arXiv subjects

Parampreet Singh

Publications and source records attributed to Parampreet Singh.

At least 109 records · Page 6Linked to original sources

arXiv2011

Loop Quantum Cosmology: A Status Report

The goal of this article is to provide an overview of the current state of the art in loop quantum cosmology for three sets of audiences: young researchers interested in entering this area; the quantum gravity community in general; and, cosmologists who wish to apply loop quantum cosmology to probe modifications in the standard paradigm of the early universe. An effort has been made to streamline the material so that, as described at the end of section I, each of these communities can read only the sections they are most interested in, without a loss of continuity.

gr-qc↗

arXiv2011

Consistent Probabilities in Wheeler-DeWitt Quantum Cosmology

We give an explicit, rigorous framework for calculating quantum probabilities in a model theory of quantum gravity. Specifically, we construct the decoherence functional for the Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmology with a free, massless, minimally coupled scalar field, thus providing a complete decoherent histories formulation for this quantum cosmological model. The decoherence functional is applied to study predictions concerning the model's Dirac (relational) observables; the behavior of semiclassical states and superpositions of such states; and to study the singular behavior of quantum Wheeler-DeWitt universes. Within this framework, rigorous formulae are given for calculating the corresponding probabilities from the wave function when those probabilities may be consistently defined, thus replacing earlier heuristics for interpreting the wave function of the universe with explicit constructions. It is shown according to a rigorously formulated standard, and in a quantum-mechanically consistent way, that in this quantization these models are generically singular. Independent of the choice of state we show that the probability for these Wheeler-DeWitt quantum universes to ever encounter a singularity is unity. In addition, the relation between histories formulations of quantum theory and relational Dirac observables is clarified.

gr-qc↗

arXiv2010

Exotic singularities and spatially curved Loop Quantum Cosmology

We investigate the occurrence of various exotic spacelike singularities in the past and the future evolution of $k = \pm 1$ Friedmann-Robertson-Walker model and loop quantum cosmology using a sufficiently general phenomenological model for the equation of state. We highlight the non-trivial role played by the intrinsic curvature for these singularities and the new physics which emerges at the Planck scale. We show that quantum gravity effects generically resolve all strong curvature singularities including big rip and big freeze singularities. The weak singularities, which include sudden and big brake singularities are ignored by quantum gravity when spatial curvature is negative, as was previously found for the spatially flat model. Interestingly, for the spatially closed model there exist cases where weak singularities may be resolved when they occur in the past evolution. The spatially closed model exhibits another novel feature. For a particular class of equation of state, this model also exhibits an additional physical branch in loop quantum cosmology, a baby universe separated from the parent branch. Our analysis generalizes previous results obtained on the resolution of strong curvature singularities in flat models to isotropic spacetimes with non-zero spatial curvature.

gr-qc↗

arXiv2010

Robustness of key features of loop quantum cosmology

Loop quantum cosmology of the k=0 FRW model (with a massless scalar field) is shown to be exactly soluble if the scalar field is used as the internal time already in the classical Hamiltonian theory. Analytical methods are then used i) to show that the quantum bounce is generic; ii) to establish that the matter density has an absolute upper bound which, furthermore, equals the critical density that first emerged in numerical simulations and effective equations; iii) to bring out the precise sense in which the Wheeler DeWitt theory approximates loop quantum cosmology and the sense in which this approximation fails; and iv) to show that discreteness underlying LQC is fundamental. Finally, the model is compared to analogous discussions in the literature and it is pointed out that some of their expectations do not survive a more careful examination. An effort has been made to make the underlying structure transparent also to those who are not familiar with details of loop quantum gravity.

gr-qc↗

arXiv2010

Consistent Histories in Quantum Cosmology

We illustrate the crucial role played by decoherence (consistency of quantum histories) in extracting consistent quantum probabilities for alternative histories in quantum cosmology. Specifically, within a Wheeler-DeWitt quantization of a flat Friedmann-Robertson-Walker cosmological model sourced with a free massless scalar field, we calculate the probability that the univese is singular in the sense that it assumes zero volume. Classical solutions of this model are a disjoint set of expanding and contracting singular branches. A naive assessment of the behavior of quantum states which are superpositions of expanding and contracting universes may suggest that a "quantum bounce" is possible i.e. that the wave function of the universe may remain peaked on a non-singular classical solution throughout its history. However, a more careful consistent histories analysis shows that for arbitrary states in the physical Hilbert space the probability of this Wheeler-DeWitt quantum universe encountering the big bang/crunch singularity is equal to unity. A quantum Wheeler-DeWitt universe is inevitably singular, and a "quantum bounce" is thus not possible in these models.

gr-qc↗

arXiv2009

Non-singular Ekpyrotic/Cyclic model in Loop Quantum Cosmology

We study the role of non-perturbative quantum gravity effects in the Ekpyrotic/Cyclic model using the effective framework of loop quantum cosmology in the presence of anisotropies. We show that quantum geometric modifications to the dynamical equations near the Planck scale as understood in the quantization of Bianchi-I spacetime in loop quantum cosmology lead to the resolution of classical singularity and result in a non-singular transition of the universe from the contracting to the expanding branch. In the Planck regime, the universe undergoes multiple small bounces and the anisotropic shear remains bounded throughout the evolution. A novel feature, which is absent for isotropic models, is a natural turn around of the moduli field from the negative region of the potential leading to a cyclic phenomena as envisioned in the original paradigm. Our work suggests that incorporation of quantum gravitational effects in the Ekpyrotic/Cyclic model may lead to a viable scenario without any violation of the null energy condition.

gr-qc↗

arXiv2009

A geometric perspective on singularity resolution and uniqueness in loop quantum cosmology

We re-examine the issue of singularity resolution in homogeneous loop quantum cosmology from the perspective of geometrical entities such as expansion rate and the shear scalar. These quantities are very reliable measures of the properties of spacetime and can be defined not only at the classical and effective level, but also at an operator level in the quantum theory. From their behavior in the effective constraint surface and in the effective loop quantum spacetime, we show that one can severely restrict the ambiguities in regularization of the quantum constraint and rule out unphysical choices. We analyze this in the flat isotropic model and the Bianchi-I spacetimes. In the former case we show that the expansion rate is absolutely bounded only for the so called improved quantization, a result which synergizes with uniqueness of this quantization as proved earlier. Surprisingly, for the Bianchi-I spacetime, we show that out of the available choices, the expansion rate and shear are bounded for only one regularization of the quantum constraint. It turns out that only for this choice, the theory exhibits quantum gravity corrections at a unique scale, and is physically viable.

gr-qc↗

arXiv2009

Are loop quantum cosmos never singular?

A unified treatment of all known types of singularities for flat, isotropic and homogeneous spacetimes in the framework of loop quantum cosmology (LQC) is presented. These include bangs, crunches and all future singularities. Using effective spacetime description we perform a model independent general analysis of the properties of curvature, behavior of geodesics and strength of singularities. For illustration purposes a phenomenological model based analysis is also performed. We show that all values of the scale factor at which a strong singularity may occur are excluded from the effective loop quantum spacetime. Further, if the evolution leads to either a vanishing or divergent scale factor then the loop quantum universe is asymptotically deSitter in that regime. We also show that there exist a class of sudden extremal events, which includes a recently discussed possibility, for which the curvature or its derivatives will always diverge. Such events however turn out to be harmless weak curvature singularities beyond which geodesics can be extended. Our results point towards a generic resolution of physical singularities in LQC.

gr-qc↗

arXiv2009

Transcending Big Bang in Loop Quantum Cosmology: Recent Advances

We discuss the way non-perturbative quantization of cosmological spacetimes in loop quantum cosmology provides insights on the physics of Planck scale and the resolution of big bang singularity. In recent years, rigorous examination of mathematical and physical aspects of the quantum theory has led to a consistent quantization which is consistent and physically viable and some early ideas have been ruled out. The latter include so called `physical effects' originating from modifications to inverse scale factors in the flat models. The singularity resolution is understood to originate from the non-local nature of curvature in the quantum theory and the underlying polymer representation. Using an exactly solvable model various insights have been gained. The model predicts a generic occurrence of bounce for states in the physical Hilbert space and a supremum for the spectrum of the energy density operator. It also provides answers to the growth of fluctuations, showing that semi-classicality is preserved to an amazing degree across the bounce.

gr-qc↗

arXiv2008

Covariant Effective Action for Loop Quantum Cosmology a la Palatini

In loop quantum cosmology, non-perturbative quantum gravity effects lead to the resolution of the big bang singularity by a quantum bounce without introducing any new degrees of freedom. Though fundamentally discrete, the theory admits a continuum description in terms of an effective Hamiltonian. Here we provide an algorithm to obtain the corresponding effective action, establishing in this way the covariance of the theory for the first time. This result provides new insights on the continuum properties of the discrete structure of quantum geometry and opens new avenues to extract physical predictions such as those related to gauge invariant cosmological perturbations.

gr-qc↗

arXiv2008

Reply to `Comment on "Quantum Bounce and Cosmic Recall"' [arXiv:0811.2790]

A recent Comment [arXiv:0811.2790] on the Letter 'Quantum Bounce and Cosmic Recall' by the authors is shown to arise from an incorrect understanding of the issues at hand and of our analysis. The conclusions of Bojowald's Comment are shown to add little to our work, to be irrelevant at best, and are further shown to be in contradiction with his own claims in the literature.

gr-qc↗

arXiv2008

Is loop quantization in cosmology unique?

We re-examine the process of loop quantization for flat isotropic models in cosmology. In particular, we contrast different inequivalent `loop quantizations' of these simple models through their respective successes and limitations and assess whether they can lead to any viable physical description. We propose three simple requirements which any such admissible quantum model should satisfy: i) independence from any auxiliary structure, such as a fiducial interval/cell introduced to define the phase space when integrating over non-compact manifolds; ii) existence of a well defined classical limit and iii) provide a sensible "Planck scale" where quantum gravitational effects become manifest. We show that even when it may seem that one can have several possible loop quantizations, these physical requirements considerably narrow down the consistent choices. Apart for the so called improved dynamics of LQC, none of the other available inequivalent loop quantizations pass above tests, showing the limitations of lattice refinement models to approximate the homogeneous sector and loop modified quantum geometrodynamics. We conclude that amongst a large class of loop quantizations in isotropic cosmology, there is a unique consistent choice.

gr-qc↗

arXiv2008

Quantum bounce and cosmic recall

Loop quantum cosmology predicts that, in simple models, the big bang singularity of classical general relativity is replaced by a quantum bounce. Because of the extreme physical conditions near the bounce, a natural question is whether the universe can retain, after the bounce, its memory about the previous epoch. More precisely, does the universe retain various properties of the state after evolving unitarily through the bounce or does it suffer from some cosmic amnesia as has been recently suggested? Here we show that this issue can be answered unambiguously at least within an exactly solvable model, derived from a small simplification of loop quantum cosmology, for which there is full analytical control on the quantum theory. We show that if there exists a semiclassical state at late times on one side, peaked around a pair of canonically conjugate variables, then there are very strong bounds on the fluctuations on the other side of the bounce, implying semi-classicality. For such a model universe which grows to a size of 1 megaparsec, at late times, the change in relative fluctuations of the only non-trivial observable of the model across the bounce is less than $10^{-56}$ (becoming smaller for universes which grow larger). The universe maintains (an almost) total recall.

gr-qc↗

arXiv2007

Graceful exit via polymerization of pre-big bang cosmology

We consider a phenomenological modification of the Pre Big Bang scenario using ideas from the resolution of curvature singularities in Loop Quantum Cosmology. We show that non-perturbative Loop modifications to the dynamics, arising from the underlying polymer representation, can resolve the graceful exit problem. The curvature and the dilaton energy stay finite at all times, in both the string and Einstein frames. In the string frame, the dilaton tends to a constant value at late times after the bounce.

hep-th↗

arXiv2007

Thermal fluctuations in loop cosmology

Quantum gravitational effects in loop quantum cosmology lead to a resolution of the initial singularity and have the potential to solve the horizon problem and generate a quasi scale-invariant spectrum of density fluctuations. We consider loop modifications to the behavior of the inverse scale factor below a critical scale in closed models and assume a purely thermal origin for the fluctuations. We show that the no-go results for scale invariance in classical thermal models can be evaded even if we just consider modifications to the background (zeroth order) gravitational dynamics. Since a complete and systematic treatment of the perturbed Einstein equations in loop cosmology is still lacking, we simply parameterize their expected modifications. These change quantitatively, but not qualitatively, our conclusions. We thus urge the community to more fully work out this complex aspect of loop cosmology, since the full picture would not only fix the free parameters of the theory, but also provide a model for a non-inflationary, thermal origin for the structures of the Universe.

astro-ph↗

arXiv2007

Loop quantum cosmology of k=1 FRW models

The closed, k=1, FRW model coupled to a massless scalar field is investigated in the framework of loop quantum cosmology using analytical and numerical methods. As in the k=0 case, the scalar field can be again used as emergent time to construct the physical Hilbert space and introduce Dirac observables. The resulting framework is then used to address a major challenge of quantum cosmology: resolving the big-bang singularity while retaining agreement with general relativity at large scales. It is shown that the framework fulfills this task. In particular, for states which are semi-classical at some late time, the big-bang is replaced by a quantum bounce and a recollapse occurs at the value of the scale factor predicted by classical general relativity. Thus, the `difficulties' pointed out by Green and Unruh in the k=1 case do not arise in a more systematic treatment. As in k=0 models, quantum dynamics is deterministic across the deep Planck regime. However, because it also retains the classical recollapse, in contrast to the k=0 case one is now led to a cyclic model. Finally, we clarify some issues raised by Laguna's recent work addressed to computational physicists.

gr-qc↗

arXiv2006

Formation and Evolution of Structure in Loop Cosmology

Inhomogeneous cosmological perturbation equations are derived in loop quantum gravity, taking into account corrections in particular in gravitational parts. This provides a framework for calculating the evolution of modes in structure formation scenarios related to inflationary or bouncing models. Applications here are corrections to the Newton potential and to the evolution of large scale modes which imply non-conservation of curvature perturbations possibly noticeable in a running spectral index. These effects are sensitive to quantization procedures and test the characteristic behavior of correction terms derived from quantum gravity.

astro-ph↗

arXiv2006

Quantum Nature of the Big Bang: Improved dynamics

An improved Hamiltonian constraint operator is introduced in loop quantum cosmology. Quantum dynamics of the spatially flat, isotropic model with a massless scalar field is then studied in detail using analytical and numerical methods. The scalar field continues to serve as `emergent time', the big bang is again replaced by a quantum bounce, and quantum evolution remains deterministic across the deep Planck regime. However, while with the Hamiltonian constraint used so far in loop quantum cosmology the quantum bounce can occur even at low matter densities, with the new Hamiltonian constraint it occurs only at a Planck-scale density. Thus, the new quantum dynamics retains the attractive features of current evolutions in loop quantum cosmology but, at the same time, cures their main weakness.

gr-qc↗