arXiv subjects

Sahil Saini

Publications and source records attributed to Sahil Saini.

12 recordsLinked to original sources

arXiv2025

Cyclic universe and uniform rate inflation in loop quantum cosmology

We investigate uniform rate inflationary universe in the framework of loop quantum cosmology (LQC) and find that this seemingly simple inflationary model is interlinked with various concepts such as cyclic evolution, HNI inflation and polymer quantized scalar fields, when the background spacetime is loop quantized. The potential for an \textit{exactly} uniform rate inflation in a loop quantized FRW spacetime turns out to be a polymerized version of the corresponding potential in general relativity, which mimics the potentials for a polymerized scalar field and that for hybrid natural inflation (HNI). There is also a radical modification of the background spacetime, leading to a cyclic universe with identical epochs separated by quantum bounces which replace the classical singularity. The energy density and Hubble rate are bounded. The predictions for cosmological perturbations depend on the value of the field at the end of inflation. The parameter space is explored to compare the results for spectral index and tensor-to-scalar ratio with observational constraints.

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arXiv2024

Ekpyrosis in Quantum Gravitational Anisotropic Bouncing Models

We explore the isotropization of a model anisotropic universe in the bouncing models using the ekpyrotic potential without assuming initial conditions corresponding to an ekpyrotic phase. In particular, we explore the way the use of ekpyrotic potentials may dynamically help isotropization for the considered initial conditions corresponding to the macroscopic classical contracting universe with potentially large anisotropies. As an example of a concrete nonsingular bouncing mechanism, we consider the effective description of loop quantum cosmology for Bianchi-I and Bianchi-IX spacetimes for ekpyrotic and ekpyrotic-like potentials. Considering two different values of potential parameters and initial conditions corresponding to a classical macroscopic universe, we show that for both of these spacetimes, the cosmological singularity is resolved via multiple short-duration nonsingular bounces caused by quantum gravitational effects. We perform a large number of numerical simulations for a wide range of initial conditions which do not favor ekpyrosis initially. Even with such unfavorable initial conditions, we show that the relative strength of the anisotropies at the end of the bounce regime is noticeably reduced in more than 90% of the simulations. This provides a strong evidence for the isotropization ability of the ekpyrotic potentials. We find that isotropization can occur over cycles of rapid nonsingular bounces in the Planck regime via enhancement of the contribution of the (isotropic) energy density relative to the anisotropies at the bounces. Achieving isotropization is found to be easier in Bianchi-I spacetimes when compared to Bianchi-IX spacetimes. Our results demonstrate that, even with initial conditions which are not most favorable for the existence of ekpyrosis, an effective isotropization can occur in nonsingular anisotropic models with ekpyrotic and ekpyrotic-like potentials.

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arXiv2024

Spherically symmetric loop quantum gravity: Schwarzschild spacetimes with a cosmological constant

We provide a quantization of the Schwarzschild spacetime in the presence of a cosmological constant, based on midisuperspace methods developed in the spherically symmetric sector of loop quantum gravity, using in particular the 'improved dynamics' scheme. We include both the de Sitter and anti-de Sitter cases. We find that the quantization puts a Planckian positive upper limit on the possible values of the cosmological constant similar to the bounds obtained earlier from studies of homogeneous spacetimes. This means that, for negative cosmological constant, no negative bound is found. Moreover, using semiclassical physical states, we obtain the effective metric and demonstrate the causal structure for various cases. Quantum gravity modifications ensure that the singularity is replaced by a transition surface in all the cases, where the curvature invariants approach mass-independent Planckian bounds. Analysis of the effective stress-energy tensor shows that the null energy condition is strongly violated in the vicinity of the transition surface. Moreover, it shows a weaker asymptotic fall off for a nonvanishing cosmological constant, which could have interesting phenomenological implications.

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arXiv2024

Workshop on the limiting compactness objects: Black holes and Buchdahl stars

The workshop was organized at IUCAA on Oct 30 - Nov 3, 2023 as a compact discussion and discourse meeting with a threadbare exposition and discussion of the various aspects and the questions arising. It was occasioned by the visit of Professor Hakan Andreasson of the Gothenburg Technical University, Sweden. He has been exploring with his collaborators the Einstein - Vlasov system for over a decade and a half as a possible matter source for compact objects. This system characterizes itself by free particles in motion and interacting only through gravity. For a limiting compactness, this may be the most appropriate state. The main thrust of the workshop was to understand this new object, Buchdahl Star (BS), of limiting compactness without a horizon. It is almost as compact as a black hole (BH) and yet has no horizon and hence is open for interaction with the outside world. Ever since the proposal of the membrane paradigm envisaging a timelike fiducial surface near BH horizon, BS offers an excellent possibility of the existence of such a real astrophysical object. It could very well compete with BH as a mimicker for various physical and astrophysical phenomena. Thus, it opens up a new vista of study and investigation of all the questions that one asks for BH, for this new creature, BS. The workshop was intended to identify certain interesting questions as well as the people interested in studying them. On this count, the workshop has been a huge success as several interesting questions have been identified, a few groups have been formed to take up different problems, and the work has already started. Nothing more could one have asked from such an exercise. A brief summary of some of the talks is included, followed by a brief discussion of the projects identified as a result of the discussions during the workshop.

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arXiv2022

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.

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arXiv2020

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-Lemaître-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.

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arXiv2019

Generic absence of strong singularities and geodesic completeness in modified loop quantum cosmologies

Different regularizations of the Hamiltonian constraint in loop quantum cosmology yield modified loop quantum cosmologies, namely mLQC-I and mLQC-II, which lead to qualitatively different Planck scale physics. We perform a comprehensive analysis of resolution of various singularities in these modified loop cosmologies using effective spacetime description and compare with earlier results in standard loop quantum cosmology. We show that the volume remains non-zero and finite in finite time evolution for all considered loop cosmological models. Interestingly, even though expansion scalar and energy density are bounded due to quantum geometry, curvature invariants can still potentially diverge due to pressure singularities at a finite volume. These divergences are shown to be harmless since geodesic evolution does not break down and no strong singularities are present in the effective spacetimes of loop cosmologies. Using a phenomenological matter model, various types of exotic strong and weak singularities, including big rip, sudden, big freeze and type-IV singularities, are studied. We show that as in standard loop quantum cosmology, big rip and big freeze singularities are resolved in mLQC-I and mLQC-II, but quantum geometric effects do not resolve sudden and type-IV singularities.

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arXiv2019

Von Neumann stability of modified loop quantum cosmologies

Von Neumann stability analysis of quantum difference equations in loop quantized spacetimes has often proved useful to understand viability of quantizations and whether general relativistic description is recovered at small spacetime curvatures. We use this technique to analyze the infra-red behavior of quantum Hamiltonian constraint in recently explored modifications of loop quantum cosmology: mLQC-I and mLQC-II, for the spatially flat FLRW model. We investigate the behavior for $μ_o$ scheme, where minimum area of loops in quantization procedure does not take physical metric in to account, and the $\bar μ$ scheme where quantization procedure uses physical metric. The fate of stability of quantum difference equations is tested for massless scalar field as well as with inclusion of a positive cosmological constant. We show that for mLQC-I and mLQC-II, difference equation fails to be von Neumann stable for the $μ_o$ scheme if cosmological constant is included signaling problematic behavior at large volumes. Both of the modified loop quantum cosmologies are von Neumann stable for $\bar μ$ scheme. In contrast to standard loop quantum cosmology, properties of roots turn out to be richer and intricate. Our results demonstrate the robustness of $\bar μ$ scheme (or `improved dynamics') in loop quantization of cosmological spacetimes even when non-trivial quantization ambiguities of Hamiltonian are considered, and show that $μ_o$ scheme is non-viable in this setting.

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arXiv2017

Generic absence of strong singularities in loop quantum Bianchi-IX spacetimes

We study the generic resolution of strong singularities in loop quantized effective Bianchi-IX spacetime in two different quantizations - the connection operator based `A' quantization and the extrinsic curvature based `K' quantization. We show that in the effective spacetime description with arbitrary matter content, it is necessary to include inverse triad corrections to resolve all the strong singularities in the `A' quantization. Whereas in the `K' quantization these results can be obtained without including inverse triad corrections. Under these conditions, the energy density, expansion and shear scalars for both of the quantization prescriptions are bounded. Notably, both the quantizations can result in potentially curvature divergent events if matter content allows divergences in the partial derivatives of the energy density with respect to the triad variables at a finite energy density. Such events are found to be weak curvature singularities beyond which geodesics can be extended in the effective spacetime. Our results show that all potential strong curvature singularities of the classical theory are forbidden in Bianchi-IX spacetime in loop quantum cosmology and geodesic evolution never breaks down for such events.

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arXiv2017

Resolution of strong singularities and geodesic completeness in loop quantum Bianchi-II spacetimes

Generic resolution of singularities and geodesic completeness in the loop quantization of Bianchi-II spacetimes with arbitrary minimally coupled matter is investigated. Using the effective Hamiltonian approach, we examine two available quantizations: one based on the connection operator and second by treating extrinsic curvature as connection via gauge fixing. It turns out that for the connection based quantization, either the inverse triad modifications or imposition of weak energy condition is necessary to obtain a resolution of all strong singularities and geodesic completeness. In contrast, the extrinsic curvature based quantization generically resolves all strong curvature singularities and results in a geodesically complete effective spacetime without inverse triad modifications or energy conditions. In both the quantizations, weak curvature singularities can occur resulting from divergences in pressure and its derivatives at finite densities. These are harmless events beyond which geodesics can be extended. Our work generalizes previous results on the generic resolution of strong singularities in the loop quantization of isotropic, Bianchi-I and Kantowski-Sachs spacetimes.

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arXiv2017

From black holes to white holes: a quantum gravitational, symmetric bounce

Recently a consistent non-perturbative quantization of the Schwarzschild interior resulting in a bounce from black hole to white hole geometry has been obtained by loop quantizing the Kantowski-Sachs vacuum spacetime. As in other spacetimes where the singularity is dominated by the Weyl part of the spacetime curvature, the structure of the singularity is highly anisotropic in the Kantowski-Sachs vacuum spacetime. As a result the bounce turns out to be in general asymmetric creating a large mass difference between the parent black hole and the child white hole. In this manuscript, we investigate under what circumstances a symmetric bounce scenario can be constructed in the above quantization. Using the setting of Dirac observables and geometric clocks we obtain a symmetric bounce condition which can be satisfied by a slight modification in the construction of loops over which holonomies are considered in the quantization procedure. These modifications can be viewed as quantization ambiguities, and are demonstrated in three different flavors which all lead to a non-singular black to white hole transition with identical masses. Our results show that quantization ambiguities can mitigate or even qualitatively change some key features of physics of singularity resolution. Further, these results are potentially helpful in motivating and constructing symmetric black to white hole transition scenarios.

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arXiv2016

Geodesic completeness and the lack of strong singularities in effective loop quantum Kantowski-Sachs spacetime

Resolution of singularities in the Kantowski-Sachs model due to non-perturbative quantum gravity effects is investigated. Using the effective spacetime description for the improved dynamics version of loop quantum Kantowski-Sachs spacetimes, we show that even though expansion and shear scalars are universally bounded, there can exist events where curvature invariants can diverge. However, such events can occur only for very exotic equations of state when pressure or derivatives of energy density with respect to triads become infinite at a finite energy density. In all other cases curvature invariants are proved to remain finite for any evolution in finite proper time. We find the novel result that all strong singularities are resolved for arbitrary matter. Weak singularities pertaining to above potential curvature divergence events can exist. The effective spacetime is found to be geodesically complete for particle and null geodesics in finite time evolution. Our results add to a growing evidence for generic resolution of strong singularities using effective dynamics in loop quantum cosmology by generalizing earlier results on isotropic and Bianchi-I spacetimes.

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