Quantum Cosmological Effects Research Articles

Consistent scalar and tensor perturbation power spectra in single fluid matter bounce with dark energy era

We investigate cosmological scenarios containing one canonical scalar field with an exponential potential in the context of bouncing models, where the bounce happens due to quantum cosmological effects. The only possible bouncing solutions in this scenario (discarding an infinitely fine tuned exception) must have one and only one dark energy phase, either occurring in the contracting era or in the expanding era. Hence,these bounce solutions are necessarily asymmetric. We calculate the spectral indexes and amplitudes of scalar and tensor perturbations numerically, considering the whole history of the model, including the bounce phase itself, without making any approximation or using any matching condition on the perturbations. As the background model is necessarily dust dominated in the far past, the usual adiabatic vacuum initial conditions can be easily imposed in this era. Hence, this is a cosmological model where the presence of dark energy behavior in the Universe does not turn problematic the usual vacuum initial conditions prescription for cosmological perturbation in bouncing models. Scalar and tensor perturbations end up being almost scale invariant, as expected. The background parameters can be adjusted, without fine tunings, to yield the observed amplitude for scalar perturbations, and also for the ratio between tensor and scalar amplitudes, $r = T/S \lesssim 0.1$. The amplification of scalar perturbations over tensor perturbations takes place only around the bounce, due to quantum effects, and it would not occur if General Relativity has remained valid throughout this phase. Hence, this is a bouncing model where a single field induces not only an expanding background dark energy phase, but also produces all observed features of cosmological perturbations of quantum mechanical origin at linear order.

Particle creation in bouncing cosmologies

We investigate scalar particle creation in a set of bouncing models where the bounce occurs due to quantum cosmological effects described by the Wheeler-DeWitt equation. The scalar field can be either conformally or minimally coupled to gravity, and it can be massive or massless, without self interaction. The analysis is made for models containing a single radiation fluid, and for the more realistic case of models containing the usual observed radiation and dust fluids, which can fit most of the observed features of our Universe, including an almost scale invariant power spectrum of scalar cosmological perturbations. In the conformal coupling case, the particle production is negligible. In the minimal coupling case, for massive particles, the results point to the same physical conclusion within observational constraints: particle production is most important at the bounce energy scale, and it is not sensitive neither to its mass nor whether there is dust in the background model. The only caveat is the case where the particle mass is larger than the bounce energy scale. On the other hand, the energy density of produced massive particles depend on their masses and the energy scale of the bounce. For very large masses and deep bounces, this energy density may overcome that of the background. In the case of massless particles, the energy density of produced particles can become comparable to the background energy density only for bounces occurring at energy scales comparable to the Planck scale or above, which lies beyond the scope of this paper: we expect that the simple Wheeler-DeWitt approach we are using should be valid only at scales some few orders of magnitude below the Planck energy. Nevertheless, in the case in which dust is present, there is an infrared divergence, which becomes important only for scales much larger than today's Hubble radius.

COHERENT STATE FUNCTIONAL INTEGRAL IN LOOP QUANTUM COSMOLOGY: ALTERNATIVE DYNAMICS

Coherent state functional integral for the minisuperspace model of loop quantum cosmology is studied. By the well-established canonical theory, the transition amplitude in the path integral representation of loop quantum cosmology with alternative dynamics can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained. It turns out that for a nonsymmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. For the corresponding symmetric Hamiltonian operator, the resulted effective theory implies a possible quantum cosmological effect in large scale limit in the alternative dynamical scenario, which coincides with the result in canonical approach. Moreover, the first-order modified Friedmann equation still contains the particular information of alternative dynamics and hence admits the possible phenomenological distinction between the different proposals of quantum dynamics.

Coherent state functional integrals in quantum cosmology

Coherent state functional integrals for the minisuperspace models of quantum cosmology are studied. By the well-established canonical theories, the transition amplitudes in the path-integral representations of Wheeler-DeWitt quantum cosmology and loop quantum cosmology can be formulated through group averaging. The effective action and Hamiltonian with higher-order quantum corrections are thus obtained in both models. It turns out that for a non-symmetric Hamiltonian constraint operator, the Moyal (star)-product emerges naturally in the effective Hamiltonian. This reveals the intrinsic relation among coherent state functional integral, effective theory and star-product. Moreover, both the resulted effective theories imply a possible quantum cosmological effect in large scale limit.

Possible observational effects of loop quantum cosmology

In this paper we consider realistic model of inflation embedded in the framework of loop quantum cosmology. Phase of inflation is preceded here by the phase of a quantum bounce. We show how parameters of inflation depend on the initial conditions established in the contracting, pre-bounce phase. Our investigations indicate that phase of the bounce easily sets proper initial conditions for the inflation. Subsequently we study observational effects that might arise due to the quantum gravitational modifications. We perform preliminary observational constraints for the Barbero-Immirzi parameter $\gamma$, critical density $\rho_{\text{c}}$ and parameter $\lambda$. In the next step we study effects on power spectrum of perturbations. We calculate spectrum of perturbations from the bounce and from the joined bounce+inflation phase. Based on these studies we indicate possible way to relate quantum cosmological models with the astronomical observations. Using the Sachs-Wolfe approximation we calculate spectrum of the super-horizontal CMB anisotropies. We show that quantum cosmological effects can, in the natural way, explain suppression of the low CMB multipoles. We show that fine-tuning is not required here and model is consistent with observations. We also analyse other possible probes of the quantum cosmologies and discuss perspectives of their implementation.

Scalar perturbations in scalar field quantum cosmology

In this paper it is shown how to obtain the simplest equations for the Mukhanov-Sasaki variables describing quantum linear scalar perturbations in the case of scalar fields without potential term. This was done through the implementation of canonical transformations at the classical level, and unitary transformations at the quantum level, without ever using any classical background equation, and it completes the simplification initiated in investigations by Langlois [D. Langlois, Classical Quantum Gravity 11, 389 (1994).], and Pinho and Pinto-Neto [E. J. C. Pinho and N. Pinto-Neto, Phys. Rev. D 76, 023506 (2007).] for this case. These equations were then used to calculate the spectrum index ${n}_{s}$ of quantum scalar perturbations of a nonsingular inflationary quantum background model, which starts at infinity past from flat space-time with Planckian size spacelike hypersurfaces, and inflates due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase. The result is ${n}_{s}=3$, incompatible with observations.

Cosmological Perturbations in Quantum Backgrounds and Confrontation with Inflationary Predictions

We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-de Witt equation, thus treating both the background and the perturbations in a fully quantum manner. We find an almost scale invariant spectrum. Taking into account the spectral index constraint as well as the CMB normalization measure yields an equation of state that should be less than ω . 8×10 −4 , implying nS −1 ∼O ` 10 −4 ´ ,a nd that the characteristic size of the Universe at the bounce is L0 ∼ 10 3 LPlanck, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects. We have also obtained a consistency relation between the tensor to scalar ratio T/ S and the scalar spectral index as T/ S ∼ 4 × 10 −2 √ n S − 1, leading to potentially measurable differences with inflationary predictions.

Inflationary nonsingular quantum cosmological model

A stiff matter-dominated universe modeled by a free massless scalar field minimally coupled to gravity in a Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) geometry is quantized. Generalized complex-width Gaussian superpositions of the solutions of the Wheeler-DeWitt equation are constructed and the Bohm-de Broglie interpretation of quantum cosmology is applied. A planar dynamical system is found in which a diversity of quantum Bohmian trajectories are obtained and discussed. One class of solutions represents nonsingular inflationary models starting at infinity past from flat space-time with Planckian size spacelike hypersurfaces, which inflates without inflaton but due to a quantum cosmological effect, until it makes an analytical graceful exit from this inflationary epoch to a decelerated classical stiff matter expansion phase.

Noninflationary model with scale invariant cosmological perturbations

We show that a contracting universe which bounces due to quantum cosmological effects and connects to the hot big-bang expansion phase, can produce an almost scale invariant spectrum of perturbations provided the perturbations are produced during an almost matter dominated era in the contraction phase. This is achieved using Bohmian solutions of the canonical Wheeler-DeWitt equation, thus treating both the background and the perturbations in a fully quantum manner. We find a very slightly blue spectrum (${n}_{\mathrm{S}}\ensuremath{-}1>0$). Taking into account the spectral index constraint as well as the cosmic microwave background normalization measure yields an equation of state that should be less than $\ensuremath{\omega}\ensuremath{\lesssim}8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$, implying ${n}_{\mathrm{S}}\ensuremath{-}1\ensuremath{\sim}\mathcal{O}({10}^{\ensuremath{-}4})$, and that the characteristic curvature scale of the Universe at the bounce is ${L}_{0}\ensuremath{\sim}{10}^{3}{\ensuremath{\ell}}_{\mathrm{Pl}}$, a region where one expects that the Wheeler-DeWitt equation should be valid without being spoiled by string or loop quantum gravity effects. We have also obtained a consistency relation between the tensor-to-scalar ratio $T/S$ and the scalar spectral index as $T/S\ensuremath{\sim}4.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}\sqrt{{n}_{\mathrm{S}}\ensuremath{-}1}$, leading to potentially measurable differences with inflationary predictions.

The Bohm Interpretation of Quantum Cosmology

I make a review on the aplications of the Bohm-De Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohm's view can avoid the initial singularity, isotropize the Universe, and even be a cause for the present observed acceleration of the Universe. In the general case, we enumerate the possible structures of quantum space and time.

The accelerated expansion of the Universe as a quantum cosmological effect

We study the quantized Friedmann–Lemaı̂tre–Robertson–Walker (FLRW) model minimally coupled to a free massless scalar field. In a previous paper, [Phys. Rev. D 62 (2000) 83507], solutions of this model were constructed as Gaussian superpositions of negative and positive modes solutions of the Wheeler–DeWitt equation, and quantum Bohmian trajectories were obtained in the framework of the Bohm–de Broglie (BdB) interpretation of quantum cosmology. In the present Letter, we analyze the quantum Bohmian trajectories of a different class of Gaussian packets. We are able to show that this new class generates Bohmian trajectories which begin classical (with decelerated expansion), undergo an accelerated expansion in the middle of its evolution due to the presence of quantum cosmological effects in this period, and return to its classical decelerated expansion in the far future. We also show that the relation between luminosity distance and redshift in the quantum cosmological model can be made close to the corresponding relation coming from the classical model supplemented by a cosmological constant, for z<1. These results suggest the possibility of interpreting the present observations of high redshift supernovae as the manifestation of a quantum cosmological effect.