arXiv subjects

Saikat Chakraborty

Publications and source records attributed to Saikat Chakraborty.

At least 19 recordsLinked to original sources

arXiv2026

Formalizing a unified dynamical system framework for $f(R)$ and $f(Q)$ gravity

Going beyond the traditional Hubble-normalized framework, we formalize a unified dynamical system formulation for $f(R)$ and coincident gauge $f(Q)$ gravity using three distinct sets of dimensionless variables: (1) kinematical cosmographic parameters, (2) the dark energy equation of state parameter $w$ (with its $N=\ln a$ derivatives) and matter density abundance $Ω_m$, and (3) theory space parameters $\{m_i\}$ characterizing the shape of the theory function. Our formulation is free of auxiliary variables, closing via three equivalent ways: (1) specifying a theory, (2) requiring a specific cosmological evolution, or (3) requiring a specific dark energy equation of state evolution. Each closure strategy is illustrated with explicit examples. The theory closure approach studies a case of Hu-Sawicki $f(R)$ and $f(Q)=-2Λ+Q+β\sqrt{-Q}$ models, where traditional formalisms fail. A heteroclinic trajectory from a GR-matter-dominated epoch to a late-time de-Sitter epoch is general for $f(Q)$, but sensitive to initial conditions for $f(R)$. The cosmographic and equation-of-state closure approaches compare $f(R)$ and $f(Q)$ gravities kinematically equivalent to $Λ$CDM ($j(z)=1$) and dynamically equivalent to $Λ$CDM ($w(z)=-1$). In both, GR acts as a cosmological past attractor for $f(Q)$ gravity, but not for $f(R)$.

gr-qc↗

arXiv2026

Exact Integrable $Λ$CDM-Mimicking $f(Q)$ Cosmology: Background, Stability, and Perturbations in the First Connection Branch

We re-examine the problem of mimicking the standard cosmological model, characterized by $j=1$ (where $j$ is the cosmographic jerk parameter), within the context of the first connection branch of $f(Q)$ gravity. While this problem has previously been addressed via reconstruction techniques$-$yielding the analytic form $f(Q)=-2Λ+αQ + β\sqrt{-Q}$ with $Q=-6H^2$ $-$here we tackle this problem from two distinct perspectives, applying either a cosmographic closure strategy or an auxiliary-variable hierarchy approach to the traditional dynamical systems formulation. Remarkably, the cosmographic closure renders the dynamical system integrable for $Λ$CDM-mimicking $f(Q)$ models. Consequently, we obtain closed-form analytical solutions for all relevant cosmological quantities at both the background and linear perturbation levels, with the perturbative solutions elegantly expressed in terms of generalized Heun functions. Furthermore, we analyze the structural stability of the $Λ$CDM-mimicking phase space against small kinematic deviations from $j=1$, demonstrating the robustness of these solutions. Our approach provides a systematic route to studying $Λ$CDM-mimicking dynamics without requiring a closed-form analytic reconstruction of the underlying action. Finally, we utilize this framework to establish a direct comparison between $Λ$CDM-mimicking dynamics in the first connection branch of $f(Q)$ gravity and those in $f(R)$ gravity.

gr-qc↗

arXiv2026

Beyond $j=1$: Observational Constraints on Almost-$Λ$CDM Cosmologies

The cosmographic condition $j(z)=1$ provides the kinematical signature of the spatially flat $Λ$CDM model independently of any specific dark-energy or modified-gravity theory. We investigate the extent to which current observations permit departures from this condition by considering three phenomenological ``almost-$Λ$CDM'' cosmographic closures, in which the cosmic jerk differs slightly from unity through a small deformation parameter $ε$. The models are constrained using Markov Chain Monte Carlo analyses of recent DESI baryon acoustic oscillation measurements together with compressed Planck cosmic microwave background likelihoods and the Union3, Pantheon+, and DESY5 Type Ia supernova compilations. Rather than assuming a parameterized dark-energy equation of state, our cosmographic framework reconstructs the expansion history directly from observations, with the effective dark-energy equation of state emerging as a derived quantity. We find that all three closures are tightly constrained to the vicinity of the $Λ$CDM cosmographic fixed point, with Planck data driving the preferred evolution toward $j_0\simeq1$ and $w_{\rm DE,0}\simeq-1$. Despite their distinct kinematical constructions, the reconstructed dark-energy evolution consistently exhibits smooth freezing behaviour close to $w=-1$, without crossing the phantom divide. Model comparison using the Akaike and Bayesian information criteria shows that the almost-$Λ$CDM models remain statistically competitive with standard dark-energy parameterizations while requiring fewer assumptions about the functional form of $w(z)$. These results demonstrate the power of model-independent cosmography for constraining the cosmic expansion history and provide a natural framework for future studies of cosmological perturbations and structure formation.

astro-ph.CO↗

arXiv2026

Unified dynamical system formulations for $f(R,ϕ,X)$ gravity with applications to nonminimal derivative coupling and $R^2$-Higgs inflation

Two different dynamical system formulations are presented that can be implemented to analyze a rather large class of modified gravity theories within the generic $f(R,ϕ,X)$ family. As illustrative examples, the first and the second formulation is applied to study the phase space of a toy model of the Non-Minimal Derivative Coupling (NMDC) without a potential, and the mixed $R^2$-Higgs inflation model, respectively. The first dynamical system formulation applied to the toy NMDC model, although able to identify several invariant submanifolds, fails to fully investigate the fixed point structure, as all the fixed points turn out to be non-hyperbolic. We, however, discover an interesting feature that the qualitative dynamics are independent of the coupling strength between the Ricci scalar and the scalar field derivative for the particular toy model under consideration. The second dynamical system formulation applied to the mixed $R^2$-Higgs inflation model performs much better, being able to correctly reduce to the individual phase spaces of the $R^2$ and Higgs inflation separately in special cases, as well as correctly delivering the expected invariant submanifolds and fixed points. For the mixed $R^2$-Higgs case, illustrative phase portraits are provided for a somewhat better visual understanding of the dynamics.

gr-qc↗

arXiv2026

Reconstructing the slope of a nearly flat quintessence potential from cosmography

We revisit thawing quintessence models with nearly flat scalar-field potentials using a cosmographic framework. Earlier work indicates that the cosmographic reconstruction of the slope $λ=-(dV/dϕ)/V$ of the quintessence potential in the general case requires the knowledge of the cosmographic paremeters up to the jerk parameter $j$. In this work we show that the slow-roll conditions $[(dV/dϕ)/V]^2 \ll 1$ and $|(d^2V/dϕ^2)/V| \ll 1$ allow the reconstruction of the slope of a nearly flat potential with knowledge of only the deceleration parameter $q$ (and the density parameter $Ω_ϕ$). Confronting the assumption of near-flatness with the cosmographic data after DESI DR2, however, reveals possible tension between the two. We further show that these models exhibit attractor behaviour in the $w$--$Ω_ϕ$ and $w$--$w'$ phase planes, corresponding to a universal thawing evolution with $w \approx -1$ at early times. We also derive the corresponding relation in the cosmographic $q$--$j$ plane and show that different cosmological expansion histories can produce the same thawing evolution. Nevertheless, all viable trajectories remain close to the $Λ$CDM limit $j=1$.

gr-qc↗

arXiv2026

Constraining Scale-Dependent Growth in $f(R)$ Gravity with Future 21 cm Surveys

Recent observations, particularly from DESI, have provided intriguing hints of dynamical behaviour in late-time dark energy. Modified gravity theories offer a compelling framework for interpreting such phenomena, with $f(R)$ gravity emerging as one of the most extensively studied examples. A central challenge in these models, however, lies in determining the precise functional form of $f(R)$. Nevertheless, several viable models have been proposed that successfully reproduce the standard $Λ$CDM cosmology at high red shifts while generating late-time cosmic acceleration without an explicit dark energy component. Within this framework, the evolution of the linear matter density contrast becomes scale dependent, leading to a growth index that varies with both scale and redshift. In this work, we explore the capability of forthcoming 21 cm observations to constrain the growth index, as well as the combined neutral hydrogen (HI) bias and growth-rate parameter. Our results indicate that future 21 cm surveys can provide meaningful, though moderate, support for these modified gravity scenarios.

astro-ph.CO↗

arXiv2026

Direct cosmographic reconstruction of the quintessence potential

We derive expressions for the first and second derivatives of the quintessence potential $V(ϕ)$, in terms of $λ= -V^{\prime}/V$ and $Γ= (V^{\prime \prime}/V)/(V^\prime/V)^2$, as functions of the quintessence density fraction $Ω_ϕ$ and the cosmographic parameters $q$, $j$, and $s$. Our mapping is not explicitly a function of the equation of state parameter $w$. We use these results, along with recent observational data, to derive expansions of $V(ϕ)$ about the present-day value of the scalar field, $ϕ_0$.

gr-qc↗

arXiv2026

Scale-free cluster-cluster aggregation during polymer collapse

An extended polymer collapses to form a globule when subjected to a quench below the collapse transition temperature. The process begins with the formation of clusters of monomers or ``pearls''. The nascent clusters merge, resulting in growth of the average cluster size $C_s$, eventually leading to a single globule. The aggregation of the clusters are known to be analogous to droplet coalescence. This suggests a striking resemblance between such an aggregation and cluster-cluster aggregation found in many {particle systems}, like in colloidal self-assembly, typically characterized by a universal dynamic scaling behavior. Motivated by that, here, we verify the presence of such dynamic scaling during the collapse of a polymer with varying bending stiffness $κ$, using molecular dynamic simulations. We probe the dynamics via time evolution of the size distribution of clusters $N_s(t)$ and growth of $C_s(t)$. Irrespective of $κ$, we observe the power-law scalings $C_s(t)\sim t^z$ and $N_s(t)\sim t^{-w} s^{-τ}$, of which only the cluster growth is universal with {$z\approx 1.67$.} Importantly, our results indeed show that $N_s(t)$ exhibits a dynamic scaling of the form $N_s(t)\sim s^{-2}f(s/t^z)$, indicative of a scale-free cluster growth. Interestingly, for flexible and weakly stiff polymers the dynamic exponents obey the relation $w=2z$, as also found in diffusion-controlled cluster-cluster aggregation of particles. For $κ\ge 5$, the exponents show deviation from this relation, which grows continuously with $κ$. We identify the differences in local structures of the clusters formed, leading to variations in cluster-size dependence of the effective diffusion constant to be the origin of the above deviation. We also discuss potential experimental strategies to directly visualize the observed dynamic scaling in a collapsing polymer.

cond-mat.soft↗

arXiv2026

Theory space and stability analysis of General Relativistic cosmological solutions in modified gravity

Some aspects of two General Relativistic cosmological solutions, an exact $Λ$CDM-like cosmological solution $j=1$ ($j$ is cosmographic jerk parameter), and a specifically designed toy cosmological solution $j=1+3\varepsilon(q-1/2)$ ($q$ is cosmographic deceleration parameter, $0<|\varepsilon|<1$) that is capable of accommodating a phantom crossing scenario as suggested by DESI DR2, are studied within the context of $f(R)$ gravity, by portraying them as a \emph{flow} in the 2-dimensional \emph{theory space} spanned by the quantities $r=\frac{R f'}{f}, m=\frac{R f''}{f'}$. For the $f(R)$ theories exactly reproducing a background $Λ$CDM-like expansion history $j=1$, it is shown by means of a \emph{cosmographic} reconstruction approach that the curvature degree of freedom need not necessarily behave like an effective cosmological constant, and that cosmologies under different possible such theories lead to different possible values of $Ω_{m0}$. With the theory space analysis, it is also shown that $Λ$CDM-mimicking $f(R)$ cosmologies that asymptote to General Relativistic $Λ$CDM in the limit $q\to1/2$, are prone to instability under small homogeneous and isotropic perturbation, casting a doubt on achieving an exact $Λ$CDM-like cosmological solution $j=1$ within $f(R)$ gravity. Regarding the toy cosmological solution $j=1+3\varepsilon(q-1/2)$ that is capable of accommodating a phantom crossing scenario, it is shown that possible underlying $f(R)$ theories that admit it as a solution are inevitably plagued by tachyonic instability ($f''(R)<0$). All the above physically interesting conclusions are derived without explicitly reconstructing, even numerically, the functional form of the underlying $f(R)$, which demonstrates the edge of the $r$-$m$ theory space analysis over the traditional explicit reconstruction approach.

gr-qc↗

arXiv2025

A Unified Dynamical Systems Framework for Cosmology in $f(Q)$ Gravity: Generic Features Beyond the Coincident Gauge

We present a unified dynamical systems framework for spatially flat FLRW cosmology in $f(Q)$ gravity, covering all three connection branches via a single set of Hubble-normalised variables without fixing $f(Q)$ \textit{a priori}. This connection-agnostic, model-independent approach enables direct comparison across branches and reveals generic structural features that are not apparent in model or connection-specific analyses. Beyond fixed points, we identify invariant submanifolds, model-independent trajectories, and viable phase-space regions common to multiple branches. For a broad class of viable $f(Q)$ models, we find generic de Sitter attractors and matter-dominated points in non-coincident branches, ensuring late-time acceleration without fine-tuning. An invariant submanifold is shown to reproduce $Λ$CDM-like backgrounds despite dynamics distinct from GR, offering a geometric origin for cosmic acceleration detectable only at the perturbation level. On this submanifold, a first integral enables analytic reconstruction of the dynamical connection and uncovers hidden conservation laws. While trivial connections display strong parameter dependence, nontrivial branches often exhibit parameter-independent behaviour. We also analyse the variation of the effective gravitational coupling $κ_{\text{eff}}=\frac{1}{f_Q}$ across branches, providing observational constraints that bridge theory and data. Applying the framework to $f(Q)=αQ+β(-Q)^n$, we recover late-time acceleration and $Λ$CDM-like behaviour without vacuum energy. Finally, we propose a general route for extending dynamical systems analysis to broader classes of $f(Q)$ models using the $m_i$-hierarchy method, which enables closure of the autonomous system for models previously inaccessible to standard approaches.

gr-qc↗

arXiv2025

LLM For Loop Invariant Generation and Fixing: How Far Are We?

A loop invariant is a property of a loop that remains true before and after each execution of the loop. The identification of loop invariants is a critical step to support automated program safety assessment. Recent advancements in Large Language Models (LLMs) have demonstrated potential in diverse software engineering (SE) and formal verification tasks. However, we are not aware of the performance of LLMs to infer loop invariants. We report an empirical study of both open-source and closed-source LLMs of varying sizes to assess their proficiency in inferring inductive loop invariants for programs and in fixing incorrect invariants. Our findings reveal that while LLMs exhibit some utility in inferring and repairing loop invariants, their performance is substantially enhanced when supplemented with auxiliary information such as domain knowledge and illustrative examples. LLMs achieve a maximum success rate of 78\% in generating, but are limited to 16\% in repairing the invariant.

cs.SE↗

arXiv2025

Dynamical dark energy in models with evolution close to $Λ$CDM

In this communication we address whether or not there is an equivalence between the kinematical and dynamical descriptions of the spatially flat $Λ$CDM model. We address this by investigating whether an almost $Λ$CDM expansion history ($j(z)\approx1$) corresponds to an almost $Λ$CDM model ($w_{\rm DE}(z)\approx-1$) by considering two particular explicit examples. At least for the cases considered, this turns out not to be the case. Instead, what we find is that an almost $Λ$CDM cosmic evolution rather corresponds to an \emph{almost unified dark fluid model}. Considering that one never gets the exact condition $j(z)=1$ from any cosmographic data sets, this raises further questions on whether the $Λ$CDM model is the best candidate for the standard model of the evolution of the universe.

gr-qc↗

arXiv2025

Teaching an Old LLM Secure Coding: Localized Preference Optimization on Distilled Preferences

LLM generated code often contains security issues. We address two key challenges in improving secure code generation. First, obtaining high quality training data covering a broad set of security issues is critical. To address this, we introduce a method for distilling a preference dataset of insecure and secure code pairs from frontier LLMs, along with a security reasoning that explains the issues and the fix. The key idea here is to make use of security knowledge sources to devise a systematic prompting strategy that ensures broad coverage. Second, aligning models to secure code requires focusing on localized regions of code. Direct preference optimization methods, like SimPO, are not designed to handle these localized differences and turn out to be ineffective. We address this with a new localized preference optimization algorithm that masks the security related tokens in both the winning (secure) and losing (insecure) responses. To prevent loss in code quality, we also add a regularizer. Evaluations show that both training on our dataset, DiSCo, and the new preference optimization algorithm, LPO, yield substantial reductions in code insecurity while also improving overall code quality. Code and dataset are available at https://github.com/StonyBrookNLP/disco-lpo.

cs.CR↗

arXiv2025

A generic dynamical system formulation for Bianchi-I cosmology with isotropic fluid in $f(Q)$ gravity

In this article, we present a generic dynamical system formulation for Bianchi-I cosmology in the presence of an isotropic fluid within the coincident gauge connection branch and one of the non-coincident gauge connection branches of $f(Q)$ gravity theory. For both the connection branches under consideration, we start from the generic Bianchi-I cosmological field equations in $f(Q)$ and present a prescription of how one can construct an autonomous dynamical system in terms of the standard Hubble-normalized dimensionless dynamical variables once an $f(Q)$ theory is provided. Particular care has been taken to single out the physically viable regions in the phase space for each of the models under consideration. This results in the finding that, for both of the connection branches under consideration, the Kasner solution marginally violates the key physical viability condition of positive effective gravitational coupling ($f_Q>0$) for all the models considered, whereas a physically viable de-Sitter future attractor appears in all the models, except for the very special case of the monomial model within the coincident gauge connection. In the context of the early universe cosmology, we find that isotropization of a homogeneously perturbed inflating FLRW universe is a generic model-independent feature in the coincident gauge, whereas the isotropization of a homogeneously perturbed pre-bounce ekpyrotically contracting FLRW universe is, although not completely generic, but a likely scenario.

gr-qc↗

arXiv2025

ClassInvGen: Class Invariant Synthesis using Large Language Models

Formal program specifications in the form of preconditions, postconditions, and class invariants have several benefits for the construction and maintenance of programs. They not only aid in program understanding due to their unambiguous semantics but can also be enforced dynamically (or even statically when the language supports a formal verifier). However, synthesizing high-quality specifications in an underlying programming language is limited by the expressivity of the specifications or the need to express them in a declarative manner. Prior work has demonstrated the potential of large language models (LLMs) for synthesizing high-quality method pre/postconditions for Python and Java, but does not consider class invariants. In this work, we describe ClassInvGen, a method for co-generating executable class invariants and test inputs to produce high-quality class invariants for a mainstream language such as C++, leveraging LLMs' ability to synthesize pure functions. We show that ClassInvGen outperforms a pure LLM-based technique to generate specifications (from code) as well as prior data-driven invariant inference techniques such as Daikon. We contribute a benchmark of standard C++ data structures along with a harness that can help measure both the correctness and completeness of generated specifications using tests and mutants. We also demonstrate its applicability to real-world code by performing a case study on several classes within a widely used and high-integrity C++ codebase.

cs.AI↗

arXiv2025

Reproducing $Λ$CDM-like Solutions in $f(Q)$ Gravity: A Comprehensive Study Across All Connection Branches

Given the remarkable success of the $Λ$CDM model in fitting various cosmological observations, a pertinent question in assessing the phenomenological viability of modified gravity theories is whether they can reproduce an exactly $Λ$CDM-like cosmic background evolution. In this paper, we address this question in the context of $f(Q)$ gravity, where $Q$ denotes the nonmetricity scalar. It is known that there are three possible symmetric teleparallel connection branches that respect the cosmological principles of spatial homogeneity, isotropy, and global spatial flatness. By enforcing a $Λ$CDM-like background evolution via the cosmographic condition $j(z)=1$, where $j$ is the jerk parameter, we reconstruct the $Λ$CDM-mimicking $f(Q)$ theory for each of the three possible connection branches. For the first connection branch, also known as the ``coincident gauge'' in cosmology, we recover the previously known result that a theory of the form $f(Q)=-2Λ+αQ+β\sqrt{-Q}$ can exactly reproduce a $Λ$CDM-like cosmic evolution. Furthermore, we establish that the stability of the $Λ$CDM-like cosmic solution within this reconstructed $f(Q)$, as well as the robustness of the reconstructed $f(Q)$ form with respect to small errors in the astrophysical measurements of the jerk parameter. For the second connection branch, we analytically reconstruct the $Λ$CDM-mimicking $f(Q)$ to be of the form $f(Q)=-2Λ+αQ-βQ^2$. For the third connection branch, we could decouple the evolution equation for the dynamical connection function, which enabled us to perform a numerical reconstruction. Our analysis proves that, at least at the background level, it is possible to obtain $Λ$CDM-mimicking $f(Q)$ models for all the three possible connection branches.

gr-qc↗

arXiv2025

Density-field structures in a few systems undergoing velocity ordering

We consider two (off-lattice) varieties of out-of-equilibrium systems, viz., granular and active matter systems, that, in addition to displaying velocity ordering, exhibit fascinating pattern formation in the density field, similar to those during vapor-liquid phase transitions. In the granular system, velocity ordering occurs due to reduction in the normal components of velocities, arising from inelastic collisions. In the active matter case, on the other hand, velocity alignment occurs because of the inherent tendency of the active particles to follow each other. Inspite of this difference, the patterns, even during density-field evolutions, in these systems can be remarkably similar. This we have quantified via the calculations of the two-point equal time correlation functions and the structure factors. These results have been compared with the well studied case of kinetics of phase separation within the framework of the Ising model. Despite the order-parameter conservation constraint in all the cases, in the density field, the quantitative structural features in the Ising case is quite different from those for the granular and active matters. Interestingly, the correlation function for the latter varieties, particularly for an active matter model, quite accurately describes the structure in a real assembly of biologically active particles.

cond-mat.soft↗

arXiv2024

A model-independent compact dynamical system formulation for exploring bounce and cyclic cosmological evolutions in $f(R)$ gravity

Using the dynamical systems approach together with the cosmographic parameters, we present a model-independent dynamical system formulation for cosmology in f(R) gravity. The formulation is model-independent in the sense that one needs to specify not a particular functional form of f(R) a-priori, but rather a particular cosmological evolution, which fixes the cosmography. In a sense, our approach is the way around the reconstruction method. This is shown using both non-compact and compact dynamical variables. The focus in this paper is on the compact analysis since we demonstrate the applicability of this formulation using examples of bouncing and cyclic cosmology. In particular, our analysis reveals, in a model-independent manner, the problem of achieving such cosmologies when the universe is globally spatially flat and devoid of matter.

gr-qc↗