Emergent universe in $$D \ge 4$$ dimensions with dynamical wormholes

We present a flat emergent universe (EU) in Einstein gravity with non-linear equation of state (nEoS) in the usual four and in higher dimensions. The EU is assumed to evolve from an initial Einstein’s static universe (ESU) in the infinite past. For a homogeneous Ricci scalar we determine the shape function and obtain a new class of dynamical wormholes that permits EU. The nEoS $$p= A\rho -B \sqrt{\rho _o \rho }$$ p = A ρ - B ρ o ρ is equivalent to three different cosmic fluids which is identified with barotropic fluid for a given A. We obtain EU models in flat, closed and open universes and tested the null energy condition (NEC). At the throat of the wormhole which is recognized as the seed of ESU, we tested the NEC for a given size of the neck. As the EU evolves from an asymptotic past and approaches $$t=0$$ t = 0 , it is found that NEC does not respect. This triggers the onset of interactions at $$t=t_i$$ t = t i , and a realistic flat EU scenario can be obtained in four and in higher dimensions. The origin of the ESU at the throat of the wormhole is also explored via a gravitational instanton mechanism. We compare the relative merits of dynamical wormholes for implementing EU.

Quantum theory of $$k(\phi )$$-FLRW-metrics its connection to Chern-Simons-models and the theta vacuum structure of quantum gravity

We show how a foliated 4-dimensional FLRW-metric becomes a gravitational instanton, if the spatial metric minimizes a three-dimensional Einstein–Hilbert action with positive cosmological constant, which is equal to the demand, that the scale factor satisfies the Bogomolny-equation, where the curvature parameter varies over the one-parameter family of hyperslices and takes the role of a potential depending on the scale factor. Additionally, we draw the connection to SO(4)-Chern–Simons theory and show how the established interpolating solutions describe the gradient flow between the minima of the vacuums of the Einstein–Hilbert action, as well as how they can be used to calculate tunnelling-amplitudes of gravitons and trivialize the calculations of path integrals in quantum gravity. All the calculations are carried out particularly for k admitting a $${\mathbb {Z}}_{2}$$ Z 2 -symmetry.

Moduli spaces of Calabi-Yau d-folds as gravitational-chiral instantons

Motivated by the swampland program, we show that the Weil-Petersson geometry of the moduli space of a Calabi-Yau manifold of complex dimension d ≤ 4 is a gravitational instanton (i.e. a finite-action solution of the Euclidean equations of motion of gravity with matter). More precisely, the moduli geometry of Calabi-Yau d-folds (d ≤ 4) describes instantons of (E)AdS Einstein gravity coupled to a standard chiral model.From the point of view of the low-energy physics of string/M-theory compactified on the Calabi-Yau X, the various fields propagating on its moduli space are the couplings appearing in the effective Lagrangian "Image missing".

Gravitational instantons with faster than quadratic curvature decay (II)

This is our second paper in a series to study gravitational instantons, i.e. complete hyperkähler 4-manifolds with faster than quadratic curvature decay. We prove two main theorems: (i) The asymptotic rate of gravitational instantons to the standard models can be improved automatically. (ii) Any ALF-D_{k} gravitational instanton must be the Cherkis–Hitchin–Ivanov–Kapustin–Lindström–Roček metric.

Entropy Product Formula for Gravitational Instanton

We investigate the entropy product formula for various gravitational instantons. We speculate that due to the mass-independent features of the said instatons they are universal as well as quantized. For isolated Euclidean Schwarzschild black hole, these properties simply fail.

Bianchi-IX, Darboux–Halphen and Chazy–Ramanujan

Bianchi-IX four metrics are SU(2) invariant solutions of vacuum Einstein equation, for which the connection-wise self-dual case describes the Euler top, while the curvature-wise self-dual case yields the Ricci flat classical Darboux–Halphen system. It is possible to see such a solution exhibiting Ricci flow. The classical Darboux–Halphen system is a special case of the generalized one that arises from a reduction of the self-dual Yang–Mills equation and the solutions to the related homogeneous quadratic differential equations provide the desired metric. A few integrable and near-integrable dynamical systems related to the Darboux–Halphen system and occurring in the study of Bianchi-IX gravitational instanton have been listed as well. We explore in details whether self-duality implies integrability.

Gravitational behavior of an effective topological field theory in a gravitational instanton background

Effective topological field theories describe the properties of Dirac fermions in the low-energy regime. In this work, we introduce a new emergent gravity model by considering Dirac fermions invariant under local de Sitter transformations in four-dimensional open manifolds. In the context of Cartan geometry, fermions couple to spacetime through a Spin(5) Cartan connection that can be decomposed in spin connection and tetrads. In presence of a gravitational instanton background, we show that the corresponding effective topological field theory becomes a dynamical gravitational theory with a positive cosmological constant and Barbero–Immirzi parameter. At the classical level and in the absence of matter, this theory is compatible with general relativity (GR).

NOVEL ACCELERATING EINSTEIN VACUA AND SMOOTH INHOMOGENEOUS RIEMANNIAN MANIFOLDS

A novel class of Einstein vacua is presented, which possess nonvanishing cosmological constant and accelerating horizon with the topology of SD-3 fibration over S1. After Euclideanization, the solution describes a conformally distorted SD-1 fibration over S1, which is smooth, compact and inhomogeneous and can be regarded as analog of Don Page's gravitational instanton.