arXiv subjects
Publications and source records attributed to Saurya Das.
We study Quantum Gravity effects in cosmology, and in particular that of the Generalized Uncertainty Principle on the Friedmann equations. We show that the Quantum Gravity induced variations of the energy density and pressure in the radiation dominated era provide a viable explanation of the observed baryon asymmetry in the Universe.
The unexplained observed baryon asymmetry in the Universe is a long-standing problem in physics, with no satisfactory resolution so far. To explain this asymmetry, three Sakharov conditions must be met. An interaction term which couples space-time and the baryon current is considered, which satisfies the first two Sakharov conditions. Furthermore, it is shown that the Generalized Uncertainty Principle (GUP) from quantum gravity induces corrections to the Friedmann equations in cosmology, via the holographic principle. GUP also induces variations of energy and pressure density in the radiation dominated era, which satisfies the third Sakharov condition. Therefore, this construction provides a viable explanation for the observed baryon asymmetry. This also fixes the GUP parameters to $α_0\approx10^4$ and $β_0\approx-10^8$.
The classical Raychaudhuri equation predicts the formation of conjugate points for a congruence of geodesics, in a finite proper time. This in conjunction with the Hawking-Penrose singularity theorems predicts the incompleteness of geodesics and thereby the singular nature of practically all spacetimes. We compute the generic corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole, arising from modifications to the algebra inspired by the generalized uncertainty principle (GUP) theories. Then we study four specific models of GUP, compute their effective dynamics as well as their expansion and its rate of change using the Raychaudhuri equation. We show that the modification from GUP in two of these models, where such modifications are dependent of the configuration variables, lead to finite Kretchmann scalar, expansion and its rate, hence implying the resolution of the singularity. However, the other two models for which the modifications depend on the momenta still retain their singularities even in the effective regime.
Quantum theories of gravity predict interesting phenomenological features such as a minimum measurable length and maximum momentum. We use the Generalized Uncertainty Principle (GUP), which is an extension of the standard Heisenberg Uncertainty Principle motivated by Quantum Gravity, to model the above features. In particular, we use a GUP with modelling maximum momentum to establish a correspondence between the GUP-modified dynamics of a massless spin-2 field and quadratic (referred to as Stelle) gravity. In other words, Stelle gravity can be regarded as the classical manifestation of a maximum momentum and the related GUP. We explore the applications of Stelle gravity to cosmology and specifically show that Stelle gravity applied to a homogeneous and isotropic background leads to inflation with an exit. Using the above, we obtain strong bounds on the GUP parameter from CMB observations. Unlike previous works, which fixed only upper bounds for GUP parameters, we obtain both \emph{lower and upper bounds} on the GUP parameter.
We show that the apparent horizon and the region near $r=0$ of an evaporating charged, rotating black hole are timelike. It then follows that for black holes in nature, which invariably have some rotation, have a channel, via which classical or quantum information can escape to the outside, while the black hole shrinks in size. We discuss implications for the information loss problem.
We compute bounds on the GUP parameters for two versions of GUP using gravitational wave data from the events GW150914 and GW190521. The speed of the graviton and photon are calculated in a curved spacetime modified by GUP, assuming that these particles have a small mass. The observational bound on the difference in their speeds translates to bounds on the GUP parameters. These bounds are some of the best obtained so far in the context of quantum gravity phenomenology.
We show that if one starts with a Universe with some matter and a cosmological constant, then quantum mechanics naturally induces an attractive gravitational potential and an effective Newton's coupling. Thus gravity is an emergent phenomenon and what should be quantized are the fundamental degrees of freedom from which it emerges.
We derive loop quantum gravity corrections to the Raychaudhuri equation in the interior of a Schwarzschild black hole and near the classical singularity. We show that the resulting effective equation implies defocusing of geodesics due to the appearance of repulsive terms. This prevents the formation of conjugate points, renders the singularity theorems inapplicable, and leads to the resolution of the singularity for this spacetime.
We study Quantum Gravity effects on the density of states in statistical mechanics and its implications for the critical temperature of a Bose Einstein Condensate and fraction of bosons in its ground state. We also study the effects of compact extra dimensions on the critical temperature and the fraction. We consider both neutral and charged bosons in the study and show that the effects may just be measurable in current and future experiments.
The Planck or the quantum gravity scale, being $16$ orders of magnitude greater than the electroweak scale, is often considered inaccessible by current experimental techniques. However, it was shown recently by one of the current authors that quantum gravity effects via the Generalized Uncertainty Principle affects the time required for free wavepackets to double their size, and this difference in time is at or near current experimental accuracies [1, 2]. In this work, we make an important improvement over the earlier study, by taking into account the leading order relativistic correction, which naturally appears in the systems under consideration, due to the significant mean velocity of the travelling wavepackets. Our analysis shows that although the relativistic correction adds nontrivial modifications to the results of [1, 2], the earlier claims remain intact and are in fact strengthened. We explore the potential for these results being tested in the laboratory.
It has been shown beyond reasonable doubt that the majority (about 95%) of the total energy budget of the universe is given by the dark components, namely Dark Matter and Dark Energy. What constitutes these components remains to be satisfactorily understood however, despite a number of promising candidates. An associated conundrum is that of the coincidence, i.e. the question as to why the Dark Matter and Dark Energy densities are of the same order of magnitude at the present epoch, after evolving over the entire expansion history of the universe. In an attempt to address these, we consider a quantum potential resulting from a quantum corrected Raychaudhuri/Friedmann equation in presence of a cosmic fluid, which is presumed to be a Bose-Einstein condensate (BEC) of ultralight bosons. For a suitable and physically motivated macroscopic ground state wavefunction of the BEC, we show that a unified picture of the cosmic dark sector can indeed emerge, thus resolving the issue of the coincidence. The effective Dark energy component turns out to be a cosmological constant, by virtue of a residual homogeneous term in the quantum potential. Furthermore, comparison with the observational data gives an estimate of the mass of the constituent bosons in the BEC, which is well within the bounds predicted from other considerations.
A large class of quantum theories of gravity show that the Heisenberg's uncertainty principle is modified to the "Generalised Uncertainty Principle" (GUP) near the Planckian scale. It has also been shown that the GUP induces perturbative corrections to all quantum mechanical Hamiltonians, even at low energies, and thereby introduces Planck scale corrections to the Schrödinger equation and to the relativistic quantum mechanical equations. Some of these corrections give rise to potentially measurable effects in the low-energy laboratory. Another prediction of these corrections is that a measured length must be quantized, as seen by studying the solutions of the GUP modified Schrödinger, Klein-Gordon, and Dirac equations in a one, two, and three dimensional box. This result was subsequently extended to spacetimes with weak gravitational fields. In this work, we further extend this length quantization to spacetimes with strong gravitational fields and show that this result continues to hold, thereby showing that it is robust.
We compute the quantum circuit complexity of the evolution of scalar curvature perturbations on expanding backgrounds, using the language of squeezed vacuum states. In particular, we construct a simple cosmological model consisting of an early-time period of de Sitter expansion followed by a radiation-dominated era and track the evolution of complexity throughout this history. During early-time de Sitter expansion the complexity grows linearly with the number of e-folds for modes outside the horizon. The evolution of complexity also suggests that the Universe behaves like a chaotic system during this era, for which we propose a scrambling time and Lyapunov exponent. During the radiation-dominated era, however, the complexity decreases until it "freezes in" after horizon re-entry, leading to a "de-complexification" of the Universe.
We compute the circuit complexity of scalar curvature perturbations on FLRW cosmological backgrounds with fixed equation of state $w$ using the language of squeezed vacuum states. Backgrounds that are accelerating and expanding, or decelerating and contracting, exhibit features consistent with chaotic behavior, including linearly growing complexity. Remarkably, we uncover a bound on the growth of complexity for both expanding and contracting backgrounds $λ\leq \sqrt{2} \ |H|$, similar to other bounds proposed independently in the literature. The bound is saturated for expanding backgrounds with an equation of state more negative than $w = -5/3$, and for contracting backgrounds with an equation of state larger than $w = 1$. For expanding backgrounds that preserve the null energy condition, de Sitter space has the largest rate of growth of complexity (identified as the Lyapunov exponent), and we find a scrambling time that is similar to other estimates up to order one factors.
We show that if Dark Matter is made up of light bosons, they form a Bose-Einstein condensate in the early Universe. This in turn naturally induces a Dark Energy of approximately equal density and exerting negative pressure.This explains the so-called coincidence problem.
Recently, the authors presented a covariant extension of the Generalized Uncertainty Principle (GUP) with a Lorentz invariant minimum length. This opens the way for constructing and exploring the observable consequences of minimum length in Relativistic Quantum Field Theories. In particular, we compute quantum gravity corrections to high energy scattering experiments, which may provide the much needed window of testing minimum length and quantum gravity theories in the laboratory. To this end, we formulate the Lagrangian of Quantum Electrodynamics for a complex scalar fields from the GUP modified minimally coupled Klein-Gordon equation and write down its Feynman rules. We then calculate the Relativistic Generalized Uncertainty Principle corrections to a Quantum Electrodynamics scattering amplitude and discuss its implications.
Continuing our earlier work on the application of the Relativistic Generalized Uncertainty Principle (RGUP) to quantum field theories, in this paper we study Quantum Electrodynamics (QED) with minimum length. We obtain expressions for the Lagrangian, Feynman rules and scattering amplitudes of the theory, and discuss their consequences for current and future high energy physics experiments. We hope this will provide an improved window for testing Quantum Gravity effects in the laboratory.
We investigate the observable consequences of Planck scale effects in the advanced gravitational wave detector by polymer quantizing the optical field in the arms of the interferometer. We construct a new set of polymer-modified creation and annihilation operators to quantize the optical field. Employing these polymer-modified operators, we obtain the fluctuations in the radiation pressure on the end mirrors and the number of output photons. We compare our results with the standard quantization scheme and corrections from the Generalized Uncertainty Principle.