arXiv subjects

Ayush Bidlan

Publications and source records attributed to Ayush Bidlan.

7 recordsLinked to original sources

arXiv2026

An Interplay Between Fractional Calculus and Holographic Dark Energy

This dissertation aims to put forth a systematic construction of a fractional-calculus extension of holographic dark energy (HDE). We show that linking late-time cosmic acceleration to non-local or memory effects encoded in a fractional (Riesz) derivative within black hole thermodynamics produces deviations from standard HDE and can address some challenges of the Hubble cutoff. In particular, a Riesz fractional spatial derivative is introduced into the Hamiltonian constraint of a Schwarzschild black hole in quantum geometrodynamics, leading to a Fractional Wheeler--DeWitt equation whose solutions yield fractionally corrected thermodynamic quantities, notably fractional Bekenstein--Hawking entropy governed by the L\'evy index $\alpha$, with $1<\alpha\leq2$. Using this entropy with Cohen's inequality, a new dark energy density is constructed, defining the Fractional Holographic Dark Energy (FHDE) framework. The cosmological implications of FHDE are then investigated. Within the Hubble cutoff, its late-time evolution is analysed through cosmological observables, and the model is reconstructed using effective field descriptions with spin-$0$ and spin-$1$ candidates, allowing kinetic and potential terms to be extracted as functions of redshift $z$ and $\alpha$. The framework is then extended to BD, DGP, EPN, and Horndeski theories to derive the equation-of-state and deceleration parameters in terms of $z$ and $\alpha$. In addition, the fate of the Universe is studied through late-time singularities, namely the big, little, and pseudo-rip, within the Granda--Oliveros FHDE setting. In short, this dissertation proposes FHDE as a theoretically motivated extension of HDE, bridging non-locality in quantum gravity with the late-time dynamics of the Universe, and offering a route toward understanding cosmic acceleration beyond $\Lambda$CDM.

gr-qc↗

arXiv2026

Causal Structure of Spacetime Singularities and Their Observable Signatures

We analyze the causal structure of horizonless compact objects via the light-cone geometry and conformal compactification of the Joshi-Malafarina-Narayan (JMN-1) and Janis-Newman-Winicour (JNW) spacetimes. Penrose diagrams reveal that JMN-1 undergoes a transition from timelike $(0<M_0<2/3)$ to null $(2/3<M_0<4/5)$ singularities, while JNW remains timelike throughout, in contrast to the spacelike singularity of the Schwarzschild spacetime. We show that photon spheres exist in Schwarzschild and JNW, but arise in JMN-1 only in the null singularity phase, establishing a direct link between causal character and null geodesic trapping. We further demonstrate that radial timelike geodesics develop turning points for certain parameter regimes in both JMN-1 and JNW spacetimes, indicating the emergence of effective repulsive behavior in the strong field region. These features lead to distinct strong field lensing and shadow signatures, potentially testable by very long baseline interferometric observations such as those of the Event Horizon Telescope.

gr-qc↗

arXiv2026

Gravitational Collapse and Singularity Formation in Brans-Dicke Gravity

We investigate gravitational collapse driven solely by a self-interacting Brans--Dicke (BD) scalar field in the absence of ordinary matter. In this framework, the spacetime dynamics are governed solely by the scalar field $\Phi$, endowed with a self-interaction potential $V(\Phi)$ and non-minimally coupled to the Ricci scalar through the Brans--Dicke action. We numerically solve for the evolution of $\Phi(t)$ and the corresponding potential $V(\Phi)$ in order to track the collapse dynamics leading to singularity formation. Our analysis demonstrates that, for the energy densities $\rho \approx 1/a$ and $\rho \approx -\ln a$, the collapse inevitably leads to the formation of a central curvature singularity while consistently satisfying the weak energy condition. We further examine the causal structure of the resulting singularity and find that future-directed null geodesics originating from the singularity can propagate to future null infinity, making the singularity globally visible. The strength of the singularity is also examined by extending Tipler's strong curvature condition to the Brans--Dicke field equations. Overall, our findings indicate that gravitational collapse in scalar--tensor gravity can give rise to scenarios that challenge the Cosmic Censorship Conjecture, while underscoring the potential observational relevance of singularities formed through BD scalar-field-driven collapse.

gr-qc↗

arXiv2026

Future Rip Scenarios in Fractional Holographic Dark Energy

In this paper, we investigate the occurrence of late-time cosmological singularities, namely, the rip scenarios within the framework of interacting Fractional Holographic Dark Energy (FHDE). We start our investigation with the Granda-Oliveros (GO) cutoff, i.e., $L=(\gamma H^{2}+\delta\dot{H})^{-\frac{1}{2}}$, and highlight the range of allowed $\alpha$ (L\'evy's index) values for which big, little and pseudo rip can occur. In particular, we highlight the occurrence of a big rip for fractional values of the L\'evy's index in the allowed range $1<\alpha\leq2$. Moreover, we conclude that the occurrence of a pseudo-rip requires L\'evy's index to be $\alpha>2$. Therefore, we reject the possibility of pseudo-rip within the GO cutoff. Furthermore, we demonstrate that the occurrence of the little rip in FHDE equipped with a GO cutoff is rather contrived and requires a specific functional form of the IR cutoff $L\sim(\gamma H^{2}+g(H))^{-\frac{1}{2}}$, which belongs to a larger class of Nojiri-Odintsov (NO) cutoffs. To extend our perspective beyond the GO cutoff, we investigate the interacting FHDE framework equipped with the Hubble cutoff, i.e., $L=H^{-1}$, in developing an ansatz-based approach to the little and pseudo-rip singularities as they fail to appear in the GO cutoff. Within this approach, we invoke the expression of the Hubble parameter, $H(t)$, which corresponds to the little and pseudo-rip, into the cosmological parameters such as the Equation of State (EoS) and Squared Sound Speed (SSS) as a function of cosmic time $t$. We produce numerical plots of these parameters in both linear and non-linear $Q$ regimes, which supplement our theoretical findings. In summary, our results highlight the occurrence of little and pseudo-rip singularities within a Hubble cutoff for a non-linear $Q$ term within the FHDE framework.

gr-qc↗

arXiv2025

Reconstructing FHDE with Scalar and Gauge Fields

We revisit the Fractional Holographic Dark Energy (FHDE) model to reconstruct it by means of dynamic candidates such as ($i$) Quintessence, ($ii$) K-essence, ($iii$) Dilaton, ($iv$) Yang-Mills condensate, ($v$) DBI-essence, and ($vi$) Tachyonic fields in a flat Friedmann-Robertson-Walker (FRW) Universe. In particular, the dark-energy possibilities ($i$)-($vi$) are formulated through suitable field descriptions. Being concrete, we establish a comprehensive correspondence between FHDE and suitable scalar and gauge field frameworks that co-substantiate our investigation and subsequent discussion. In more detail, we methodically compute the corresponding Equation of State (EoS) parameters and field (kinetic and potential) features for the fractional parameter ($\alpha$) range, viz. $1<\alpha\leq2$. Conclusively, our results show that the modifications brought by the fractional features satisfactorily enable late-time cosmic acceleration, together with avoiding quantum instabilities by preventing the EoS from entering the phantom divide i.e., $\omega(z)\rightarrow-\infty$, which is a common issue in standard scalar field models without fractional dynamics (e.g., K-essence field). Our findings further indicate that fractional calculus attributes can be significant in addressing the challenges of dark-energy models by offering a robust framework to prospect late-time acceleration and properly fitting observational constraints. Notably, we find that as the fractional features start to dominate, the EoS parameter of all the effective field configurations asymptotically approaches a $\Lambda$CDM behaviour in the far-future limit $z\rightarrow-1$. In summary, the recent perspective introduced by FHDE \citep{Trivedi:2024inb} can indeed be cast as a promising aspirant through the use of prominent field frameworks.

gr-qc↗

arXiv2024

Non-Local Classical Field Theory with Fractional Operators on $\mathbb{S}^3 \times \mathbb{R}^1$ Space

We present a theoretical framework on non-local classical field theory using fractional integrodifferential operators. Due to the lack of easily manageable symmetries in traditional fractional calculus and the difficulties that arise in the formalism of multi-fractional calculus over $\mathbb{R}^{\text{D}}$ space, we introduce a set of new fractional operators over the $\mathbb{S}^3 \times \mathbb{R}^1$ space. The redefined fractional integral operator results in the non-trivial measure canonically, and they can account for the spacetime symmetries for the underlying space $\mathbb{S}^3 \times \mathbb{R}^1$ with the Lorentzian signature $(+, -, -, -, -)$. We conclude that the field equation for the non-local classical field can be obtained as the consequence of the optimisation of the action by employing the non-local variations in the field after defining the non-local Lagrangian density, namely, $\mathcal{L}(\phi_{a}\left(x\right), \mathbb{\eth}^\alpha \phi_{a}\left(x\right))$, as the function of the symmetric fractional derivative of the field, e.g. in the context of the kinetic term, and the field itself.

physics.class-ph↗

arXiv2024

Fractional Holographic Dark Energy

Holographic dark energy theories present a fascinating interface to probe late-time cosmology, as guided by contemporary ideas about quantum gravity. In this work, we present a new holographic dark energy scenario designated Fractional Holographic Dark Energy (FHDE). This model extends the conventional framework of HDEs by incorporating specific features from fractional calculus recently applied, e.g., in cosmological settings. In this manner, we retrieve a novel form of HDE energy density. We then show how FHDE can provide a consistent picture of the evolution of the late-time universe even with the simple choice of the Hubble horizon as the IR (infrared) cutoff. We provide detailed descriptions of the cosmological evolution, showing how the fractional calculus ingredients can alleviate quite a few issues associated with the conventional HDE scenario. Concretely, we compute and plot diagrams using the Hubble horizon cutoff for HDE. The density parameters for DE and dark matter (DM), the deceleration parameter, and the DE EoS parameter indicate how the universe may evolve within our FHDE model, fitting within an appropriate scenario of late-time cosmology.

gr-qc↗