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

In this paper, we study the gravitational collapse in the k-essence emergent gravity using a generalized Vaidya-type metric as a background. We also analyze the cosmic censorship hypothesis for this system. We show that the emergent gravity metric resembles closely to the new type of the generalized Vaidya metrics for null fluid collapse with the k-essence emergent mass function, where we consider the k-essence scalar field being a function solely of the advanced or the retarded time. This new type of k-essence emergent Vaidya metric has satisfied the required energy conditions. The existence of the locally naked central singularity, the strength and the strongness of the singularities for the k-essence emergent Vaidya metric are the interesting outcomes of the present work.

Gravitational collapse for the K-essence emergent Vaidya spacetime

We show that the Hawking temperature is modified in the presence of dark energy in an emergent gravity scenario for Kerr–Newman(KN) and Kerr–Newman–AdS(KNAdS) background metrics. The emergent gravity metric is not conformally equivalent to the gravitational metric. We calculate the Hawking temperatures for these emergent gravity metrics along $$\theta =0$$ <math><mrow><mi>θ</mi><mo>=</mo><mn>0</mn></mrow></math> . Also we show that the emergent black hole metrics are satisfying Einstein’s equations for large r and $$\theta =0$$ <math><mrow><mi>θ</mi><mo>=</mo><mn>0</mn></mrow></math> . Our analysis is done in the context of dark energy in an emergent gravity scenario having $$k-$$ <math><mrow><mi>k</mi><mo>-</mo></mrow></math> essence scalar fields $$\phi $$ <math><mi>ϕ</mi></math>  with a Dirac–Born–Infeld type Lagrangian. In KN and KNAdS background, the scalar field $$\phi (r,t)=\phi _{1}(r)+\phi _{2}(t)$$ <math><mrow><mi>ϕ</mi><mrow><mo>(</mo><mi>r</mi><mo>,</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>ϕ</mi><mn>1</mn></msub><mrow><mo>(</mo><mi>r</mi><mo>)</mo></mrow><mo>+</mo><msub><mi>ϕ</mi><mn>2</mn></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math>  satisfies the emergent gravity equations of motion at $$r\rightarrow \infty $$ <math><mrow><mi>r</mi><mo>→</mo><mi>∞</mi></mrow></math>  for $$\theta =0$$ <math><mrow><mi>θ</mi><mo>=</mo><mn>0</mn></mrow></math> .

Bivash Majumder

The Hawking temperature in the context of dark energy for Kerr–Newman and Kerr–Newman–AdS backgrounds

For emergent gravity metrics, the presence of dark energy modifies the Hawking temperature. We show that for the spherically symmetric Reissner–Nordstrom background metric, the emergent metric can be mapped into a Robinson–Trautman black hole. Allowed values of the dark energy density follow from rather general conditions. For some allowed values of the dark energy density this black hole can have zero Hawking temperature, i.e. the black hole does not radiate. For a Kerr background along &lt;math&gt;&lt;mrow&gt;&lt;mi mathvariant="italic"&gt;θ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt; , the emergent black hole metric satisfies Einstein’s equations for large &lt;math&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;/math&gt; and always radiates. Our analysis is done in the context of emergent gravity metrics having &lt;math&gt;&lt;mi&gt;k&lt;/mi&gt;&lt;/math&gt; -essence scalar fields &lt;math&gt;&lt;mi mathvariant="italic"&gt;ϕ&lt;/mi&gt;&lt;/math&gt; with a Born–Infeld type lagrangian. In both cases the scalar field &lt;math&gt;&lt;mrow&gt;&lt;mi mathvariant="italic"&gt;ϕ&lt;/mi&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;msub&gt;&lt;mi mathvariant="italic"&gt;ϕ&lt;/mi&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;mo&gt;+&lt;/mo&gt;&lt;msub&gt;&lt;mi mathvariant="italic"&gt;ϕ&lt;/mi&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/msub&gt;&lt;mrow&gt;&lt;mo stretchy="false"&gt;(&lt;/mo&gt;&lt;mi&gt;t&lt;/mi&gt;&lt;mo stretchy="false"&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/mrow&gt;&lt;/math&gt; also satisfies the emergent gravity equations of motion for &lt;math&gt;&lt;mrow&gt;&lt;mi&gt;r&lt;/mi&gt;&lt;mo stretchy="false"&gt;→&lt;/mo&gt;&lt;mi&gt;∞&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt; and &lt;math&gt;&lt;mrow&gt;&lt;mi mathvariant="italic"&gt;θ&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt; .