Holonomy Corrections Research Articles

Multi-fluid potential in the loop cosmology

The scalar field can behave like a fluid with equation of state pϕ=wρϕ, where w∈[−1,1]. In this Letter we derive a class of the scalar field potentials for which w=const. Scalar field with such a potential can mimic ordinary matter, radiation, cosmic strings, etc. We perform our calculations in the framework of the loop cosmology with holonomy corrections. We solve the model analytically for the whole parameter space. Subsequently, we perform similar consideration for the model with a phantom field (w<−1). We show that scalar field is monotonic function in both cases. This indicates that it can be treated as a well-defined internal time for these models. Moreover we perform preliminary studies of the scalar field perturbations with this potential. We indicate that non-Gaussian features are present admitting for the possible observational constraints of the model.

Inverse volume corrections from loop quantum gravity and the primordial tensor power spectrum in slow-roll inflation

Together with holonomy corrections, inverse volume terms should be taken into account when studying the primordial universe in loop quantum cosmology. We investigate how the tensor power spectrum is modified with respect to the standard general relativistic prediction by those semiclassical corrections. Depending on the values of the free parameters of the model, it is shown that the spectrum can exhibit a very large deviation from its usual shape, in particular with a very red slope and a strong running in the infrared limit.

How loopy is the quantum bounce? A heuristic analysis of higher order holonomy corrections in loop quantum cosmology

A well-motivated extension of higher order holonomy corrections in loop quantum cosmology (LQC) for the k=0 Friedmann-Robertson-Walker model is investigated at the level of heuristic effective dynamics. It reveals that the quantum bounce is generic, regardless of the order of corrections, and the matter density remains finite, bounded from above by an upper bound in the regime of the Planckian density, even if all orders of corrections are included. This observation provides further evidence that the quantum bounce is essentially a consequence of the loopy nature (i.e. intrinsic discreteness) of LQC and LQC is fundamentally different from the Wheeler-DeWitt theory; it also encourages one to construct the quantum theory of LQC with the higher order holonomy corrections, which might be understood as related to the higher j representations in the Hamiltonian operator of loop quantum gravity.

Loop Quantum Cosmology: holonomy corrections to inflationary models

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 the LQC holonomy correctionsgenerate 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. LQC corrections other than the holonomy one are assumed to be subdominant.

Gravitational waves from the big bounce

In this paper we investigate gravitational wave production during the big bounce phase,inspired by loop quantum cosmology. We consider the influence of the holonomy correctionsto the equation for tensor modes. We show that they act like additional effective gravitonmass, suppressing gravitational wave creation. However, such effects can be treatedperturbatively. We investigate a simplified model without holonomy corrections to theequation for modes and find its exact analytical solution. Assuming the form for matter we calculate the full spectrum of the gravitational waves from the big bounce phase. Thespectrum obtained decreases to zero for the low energy modes. On the basis of thisobservation we infer that this effect can lead to low cosmic microwave background (CMB)multipole suppression and gives a potential way for testing loop quantum cosmologymodels. We also consider a scenario with a post-bounce inflationary phase. The powerspectrum obtained gives a qualitative explanation of the CMB spectra, including lowmultipole suppression.

Loop Quantum Cosmology and Tensor Perturbations in the Early Universe

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.

Exact solutions for a big bounce in loop quantum cosmology

In this paper we study the flat ($k=0$) cosmological Friedmann-Robertson-Walker model with holonomy corrections of loop quantum gravity. The considered universe contains a massless scalar field and the cosmological constant $\ensuremath{\Lambda}$. We find analytical solutions for this model in different configurations and investigate its dynamical behavior in the whole phase space. Such an approach might be significant e.g. as a phenomenological reference for a further, fully quantum treatment. We show the explicit influence of $\ensuremath{\Lambda}$ on the qualitative and quantitative character of solutions. Even in the case of positive $\ensuremath{\Lambda}$ the oscillating solutions without the initial and final singularity appear as a generic case for some quantization schemes.