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

Three-flavoured neutrino oscillations are investigated in the light of the Leggett–Garg inequality (LGI). The results obtained are: (a) The maximum violation of the LGI is 2.17036 for neutrino path length L1=140.15 km and ΔL=1255.7 km. (b) The presence of the mixing angle θ13 enhances the maximum violation of LGI by 4.6% . (c) The currently known mass hierarchy parameter α=0.0305 increases the maximum violation of LGI by 3.7% . (d) The presence of a CP-violating phase parameter enhances the maximum violation of LGI by 0.24% , thus providing an alternative indicator of CP violation in three-flavoured neutrino oscillations. The outline of an experimental proposal is suggested whereby the findings of this investigation may be verified.

Animesh Sinha Roy

Three-flavoured neutrino oscillations and the Leggett–Garg inequality

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; .

The Hawking temperature in the context of dark energy for Reissner–Nordstrom and Kerr background