We present a new avenue of the Raychaudhuri Equation (RE) by introducing a non-affine parametrization within the k-essence framework. This modification accounts for non-geodesic flow curves, leading to emergent repulsive effects in cosmic evolution. Using a DBI-type k-essence Lagrangian, we derive a modified RE and demonstrate its ability to address the Hubble tension while predicting a natural emergence of a dynamical dark energy equation of state. Our Bayesian analysis, constrained by cosmological data, supports the theoretical scaling relation of the k-essence field ( <math altimg='si1.svg'><mover accent='true'><mrow><mi>&#981;</mi></mrow><mrow><mo>&#729;</mo></mrow></mover></math>) and the cosmic scale factor ( <italic>a</italic>). Furthermore, we reinterpret the modified RE as an anti-damped harmonic oscillator, we found a caustic avoidance signature, it may reveal classical or quantum-like effects in cosmic expansion. These results suggest a deep connection between scalar field dynamics and modified gravity, offering new perspectives on the nature of the expansion history of the universe.

India

Samit Ganguly

Goutam Manna

Debashis Gangopadhyay

Germany

Israel

Bahamas

Eduardo Guendelman

Abhijit Bhattacharyya

Non-affine extensions of the Raychaudhuri equation in the K-essence framework

This article investigates the modified Raychaudhuri Equation (RE) in the context of Non-Gravitating Vacuum Energy (NGVE) theory and its implications for various cosmological characteristics. The equation is formulated based on the NGVE framework, in which global scale invariance generates a unique geometry. The newly developed geometry introduces a metric that is conformally connected to the conventional metric, with the conformal factor dependent on scalar field potentials. The cosmological study is carried out under the framework of a flat Friedmann–Lemaître–Robertson–Walker (FLRW) universe. Assuming matter behaves as an ideal fluid in the modified geometry, we formulate models for conditional expansion, collapse, and steady state, governed by the scalar field $$(\phi )$$ . In this context, the caustic solution and the focusing theorem are also studied. Scalar field solutions for exponential and power-law scale factors are also derived using NGVE theory’s equations of motion. Finally, graphical analysis is used to investigate the behavior of the interaction terms that appear in the modified RE under these scale factors.

Arijit Panda

Exploring cosmological implications of the modified Raychaudhuri equation in non-gravitating vacuum energy theory

We show by matching two flat spaces one in Minkowski coordinates ( empty space) and the other in Minkowski coordinates after a special conformal transformation (also empty space) through a bubble with positive and constant surface tension, that the motion of the bubble is hyperbolic. If the surface tension is very big the initial size of the bubble is as small as we wish, so that we can indeed obtain an infinite universe out of empty spaces. The induced space in the bubble is de Sitter type.

Jacov Portnoy

Bubble universe from flat spaces

We propose a new approach to investigate inflation in a model-independent way, and in particular to elaborate the involved observables, through the introduction of the “scale factor potential”. Through its use one can immediately determine the inflation end, which corresponds to its first (and global) minimum. Additionally, we express the inflationary observables in terms of its logarithm, using as independent variable the e-folding number. As an example, we construct a new class of scalar potentials that can lead to the desired spectral index and tensor-to-scalar ratio, namely $$n_s \approx 0.965$$ <math><mrow><msub><mi>n</mi><mi>s</mi></msub><mo>≈</mo><mn>0.965</mn></mrow></math>  and $$r \sim 10^{-4}$$ <math><mrow><mi>r</mi><mo>∼</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>4</mn></mrow></msup></mrow></math>  for 60 e-folds, in agreement with observations.

David Benisty

China

Greece

Emmanuel Saridakis

The scale factor potential approach to inflation

Türkiye

Izzet Sakalli

United States

Douglas Singleton

S. Habib Mazharimousavi

Black Holes: Insights and Enigmas

We consider a modified gravity plus single scalar-field model, where the scalar Lagrangian couples symmetrically both to the standard Riemannian volume-form (spacetime integration measure density) given by the square root of the determinant of the Riemannian metric, as well as to another non-Riemannian volume-form in terms of an auxiliary maximal-rank antisymmetric tensor gauge field. As shown in a previous paper, the pertinent scalar-field dynamics provides an exact unified description of both dark energy via dynamical generation of a cosmological constant, and dark matter as a “dust” fluid with geodesic flow as a result of a hidden Noether symmetry. Here we extend the discussion by considering a non-trivial modification of the purely gravitational action in the form of f(R)=R-αR2 generalized gravity. Upon deriving the corresponding “Einstein-frame” effective action of the latter modified gravity-scalar-field theory we find explicit duality (in the sense of weak versus strong coupling) between the original model of unified dynamical dark energy and dust fluid dark matter, on one hand, and a specific quadratic purely kinetic “k-essence” gravity–matter model with special dependence of its coupling constants on only two independent parameters, on the other hand. The canonical Hamiltonian treatment and Wheeler–DeWitt quantization of the dual purely kinetic “k-essence” gravity–matter model is also briefly discussed.

Bulgaria

Emil Nissimov

Svetlana Pacheva

Unified dark energy and dust dark matter dual to quadratic purely kinetic K-essence

We show that dark energy and dark matter can be described simultaneously by ordinary Einstein gravity interacting with a single scalar field provided the scalar field Lagrangian couples in a symmetric fashion to two different spacetime volume forms (covariant integration measure densities) on the spacetime manifold – one standard Riemannian given by -g (square root of the determinant of the pertinent Riemannian metric) and another non-Riemannian volume form independent of the Riemannian metric, defined in terms of an auxiliary antisymmetric tensor gauge field of maximal rank. Integration of the equations of motion of the latter auxiliary gauge field produce an a priori arbitrary integration constant that plays the role of a dynamically generated cosmological constant or dark energy. Moreover, the above modified scalar field action turns out to possess a hidden Noether symmetry whose associated conserved current describes a pressureless “dust” fluid which we can identify with the dark matter completely decoupled from the dark energy. The form of both the dark energy and dark matter that results from the above class of models is insensitive to the specific form of the scalar field Lagrangian. By adding an appropriate perturbation, which breaks the above hidden symmetry and along with this couples dark matter and dark energy, we also suggest a way to obtain growing dark energy in the present universe’s epoch without evolution pathologies.

Dark energy and dark matter from hidden symmetry of gravity model with a non-Riemannian volume form

In this paper we give a variation of the gauge procedure which employs a scalar gauge field, B ( x ), in addition to the usual vector gauge field, A μ ( x ). We study this variant of the usual gauge procedure in the context of a complex scalar, matter field ϕ ( x ) with a U(1) symmetry. We will focus most on the case when ϕ develops a vacuum expectation value via spontaneous symmetry breaking. We find that under these conditions the scalar gauge field mixes with the Goldstone boson that arises from the breaking of a global symmetry. Some other interesting features of this scalar gauge model are: (i) The new gauge procedure gives rise to terms which violate C and CP symmetries. This may have have applications in cosmology or for CP violation in particle physics; (ii) the existence of mass terms in the Lagrangian which respect the new extended gauge symmetry. Thus one can have gauge field mass terms even in the absence of the usual Higgs mechanism; (iii) the emergence of a sine-Gordon potential for the scalar gauge field; (iv) a natural, axion-like suppression of the interaction strength of the scalar gauge boson.

Scalar gauge fields