Despite the significant accomplishments of general relativity, numerous unresolved issues persist in our understanding of the cosmos. One of the most perplexing challenges is the ongoing accelerated expansion of the Universe, which continues to elude a complete explanation. Consequently, scientists have proposed various alternative theories to GR in pursuit of a deeper understanding. In our analysis, we delve into the recently proposed modified $f(Q)$ gravity, where $Q$ represents the non-metricity scalar responsible for gravitational effects. Specifically, we investigate a cosmological model characterized by the functional form $f(Q) = Q+\alpha Q^n$, where $\alpha$ (with $\alpha \neq 0$) and $n$ serve as free parameters. Utilizing this functional form, we construct our Hubble rate, incorporating a specific equation of state to describe the cosmic fluid. Furthermore, we leverage a dataset consisting of 31 data points from Hubble measurements and an additional 1048 data points from the Pantheon dataset. These data serve as crucial constraints for our model parameters, and we employ the Markov Chain Monte Carlo (MCMC) method to explore the parameter space and derive meaningful results. With our parameter values constrained, our analysis yields several noteworthy findings. The deceleration parameter suggests a recent accelerated phase in the cosmic expansion. In addition, the EoS parameter paints a portrait of dark energy exhibiting phantom-like characteristics. Furthermore, we delve into the application of cosmological diagnostic tools, specifically the statefinder and the $Om(z)$ diagnostics. Both of these tools align with our previous conclusions, confirming the phantom-like behavior exhibited by our cosmological model. These results collectively contribute to our understanding of the dynamic interplay between gravity, dark energy, and the expanding cosmos.

We study the structure of the Hilbert space of gauged matrix models with a global symmetry. In the first part of the paper, we focus on bosonic matrix models with $U(2)$ gauge group and $SO(d)$ global symmetry, and consider singlets under both the gauge and global symmetry. We show how such "double-gauged'' matrix models can be described in terms of a simpler $SO(3)$ single-matrix model. In the second part of the paper, we consider the so-called BMN subsector of the $\mathcal{N}=4$ $SU(N)$ super Yang-Mills theory, which is closely related to the BMN matrix model. Among the 1/16 BPS operators in this sector, "non-graviton'' operators were recently discovered, which are expected to relate to the microstates of supersymmetric $AdS_5$ black holes. We show that a double gauging of this model, where one projects onto $SU(3)_R$ $R$-symmetry singlets, considerably simplifies the analysis of the non-graviton spectrum. In particular, for low values of $N$, we show that (almost) all graviton operators project out of the spectrum, while important classes of non-graviton operators remain. In the $N=3$ case, we obtain a closed form expression for the superconformal index of singlet non-gravitons, which reveals structural features of their spectrum.

We investigate FLRW cosmology in the framework of symmetric teleparallel $f(Q)$ gravity with a nonminimal coupling between dark matter and the gravitational field. In the noncoincidence gauge, the field equations admit an equivalent multi-scalar field representation, which we investigate the phase-space using the Hubble-normalization approach. We classify all stationary points for arbitrary function $f(Q)$ and we discuss the physical properties of the asymptotic solutions. For the power-law theory, we perform a detailed stability analysis and show that the de Sitter solution is the unique future attractor, while the matter-dominated point appears as a saddle point. Moreover, there exist a family of scaling solutions that can be related to inflationary dynamics. In contrast with uncoupled $f(Q)$ models, the presence of the coupling introduces a viable matter-dominated era alongside late-time accelerated expansion. Our study shows that the coupling function plays a crucial role in cosmological dynamics in $f(Q)$ gravity.

Quiver Yangians are infinite-dimensional algebras capturing the BPS structure of a large class of supersymmetric models. Quiver theories related by Seiberg duality are expected to have isomorphic quiver Yangians, and this isomorphism has previously been shown for quivers corresponding to generalised conifold geometries. In this work, we present an explicit isomorphism for the two Seiberg dual phases of the F0 quiver theory, which falls outside of the above class. Some aspects of our construction are similar to the known cases, while others appear to be specific to the F0 quiver. In particular, the map involves square roots of operators bilinear in the fermionic fields of the mode being dualised.

We introduce a method that generates ground-state ansatzes for quantum many-body systems which are both analytically tractable and accurate over wide parameter regimes. Our approach leverages a custom symbolic language to construct tensor network states (TNS) via an evolutionary algorithm. This language provides operations that allow the generated TNS to automatically scale with system size. Consequently, we can evaluate ansatz fitness for small systems, which is computationally efficient, while favouring structures that continue to perform well with increasing system size. This ensures that the ansatz captures robust features of the ground state structure. Remarkably, we find analytically tractable ansatzes with a degree of universality, which encode correlations, capture finite-size effects, accurately predict ground-state energies, and offer a good description of critical phenomena. We demonstrate this method on the Lipkin-Meshkov-Glick model (LMG) and the quantum transverse-field Ising model (TFIM), where the same ansatz was independently generated for both. The simple structure of the ansatz allows us to obtain exact expressions for the expectation values of local observables as well as for correlation functions. In addition, it permits symmetries that are broken in the ansatz to be restored, which provides a systematic means of improving the accuracy of the ansatz.

Studying large samples of massive, passively evolving galaxies (called cosmic chronometers, CC) provides us with the unique ability to measure the Universe's expansion history without assuming a cosmological model. The Dark Energy Spectroscopic Instrument (DESI) DR1 is currently the largest, publicly available, homogeneous set of galaxies with reliable spectroscopic redshifts, and covers a wide range in redshift. We extracted all massive galaxies (stellar mass \log M_{\star}/M_{\odot} > 10.75, and velocity dispersion \sigma > 280 km s$^{-1}$), with no emission in [OII] $\lambda$ 3727 $Å$, with reliable redshifts as well as reliable D4000$_{\rm n}$ measurements from DR1. From this sample of 360 000 massive, passive galaxies, we used D4000$_{\rm n}$ and the method of cosmic chronometers to get three new direct, independent measurements of $H(z)=$ 88.48 $\pm\ 0.57(\rm stat) \pm 12.32(\rm syst)$, $H(z)=$ 119.45 $\pm\ 6.39(\rm stat) \pm 16.64(\rm syst)$, and $H(z)= 108.28 \pm 10.07(\rm stat) \pm 15.08(\rm syst)$ $\rm km\ s^{-1}\ Mpc^{-1}$ at $z=0.46$, $z=0.67$, and $z=0.83$, respectively. This sample, which covers 0.3 < z < 1.0, is the largest CC sample to date, and we reach statistical uncertainties of 0.65$\%$, 5.35$\%$, and 9.30$\%$ on our three measurements. Our measurements show no significant tension with the $\textit{Planck}$ $\Lambda$CDM cosmology. In our analysis, we also illustrate that even amongst samples of massive, passive galaxies, the effect of downsizing can clearly be seen.

Spin networks in loop quantum gravity provide a kinematical picture of quantum geometry but lack a natural mechanism for dynamical Dirac-type evolution, while the Wheeler--DeWitt equation typically enters only as an imposed constraint. We propose a stochastic framework in which each spin-network edge carries helicity-resolved amplitudes -- two-state internal labels that undergo Poisson-driven flips. The resulting coupled master equations, after analytic continuation and the introduction of a fundamental length scale, generate Dirac-type dynamics on discrete geometry. At long times, the same process relaxes to helicity-symmetric equilibrium states, which are shown to satisfy a Wheeler--DeWitt-type condition. In this way, both quantum evolution and the gravitational constraint emerge within a single probabilistic framework. Our approach thus provides a background-independent and stochastic route to quantum geometry, offering an alternative to canonical quantization and a fresh perspective on the problem of time.

When simulating the dynamics of open quantum systems with quantum computers, it is essential to accurately approximate the system's behaviour while preserving the physicality of its evolution. Traditionally, for Markovian open quantum systems, this has been achieved using first and second-order Trotter-Suzuki product formulas or probabilistic algorithms. In this work, we introduce novel non-probabilistic algorithms for simulating Markovian open quantum systems using randomisation. Our methods, including first and second-order randomised Trotter-Suzuki formulas and the QDRIFT channel, not only maintain the physicality of the system's evolution but also enhance the scalability and precision of quantum simulations. We derive error bounds and step count limits for these techniques, bypassing the need for the mixing lemma typically employed in Hamiltonian simulation proofs. We also present two implementation approaches for these randomised algorithms: classical sampling and quantum forking, demonstrating their gate complexity advantages over deterministic Trotter-Suzuki product formulas. This work is the first to apply randomisation techniques to the simulation of open quantum systems, highlighting their potential to enable faster and more accurate simulations.

Context. Open clusters (OCs) are valuable probes of stellar population characteristics. Their age and metallicity provide insights into the chemical enrichment history of the Milky Way. By studying the metallicity of OCs, we can explore the spatial distribution of composition across the Galaxy and understand stellar birth radii through chemical tagging. However, inferring the original positions of OCs remains a challenge. Aims. This study investigates the distribution of metallicity in the solar neighborhood using data from Gaia DR3 and LAMOST spectra. By measuring accurate ages and metallicities, we aim to derive birth radii and understand stellar migration patterns. Methods. We selected 1131 OCs within 3 kpc of the Sun from Gaia DR3 and LAMOST DR8 low-resolution spectra (R=1800). To correct the LAMOST data, we incorporated high-resolution spectra from GALAH DR3 (R=28000) using an artificial neural network. The average metallicity of the OCs was derived from reliable [Fe/H] values of their members. We examined the metallicity distribution across the Galaxy and calculated birth radii based on age and metallicity. Results. The correction method reduces the systematic offset in LAMOST data. We found a metallicity gradient as a function of Galactocentric distance and guiding radii. Comparisons with chemo-dynamic simulations show that observed metallicity values are slightly lower than predicted when uncertainties are ignored, but the metallicity gradients align with previous studies. We also inferred that many OCs near the Sun likely originated from the outer Galactic disk.

Several cosmological observations (e.g., Cosmic Microwave Background (CMB), Supernovae Type Ia, and local distance ladder measurements such as Cepheids) have been used to measure the global expansion rate of the Universe, i.e., the Hubble constant, $H_{0}$. However, these precision measurements have revealed tensions between different probes that are proving difficult to solve. Independent, robust techniques must be exploited to validate results or mitigate systematic effects. We use the Cosmic Chronometer (CC) method, which leverages the differential age evolution of passive galaxies, to measure $H(z)$, without any assumption of the underlying cosmology. Unlike previous CC studies, we used only brightest cluster galaxies (BCGs), the oldest and most massive galaxies in the Universe, to construct a pure and homogeneous sample. In this work we used a sample of 53 BCGs in massive, Sunyaev-Zel'dovich selected galaxy clusters (0.3 < z < 0.7) with Southern African Large Telescope (SALT) spectroscopic observations. We used optical spectra to measure D4000$_{\rm n}$ of the BCGs to obtain a new direct measurement of $H(z) = 72.1 \pm 33.9(\rm stat) \pm 7.3$(syst) km s$^{-1}$Mpc$^{-1}$at$z=0.5$. By using BCGs, we significantly reduced the systematic errors to 10% by minimising the stellar mass and metallicity dependence of the method. The dominant uncertainty, and limitation for our study, is statistical, and we need larger, homogeneous samples of the oldest, most massive galaxies. By using the $Planck$+BAO prior of $\Omega_{m}$ and $\Omega_{\Lambda}$, the projected Hubble constant is $H_{0}$ = $54.6 \pm 25.7(\rm stat) \pm 5.5$(syst) km s$^{-1}$ Mpc$^{-1}$, consistent with both CMB and Cepheid measurements.

Gamma-ray bursts (GRBs) have emerged as powerful cosmological probes for exploring the distant Universe, owing to their immense luminosities and detectability at high redshifts. Several empirical correlations have been established, particularly involving their energy properties. This work aims to enhance the precision of these correlations through joint spectral analysis, focusing on reducing uncertainties in both the spectral indices and the peak energy ($E_{\rm p}$) derived from spectral fitting. We extend previous studies using both traditional and novel spectral models, utilizing a sample of 37 GRBs observed by the Fermi Gamma-ray Burst Monitor (GBM) and Large Area Telescope (LAT), incorporating the LAT Low-Energy (LLE) technique, over the period 2008-2024. Our analysis compares results from joint fits (GBM-LAT-LLE) against those from GBM-only fits. The study focuses on fitting time-integrated ${\rm T}_{90}$ and peak flux in the rest frame. Among the observable phenomenological correlations, we revisit the Amati and Yonetoku relations: the Amati relation links the intrinsic peak energy ($E_{i,\rm p}$) to the total isotropic energy ($E_{\rm iso}$) emitted during ${\rm T}_{90}$, while the Yonetoku relation connects $E_{i,\rm p}$ to the isotropic luminosity ($L_{\rm iso}$). Refining these correlations aims to deepen our understanding of GRB energetics and improve the precision of cosmological parameter estimates derived from GRB observations.

GRB~160821B is the only short GRB detected to date at very high energy (VHE, $\gtrsim 100$ GeV). At a redshift $z=0.161$, it was detected by MAGIC telescopes approximately four hours since the trigger. VHE dataset was complied with the datasets of other wavelengths in between the timescale of 1.7 to 4 hours to construct the broadband spectral energy distribution (SED). In previous studies of GRB~160821B, synchrotron and external Compton (EC) model could explain the VHE emission better than the synchrotron and synchrotron self-Compton (SSC) model. Although, these fits were mostly eyeballing data without any optimisation. Our model includes the combination of synchrotron, SSC, and EC models with Markov Chain Monte Carlo (MCMC) techniques. Our analysis reveals that the EC contribution is negligible in comparison with the SSC and our model explains the VHE data well for the wind medium. We found that GRB~160821B is the least energetic VHE GRB and it occurred in high density wind medium which is quiet unusual for a short GRB. But like other long-duration VHE GRBs, GRB~160821B occurred in a poorly magnetised medium. As there is no statistical study on afterglow modelling of short GRB sample, we compare the inferred properties of GRB~160821B with other VHE GRBs. It stands out distinctively in the $E_{k, \rm iso}$ - $\epsilon_B$ parameter space and lies outside the 3-$\sigma$ region of the correlation. In future, more VHE detections of short GRBs, in the CTA era, will provide crucial insights into the emission sites, radiation mechanisms, and particle acceleration, as well as their connection to long GRBs.

We explore the cosmological consequences of a modified cosmology inspired by string T-duality. We incorporate the zero-point length correction, $l_0$, into the gravitational potential and derive the modified Friedmann equations via thermodynamic approach at the apparent horizon of a Friedmann-Robertson-Walker (FRW) universe. The resulting framework introduces a dimensionless coupling parameter $\beta\sim l_0^2H_0^2$ quantifying deviations from the standard $\Lambda$CDM model. Using Bayesian inference with \textsc{Cobaya} and MCMC sampling, we constrain the model parameter against late-time observations, including PantheonPlus and Union3 Type~Ia supernovae, cosmic chronometers, DESI~DR2 BAO measurements, and Amati-calibrated GRBs. The joint analysis yields an upper bound $\beta \lesssim \mathcal{O}(10^{-3})$ (68\% C.L.), implying that departures from $\Lambda$CDM are extremely small within current precision. Model comparison through the Akaike Information Criterion shows that the $\Lambda$CDM and T-duality models provide statistically equivalent fits to the data, exhibiting only a marginal preference for $\Lambda$CDM. These results provide the first quantitative observational constraints on string T-duality inspired modified cosmology and underscore the potential of future high-precision surveys to test quantum-gravity induced corrections in a late-time universe.

UGCA 320 is a gas-rich dwarf irregular galaxy which belongs to a nearby, relatively isolated group of dwarf galaxies. Here, we combine multi-band HST imaging data with deep long-slit SALT/RSS and integral-field VLT/MUSE spectral data to study the stellar and ionized gas components of UGCA 320. Our imaging data analysis reveals a very blue (V-I~0.1 mag), flattened radial colour profile. We detect an abundance of ionized gas in UGCA 320 powered mostly by recent star formation. The stellar disc in UGCA 320 is populated predominantly by young (~120 Myr) and metal-poor (~15-30 per cent solar metallicity) stars and it rotates in the same sense as the ionized gas disc but with higher rotation velocities, and possibly in different planes. Our analysis reveals a sharp transition in the kinematic properties of the discs at radius ~10" (~0.3 kpc) and distortions in the outer disc region. We show that these features are consistent with a recent tidal interaction most likely with its close neighbour - UGCA 319. We discuss our results in the context of interacting dwarf galaxies and also show that similar inferences can be made independently from the long-slit data analysis as with the integral-field data.

We present a computational method to automatically design the n-qubit realisations of quantum algorithms. Our approach leverages a domain-specific language (DSL) that enables the construction of quantum circuits via modular building blocks, making it well-suited for evolutionary search. In this DSL quantum circuits are abstracted beyond the usual gate-sequence description and scale automatically to any problem size. This enables us to learn the algorithm structure rather than a specific unitary implementation. We demonstrate our method by automatically designing three known quantum algorithms--the Quantum Fourier Transform, the Deutsch-Jozsa algorithm, and Grover's search. Remarkably, we were able to learn the general implementation of each algorithm by considering examples of circuits containing at most 5-qubits. Our method proves robust, as it maintains performance across increasingly large search spaces. Convergence to the relevant algorithm is achieved with high probability and with moderate computational resources.

Randomized algorithms such as qDRIFT provide an efficient framework for quantum simulation by sampling terms from a decomposition of the system's generator. However, existing error bounds for qDRIFT scale quadratically with the norm of the generator, limiting their efficiency for large-scale closed or open quantum system simulation. In this work, we refine the qDRIFT error bound by incorporating Jensen's inequality and a careful treatment of the integral form of the error. This yields an improved scaling that significantly reduces the number of steps required to reach a fixed simulation accuracy. Our result applies to both closed and open quantum systems, and we explicitly recover the improved bound in the Hamiltonian case. To demonstrate the practical impact of this refinement, we apply it to three settings: quantum chemistry simulations, dissipative transverse field Ising models, and Hamiltonian encoding of classical data for quantum machine learning. In each case, our bound leads to a substantial reduction in gate counts, highlighting its broad utility in enhancing randomized simulation techniques.

We investigate cosmology-driven modifications to Schwarzschild-like black hole spacetimes and analyze their impact on photon propagation, gravitational lensing, and shadow observation. The gravitational deflection angle is computed using the Rindler-Ishak method, which incorporates finite-distance corrections and provides a consistent framework for non-asym-ptotically flat spacetimes. The effective potential for null geodesics exhibits a single unstable maximum corresponding to the photon sphere, and we study photon orbits classified according to the critical impact parameter into capture, escape, and unstable circular trajectories. Our analysis shows that the deflection angle decreases with increasing model parameter $(\alpha)$, resulting in weaker light bending compared to the Schwarzschild case. In addition, we examine the angular diameter of the black hole shadow as measured by a static observer, highlighting its dependence on the cosmological modification parameters. These results suggest that high-precision astrometric and lensing observations can place meaningful constraints on cosmology-inspired modifications to gravity, thereby linking astrophysical black holes with cosmic expansion and offering a novel probe of gravitational physics in strong-field regimes.