Glimpses of Space-Time Beyond the Singularities Using Supercomputers

A fundamental problem of Einstein's theory of classical general relativity is the existence of singularities such as the big bang. All known laws of physics end at these boundaries of classical space-time. Thanks to recent developments in quantum gravity, supercomputers are now playing an important role in understanding the resolution of big bang and black hole singularities. Using supercomputers, explorations of the very genesis of space and time from quantum geometry are revealing a novel picture of what lies beyond classical singularities and the new physics of the birth of our universe.Comment: Invited semi-technical overview article appeared in IEEE publication Computing in Science and Engineering, special issue on "Supercomputing-Enabled Advances in Science and Engineering" edited by S. Gottlieb and G. Khanna. 8 pages, 3 figures. Uses IEEE style fil

Does the Loop Quantum μo Scheme Permit Black Hole Formation?

We explore the way different loop quantization prescriptions affect the formation of trapped surfaces in the gravitational collapse of a homogeneous dust cloud, with particular emphasis on the so-called mu o scheme in which loop quantum cosmology was initially formulated. Its undesirable features in cosmological models led to the so-called improved dynamics or the mu over bar scheme. While the jury is still out on the right scheme for black hole spacetimes, we show that as far as black hole formation is concerned, the mu o scheme has another, so far unknown, serious problem. We found that in the mu o scheme, no trapped surfaces would form for a nonsingular collapse of a homogeneous dust cloud in the marginally bound case unless the minimum nonzero area of the loops over which holonomies are computed or the Barbero-Immirzi parameter decreases almost four times from its standard value. It turns out that the trapped surfaces in the mu o scheme for the marginally bound case are also forbidden for an arbitrary matter content as long as the collapsing interior is isometric to a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. We found that in contrast to the situation in the mu o scheme, black holes can form in the mu over bar scheme, as well as other lattice refinements with a mass gap determined by quantum geometry

A diffeomorphism invariant family of metric-affine actions for loop cosmologies

In loop quantum cosmology (LQC) the big bang singularity is generically resolved by a big bounce. This feature holds even when modified quantization prescriptions of the Hamiltonian constraint are used such as in mLQC-I and mLQC-II. While the later describes an effective description qualitatively similar to that of standard LQC, the former describes an asymmetric evolution with an emergent Planckian de-Sitter pre-bounce phase even in the absence of a potential. We consider the potential relation of these canonically quantized non-singular models with effective actions based on a geometric description. We find a 3-parameter family of metric-affine $f(\mathcal{R})$ theories which accurately approximate the effective dynamics of LQC and mLQC-II in all regimes and mLQC-I in the post-bounce phase. Two of the parameters are fixed by enforcing equivalence at the bounce, and the background evolution of the relevant observables can be fitted with only one free parameter. It is seen that the non-perturbative effects of these loop cosmologies are universally encoded by a logarithmic correction that only depends on the bounce curvature of the model. In addition, we find that the best fit value of the free parameter can be very approximately written in terms of fundamental parameters of the underlying quantum description for the three models. The values of the best fits can be written in terms of the bounce density in a simple manner, and the values for each model are related to one another by a proportionality relation involving only the Barbero-Immirzi parameter.Comment: 19 pages, 4 figures and 3 table

Tunneling wavefunction proposal with loop quantum geometry effects

In Vilenkin's tunneling wavefunction proposal our expanding universe is born via a tunneling through a barrier from nothing at the zero scale factor. We explore the viability of this proposal for the spatially closed FLRW model with a positive cosmological constant including quantum gravity modifications in the Planck regime. Our setting is the effective spacetime description of loop quantum cosmology (LQC) which is known to replace the big bang singularity with a bounce due to the holonomy modifications. Due to the bounce, the barrier potential of the Wheeler-DeWitt theory is replaced by a step like potential which makes the tunneling proposal incompatible. But for a complete picture of singularity resolution, inverse scale factor modifications from quantum geometry must be included which play an important role at very small scale factors in the spatially closed models. We show that with inclusion of inverse scale factor modifications the resulting potential is again a barrier potential. The universe at the vanishing scale factor is dynamically non-singular and in an Einstein static like phase. We show that quantum geometric effects in LQC provide a non-singular completion of Vilenkin's tunneling proposal. We also find that quantum geometric effects result in a possibility of a tunneling to a quantum cyclic universe albeit for a very large value of cosmological constant determined by the quantum geometry.Comment: 19 pages, 6 figure

Loop quantum cosmology and its gauge-covariant avatar: a weak curvature relationship

We explore the relationship between the effective dynamics in standard loop quantum cosmology (LQC) based on holonomies and triads obtained from gauge-fixing fluxes, and a modification of LQC based on holonomies and gauge-covariant fluxes (referred to as gLQC). Both the models yield singularity resolution via a bounce because of non-perturbative quantum geometric effects resulting in a maximum for energy density. In LQC, the bounce is extremely well captured by a $\rho^2$ term in energy density with a negative sign which emerges as a non-perturbative modification to the classical Friedmann and Raychaudhuri equations. But, details of such modifications in gLQC have remained hidden due to an arduous nature of gauge-covariant flux modifications which do not allow writing above equations in a closed form. To extract these modifications we explore the large volume, weak curvature limit for matter with a fixed equation of state and obtain higher order corrections to the classical theory. We find that in the weak curvature limit of gLQC, in the post-bounce branch, the first order correction beyond classical theory fully recovers the form of modified Friedmann and Raychaudhuri equations of LQC. In contrast, due to an asymmetric bounce in gLQC, the weak curvature limit of the pre-bounce branch exhibits a novel structure with a $\rho^{3/2}$ term as a first order correction beyond classical theory while the $\rho^2$ term appears as a second order correction. Our work shows that gLQC has a far richer structure which includes the form of dynamical equations with non-perturbative modifications in LQC in its weak curvature limit. This indicates that more general loop quantizations of cosmological sectors can reveal LQC at some truncation, and possibly there exist a tower of potentially interesting higher order modifications from quantum geometry which are hidden in the setting of LQC.Comment: 14 page

Nonsingular quantum gravitational dynamics of an Lemaitre-Tolman-Bondi dust shell model: The role of quantization prescriptions

We study some consequences of the loop quantization of the outermost dust shell in the LemaitreTolman-Bondi spacetime with a homogeneous dust density using different quantization strategies motivated by loop quantum gravity. Prior work has dealt with loop quantizing this model by employing holonomies and the triads, following the procedure in standard loop quantum cosmology. In this work we compare this quantization with the one in which holonomies and gauge-covariant fluxes are used. While both of the quantization schemes resolve the central singularity, they lead to different mass gaps at which a trapped surface forms. This trapped surface which is matched to an exterior generalized Vaidya spacetime disappears when the density of the dust cloud is in the Planck regime. We find that the quantization based on holonomies and gauge-covariant fluxes generically results in an asymmetric evolution of the dust shell in which the Vaidya mass associated with the white hole as seen by an external observer is 2/pi of the one for the black hole. This effective difference in masses results from difference in the classical limits in preand postbounce regimes in the two quantizations. This distinctive feature rules out formation of any blackhole-white-hole twins in presence of gauge-covariant flux modifications, which is in contrast to the quantization using holonomies and triads where the gravitational collapse always leads to black hole-white hole twins. Another striking difference lies in the fact that for the quantization based on holonomies and gauge-covariant fluxes there can be situations in which during a nonsingular collapse only a black hole forms without a white hole

Primordial power spectrum from a matter-Ekpyrotic bounce scenario in loop quantum cosmology

A union of matter bounce and Ekpyrotic scenarios is often studied in an attempt to combine the most promising features of these two models. Since non-perturbative quantum geometric effects in loop quantum cosmology (LQC) result in natural bouncing scenarios without any violation of energy conditions or fine tuning, an investigation of matter-Ekpyrotic bounce scenario is interesting to explore in this quantum gravitational setting. In this work, we explore this unified phenomenological model for a spatially flat Friedmann-Lema\^itre-Robertson-Walker (FLRW) universe in LQC filled with dust and a scalar field in an Ekpyrotic scenario like negative potential. Background dynamics and the power spectrum of the comoving curvature perturbations are numerically analyzed with various initial conditions and a suitable choice of the initial states. By varying the initial conditions we consider different cases of dust and Ekpyrotic field domination in the contracting phase. We use the dressed metric approach to numerically compute the primordial power spectrum of the comoving curvature perturbations which turns out to be almost scale invariant for the modes which exit the horizon in the matter-dominated phase. But, in contrast with a constant magnitude power spectrum obtained under approximation of a constant Ekpyrotic equation of state using deformed algebra approach in an earlier work, we find that the magnitude of power spectrum changes during evolution. Our analysis shows that the bouncing regime only leaves imprints on the modes outside the scale-invariant regime. However, an analysis of the spectral index shows inconsistency with the observational data, thus making further improvements in such a model necessary.Comment: 20 pages, 8 figures, 1 tabl

The Evolution of Quantum Field Theory, From QED to Grand Unification

In the early 1970s, after a slow start, and lots of hurdles, Quantum Field Theory emerged as the superior doctrine for understanding the interactions between relativistic sub-atomic particles. After the conditions for a relativistic field theoretical model to be renormalizable were established, there were two other developments that quickly accelerated acceptance of this approach: first the Brout-Englert-Higgs mechanism, and then asymptotic freedom. Together, these gave us a complete understanding of the perturbative sector of the theory, enough to give us a detailed picture of what is now usually called the Standard Model. Crucial for this understanding were the strong indications and encouragements provided by numerous experimental findings. Subsequently, non-perturbative features of the quantum field theories were addressed, and the first proposals for completely unified quantum field theories were launched. Since the use of continuous symmetries of all sorts, together with other topics of advanced mathematics, were recognised to be of crucial importance, many new predictions were pointed out, such as the Higgs particle, supersymmetry and baryon number violation. There are still many challenges ahead.Comment: 25 pages in total. A contribution to: The Standard Theory up to the Higgs discovery - 60 years of CERN - L. Maiani and G. Rolandi, ed

On a novel relationship between shear and energy density at the bounce in non-singular Bianchi-I spacetimes

In classical Bianchi-I spacetimes, underlying conditions for what dictates the singularity structure - whether it is anisotropic shear or energy density, can be easily determined from the generalized Friedmann equation. However, in non-singular bouncing anisotropic models these insights are difficult to obtain in the quantum gravity regime where the singularity is resolved at a non-vanishing mean volume which can be large compared to the Planck volume, depending on the initial conditions. Such non-singular models may also lack a generalized Friedmann equation making the task even more difficult. We address this problem in an effective spacetime description of loop quantum cosmology (LQC) where energy density and anisotropic shear are universally bounded due to quantum geometry effects, but a generalized Friedmann equation has been difficult to derive due to the underlying complexity. Performing extensive numerical simulations of effective Hamiltonian dynamics, we bring to light a surprising, seemingly universal relationship between energy density and anisotropic shear at the bounce in LQC. For a variety of initial conditions for a massless scalar field, an inflationary potential, and two types of ekpyrotic potentials we find that the values of energy density and the anisotropic shear at the quantum bounce follow a novel parabolic relationship which reveals some surprising results about the anisotropic nature of the bounce, such as the maximum value of the anisotropic shear at the bounce is reached when the energy density reaches approximately half of its maximum allowed value. The relationship we find can prove very useful for developing our understanding of the degree of anisotropy of the bounce, isotropization of the post-bounce universe, and discovering the modified generalized Friedmann equation in Bianchi-I models with quantum gravity corrections.Comment: 24 pages, 12 figures. A figure added to discuss cigar like approach in ekpyrotic model. Published version in Phys. Rev.