dynamics, shared with loop quantum cosmology, are established using analytical and numerical solutions. Detailed properties of three distinct phases in dynamics separating bounce regime, transition stage and inflationary phase are studied. For the potential energy dominated bounce, we qualitatively describe its generic features and confirm by simulations that they all lead to the desired slow-roll phase in the chaotic inflation. However, in the Starobinsky potential, the potential energy dominated bounce cannot give rise to any inflationary phase. Finally, we compute the probability for the desired slow-roll inflation to occur in the chaotic inflation and as in loop quantum cosmology, find a very large probability for the universe to undergo inflation.
Universal features of quantum bounce in loop quantum cosmology
Loop quantum cosmology (LQC) provides an elegant resolution of the classical big bang singu-larity by a quantum bounce in the deep Planck era. The evolutions of the flat Friedmann-Lemaitre-Robertson-Walker (FLRW) background and its linear scalar and tensor perturbations are universal during the pre-inflationary phase. In this period the potentials of the perturbations can be well approximated by a Pöschl-Teller (PT) potential, from which we find analytically the mode functions and then calculate the Bogoliubov coefficients at the onset of the slow-roll inflation, valid for any inflationary models with a single scalar field. Matching them to those given in the slow-roll inflationary phase, we investigate the effects of the quantum bounce on the power spectra and find unique features that can be tested by current and forthcoming observations. In particular, fitting the power spectra to the Planck 2015 data, we find that the universe must have expanded at least 132 e-folds from the bounce until now.
Observational constraints on warm inflation in loop quantum cosmology
Journal of Cosmology and Astroparticle Physics, 2019
By incorporating quantum aspects of gravity, Loop Quantum Cosmology (LQC) provides a self-consistent extension of the inflationary scenario, allowing for modifications in the primordial inflationary power spectrum with respect to the standard General Relativity one. We investigate such modifications and explore the constraints imposed by the Cosmic Microwave Background (CMB) Planck Collaboration data on the Warm Inflation (WI) scenario in the LQC context. We obtain useful relations between the dissipative parameter of WI and the bounce scale parameter of LQC. We also find that the number of required e-folds of expansion from the bounce instant till the moment the observable scales crossed the Hubble radius during inflation can be smaller in WI than in CI. In particular, we find that this depends on how large is the dissipation in WI, with the amount of required e-folds decreasing with the increasing of the dissipation value. Furthermore, by performing a Monte Carlo Markov Chain anal...
Loop Quantum Cosmology and Tensor Perturbations in the Early Universe
Advanced Science Letters, 2009
We study the tensor modes of linear metric perturbations within an effective framework of loop quantum cosmology. After a review of inverse-volume and holonomy corrections in the background equations of motion, we solve the linearized tensor modes equations and extract their spectrum. Ignoring holonomy corrections, the tensor spectrum is blue tilted in the near-Planckian superinflationary regime and may be observationally disfavoured. However, in this case background dynamics is highly nonperturbative, hence the use of standard perturbative techniques may not be very reliable. On the other hand, in the quasi-classical regime the tensor index receives a small negative quantum correction, slightly enhancing the standard red tilt in slow-roll inflation. We discuss possible interpretations of this correction, which depends on the choice of semiclassical state.
Loop quantum cosmology and slow roll inflation
Physics Letters B, 2010
In loop quantum cosmology the big bang is replaced by a quantum bounce which is followed by a robust phase of super-inflation. We show that this phase has an unforeseen implication: in presence of suitable inflationary potentials it funnels all dynamical trajectories to conditions which virtually guarantee a slow roll inflation with more than 68 e-foldings, without any input from the pre-big bang regime. This is in striking contrast to the situation in general relativity where it has been argued that the a priori probability of obtaining a slow roll inflation with N e-foldings is suppressed by a factor e −3N .
Inflationary observables in loop quantum cosmology
Journal of Cosmology and Astroparticle Physics, 2011
The full set of cosmological observables coming from linear scalar and tensor perturbations of loop quantum cosmology is computed in the presence of inverse-volume corrections. Background inflationary solutions are found at linear order in the quantum corrections; depending on the values of quantization parameters, they obey an exact or perturbed power-law expansion in conformal time. The comoving curvature perturbation is shown to be conserved at large scales, just as in the classical case. Its associated Mukhanov equation is obtained and solved. Combined with the results for tensor modes, this yields the scalar and tensor indices, their running, and the tensor-to-scalar ratio, which are all first order in the quantum correction. The latter could be sizable in phenomenological scenarios. Contrary to a pure minisuperspace parametrization, the lattice refinement parametrization is in agreement with both anomaly cancellation and our results on background solutions and linear perturbations. The issue of the choice of parametrization is also discussed in relation with a possible superluminal propagation of perturbative modes, and conclusions for quantum spacetime structure are drawn.
Loop Quantum Cosmology corrections to inflationary models
2008
In the recent years the quantization methods of Loop Quantum Gravity have been successfully applied to the homogeneous and isotropic Friedmann-Robertson-Walker space-times. The resulting theory, called Loop Quantum Cosmology (LQC), resolves the Big Bang singularity by replacing it with the Big Bounce. We argue that LQC generates also certain corrections to field theoretical inflationary scenarios. These corrections imply that in the LQC the effective sonic horizon becomes infinite at some point after the bounce and that the scale of the inflationary potential implied by the COBE normalisation increases. The evolution of scalar fields immediately after the Bounce becomes modified in an interesting way. We point out that one can use COBE normalisation to establish an upper bound on the quantum of length of LQG.
Extension of the quantum theory of cosmological perturbations to the Planck era
Physical Review D, 2013
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.