Stringy Bubbles Solve de Sitter Troubles

Finding four-dimensional de Sitter spacetime solutions in string theory has been a vexing quest ever since the discovery of the accelerating expansion of the universe. Building on a recent analysis of bubble-nucleation in the decay of (false-vacuum) AdS backgrounds where the interfacing bubbles themselves exhibit a de Sitter geometry we show that this resonates strongly with a stringy cosmic brane construction that naturally provides for an exponential mass-hierarchy and the localization of both gravity and matter, in addition to an exponentially suppressed positive cosmological constant. Finally, we argue that these scenarios can be realized in terms of a generalization of a small resolution of a conifold singularity in the context of a (Lorentzian) Calabi–Yau 5-fold, where the isolated (Lorentzian) two complex dimensional Fano variety is a four-dimensional de Sitter spacetime.

Nonlinear dynamics of flux compactification

We study the nonlinear evolution of unstable flux compactifications, applying numerical relativity techniques to solve the Einstein equations in D dimensions coupled to a q-form field and positive cosmological constant. We show that initially homogeneous flux compactifications are unstable to dynamically forming warped compactifications. In some cases, we find that the warping process can serve as a toy-model of slow-roll inflation, while in other instances, we find solutions that eventually evolve to a singular state. Analogous to dynamical black hole horizons, we use the geometric properties of marginally trapped surfaces to characterize the lower dimensional vacua in the inhomogeneous and dynamical settings we consider. We find that lower-dimensional vacua with a lower expansion rate are dynamically favoured, and in some cases find spacetimes that undergo a period of accelerated expansion followed by contraction.

The two-sphere partition function in two-dimensional quantum gravity

We study the Euclidean path integral of two-dimensional quantum gravity with positive cosmological constant coupled to conformal matter with large and positive central charge. The problem is considered in a semiclassical expansion about a round two-sphere saddle. We work in the Weyl gauge whereby the computation reduces to that for a (timelike) Liouville theory. We present results up to two-loops, including a discussion of contributions stemming from the gauge fixing procedure. We exhibit cancelations of ultraviolet divergences and provide a path integral computation of the central charge for timelike Liouville theory. Combining our analysis with insights from the DOZZ formula we are led to a proposal for an all orders result for the two-dimensional gravitational partition function on the two-sphere.

ISCOs and OSCOs in the Presence of a Positive Cosmological Constant in Massive Gravity

We study the impact of a non-vanishing (positive) cosmological constant on the innermost and outermost stable circular orbits (ISCOs and OSCOs, respectively) within massive gravity in four dimensions. The gravitational field generated by a point-like object within this theory is known, generalizing the usual Schwarzschild–de Sitter geometry of General Relativity. In the non-relativistic limit, the gravitational potential differs by the one corresponding to the Schwarzschild–de Sitter geometry by a term that is linear in the radial coordinate with some prefactor γ, which is the only free parameter. Starting from the geodesic equations for massive test particles and the corresponding effective potential, we obtain a polynomial of fifth order that allows us to compute the innermost and outermost stable circular orbits. Next, we numerically compute the real and positive roots of the polynomial for several different structures (from the hydrogen atom to stars and globular clusters to galaxies and galaxy clusters) considering three distinct values of the parameter γ, determined using physical considerations, such as galaxy rotation curves and orbital precession. Similarly to the Kottler spacetime, both ISCOs and OSCOs appear. Their astrophysical relevance as well as the comparison with the Kottler spacetime are briefly discussed.

BLACK-HOLE HAVING ELECTRIC HAIRS FOR POSITIVE COSMOLOGICAL CONSTANT Λ>0 ON A COSMIC HORIZON SCALE ~1/√Λ

This paper is a technical review for a more deliberate paper (Bhattacharya & Lahiri, 2007) where it has been shown that on a positive cosmological scale with Λ>0 having a cosmic horizon scale ~1/√Λ, there exists the soft electric hairs for the solution having the T_00 components of the stress-energy tensor T_μν i.e., ρ=0 on black hole horizon B_H having the maximum density at black hole singularity B_S where cosmic horizon C_H and black hole horizon B_H has only been considered. KEYWORDS: Black Hole – Cosmic Horizon – TOV Limit – Stress-Energy Tensor – Positive Cosmological Constant

Global solutions to the spherically symmetric Einstein-scalar field system with a positive cosmological constant in Bondi coordinates

We consider a characteristic initial value problem, with initial data given on a future null cone, for the Einstein (massless) scalar field system with a positive cosmological constant, in Bondi coordinates. We prove that, for small data, this system has a unique global classical solution which is causally geodesically complete to the future and decays polynomially in radius and exponentially in Bondi time, approaching the de Sitter solution.

Circuit Complexity from Cosmological Islands

Recently in various theoretical works, path-breaking progress has been made in recovering the well-known Page Curve of an evaporating black hole with Quantum Extremal Islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of Quantum Extremal Islands in negative (or positive) Cosmological Constant with radiation in the background of Friedmann-Lemaî tre-Robertson-Walker (FLRW) space-time. Without using any explicit details of any gravity model, we study the behaviour of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, Out-of-Time Ordered Correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration.

Symmetry enhancement in a two-logarithm matrix model and the canonical tensor model

I study a one-matrix model of a real symmetric matrix with a potential which is a sum of two logarithmic functions and a harmonic one. This two-logarithm matrix model is the absolute square norm of a toy wave function which is obtained by replacing the tensor argument of the wave function of the canonical tensor model (CTM) with a matrix. I discuss a symmetry enhancement phenomenon in this matrix model and show that symmetries and dimensions of emergent spaces are stable only in a phase which exists exclusively for the positive cosmological constant case in the sense of CTM. This would imply the importance of the positivity of the cosmological constant in the emergence phenomena in CTM.