arXiv subjects

Xin Ren

Publications and source records attributed to Xin Ren.

At least 19 recordsLinked to original sources

arXiv2026

A short review on Quintom dark energy theory

In this paper, we provide a short review on the Quintom dark energy theory. Firstly, we discuss the No-Go theorem associated with dynamical dark energy, then present some examples of models in which the equation of state (EoS) evolves with time and can cross $w=-1$ . Secondly, we discuss the bouncing universe and emergent universe with Quintom matter. Finally, we discuss the possibility of studying the nature of dark energy by measuring the Cosmic Microwave Background (CMB) polarization rotation angle.

astro-ph.CO↗

arXiv2026

Interstellar Object 3I/ATLAS Observed from Mars by China's Tianwen-1 Spacecraft

China's Tianwen-1 Mars orbiter successfully imaged the third interstellar object, 3I/ATLAS, during its close encounter with Mars using the onboard HiRIC CMOS camera. This is China's first deep-space observation of an astronomical object. These observations constitute the first imaging of this object from a vantage point significantly out of its orbital plane, providing a unique constraint on dust dynamics. Three observing epochs between 2025 September 30 and October 3 reveal clear changes in coma and tail morphology driven by the rapidly evolving viewing geometry. Comparison with Finson-Probstein dust dynamical models indicates that the coma is dominated by large grains with solar radiation pressure parameter $\beta \approx 10^{-3} $ - $10^{-2}$, corresponding to grain sizes of a few 100s $\mu$m. The extent of the sunward coma implies dust ejection velocities of $3$ - $10$ m s$^{-1}$. Despite the morphological evolution, the azimuthally averaged surface brightness profile remains nearly unchanged through the three epochs, transitioning from a radial slope near -1 close to the nucleus to slightly steeper than -1.5 at larger cometocentric distances, consistent with steady-state dust outflow accelerated by solar radiation pressure. Photometry yields an average $Af\rho \sim (2.0\pm0.2)\times10^4$ cm and a corresponding dust mass loss rate of $\dot{M} \sim 10^3$ kg s$^{-1}$.

astro-ph.EP↗

arXiv2026

Applications of the finite specializations of the $q$-deformed modular group

Recently, Morier-Genoud and Ovsienko introduced the $q$-deformed modular group. For the construction, they first gave a group $G_q \subset \operatorname{GL}(2, \mathbb{Z}[q^{\pm}])$ and then set $\operatorname{PSL}_q(2,\mathbb{Z}):=G_q/Z(G_q)$. We show that, for $\zeta \in \mathbb{C}^*$, $\operatorname{PSL}_q(2,\mathbb{Z})|_{q=\zeta}$ is finite, if and only if so is $G_q(\zeta):=G_q|_{q=\zeta} \subset \operatorname{GL}(2,\mathbb{C})$, if and only if $\zeta=\zeta_n$ for $n=2,3,4,5$, where $\zeta_n$ is a primitive $n$-th root of unity. Although this result is essentially available in the existing literature, we give a precise proof for further developments. For example, we show that the set of traces of elements in $G_q(\zeta)$ and the set of the special values at $\zeta$ of the normalized Jones polynomials of rational links are finite if and only if $\zeta =\zeta_n$ for $n=2,3,4,5$ and also for $n=6$. We also study the quantized Pythagorean triples.

math.QA↗

arXiv2025

Decoupling perturbations from background in $f(Q)$ gravity: the square-root correction and the impact on the $\sigma_8$ tension

We investigate a perturbation-level modification of symmetric teleparallel gravity of the form $f(Q)=F(Q)+M\sqrt{Q}$ and assess its potential to ease the $\sigma_8$ tension. The square-root term leaves the background expansion unchanged at the level of FLRW cosmology, while modifying the effective gravitational coupling and thereby providing a decoupling between background evolution and structure-growth. Using the latest redshift-space distortion data, including DESI DR1 Full-Shape measurements, we constrain the model through its impact on the growth observable $f\sigma_8(z)$ across three representative backgrounds: $\Lambda$CDM, an $H_0$-tension-reducing model, and a DESI-motivated dynamical dark energy scenario. In all cases, the square-root correction suppresses the growth of structure and induces a degeneracy with $\sigma_8$, leading to weaker constraints from current data. This allows for a wider range of $\sigma_8$ values consistent with Planck, with the effect being most pronounced in the $H_0$-tension-oriented background model. However, because RSD data constrain $f\sigma_8$ rather than $\sigma_8$ directly, a residual degeneracy between $M$ and $\sigma_8$ remains, indicating that future multi-probe analyses combining lensing and full-shape clustering will be required to determine whether the $\sqrt{Q}$ term represents a genuine signal of modified gravity.

astro-ph.CO↗

arXiv2025

Probing the sound speed and clustering of dark energy

Recent Dark Energy Spectroscopic Instrument (DESI) observations favor a dynamical dark energy component with a time-varying equation-of-state, potentially crossing the cosmological-constant boundary $w=-1$, challenging the standard $\Lambda$CDM paradigm. In this paper we present the first joint observational constraints on the clustering properties of such dynamical dark energy, using both the Parameterized Post-Friedmann (PPF) framework and the effective field theory (EFT) of dark energy. Combining DESI DR2 baryon acoustic oscillations with Planck 2018 cosmic microwave background data and the Union3 supernova sample, we constrain the effective sound speed $c_s^{2}$. For a time-varying equation-of-state, the degeneracy between $(1+w)$ and $c_s^{2}$ is broken, yielding the first meaningful constraint $\log_{10}c_{s}^{2}=-3.00^{+2.9}_{-0.99}$, while constant-$w$ models remain unconstrained. A complementary EFT analysis gives consistent results, favoring $c_s^{2}\sim 0.3$ or $0.4$. Our findings demonstrate that current data are now sensitive to the perturbative properties of dynamical dark energy, opening a new observational window on the nature of cosmic acceleration.

astro-ph.CO↗

arXiv2025

The Quintom theory of dark energy after DESI DR2

Observations from DESI DR2 are challenging the $\Lambda$CDM paradigm by suggesting that the equation-of-state parameter of dark energy evolves across $w = -1$, a phenomenon known as the Quintom scenario. Inspired by this development, we present a staged review of Quintom cosmology including its theoretical foundations, observational supports, and implications as well as possible extensions. We first trace the historical progression from Einstein's static cosmological constant to modern dynamical dark energy, summarizing recent cosmological constraints that favor an evolving $w(z)$ along time. A key focus is the theoretical no-go theorem for dark energy showing that no single canonical field or perfect fluid model can smoothly cross the $w = -1$ boundary. We then survey viable Quintom constructions, including two-field models, single-scalar fields with higher derivatives, modified gravity frameworks, interacting dark energy, and an effective field theory approach that unifies these mechanisms. Possible interactions of Quintom fields with ordinary matter and the potential roles in yielding non-singular universe solutions are discussed.

astro-ph.CO↗

arXiv2025

Modified gravity realizations of quintom dark energy after DESI DR2

We investigate the realization of quintom scenario for dynamical dark energy within modified gravity theories that can efficiently fit the recent observational datasets. Starting from a general effective field theory formulation of dark energy in metric-affine geometry, we derive the background action in unitary gauge and we demonstrate how both $f(T)$ and $f(Q)$ gravity can naturally realize quintom behavior through appropriate forms and parameter choices. Additionally, using the Gaussian process reconstruction of the latest DESI DR2 BAO data combined with SNe and CMB observations, we extract the reconstructed dark-energy equation-of-state parameter, showing that it exhibits quintom-type evolution, crossing the phantom divide from below. Moreover, through detailed parameter estimations and application of information criteria, we compare the model with the quadratic one and the $\Lambda$CDM model. Our results show that, due to its rich structure, modified gravity stands as one of the main candidates for the realization of the data-favoured dynamical dark energy.

astro-ph.CO↗

arXiv2025

Transposes in the $q$-deformed modular group and their applications to $q$-deformed rational numbers

The (right) $q$-deformed rational numbers was introduced by Morier-Genoud and Ovsienko, and its left variant, whose numerators and denominators are essentially the normalized Jones polynomials of rational links, by Bapat, Becker and Licata. These notions are based on continued fractions and the $q$-deformed modular group $\operatorname{PSL}_q(2,\mathbb{Z})$-actions. In this paper, we introduce the \textit{$q$-transpose} for matrices in $\operatorname{PSL}_q(2,\mathbb{Z})$ to refine the basic perspective of the theory. For example, we present a new proof and a refinement of a theorem of Leclere and Morier-Genoud stating that the trace of $A \in \operatorname{PSL}(2,\mathbb{Z})$ is always palindromic and sign coherent. We also show arithmetic/combinatorial results on left $q$-deformed rationals (e.g., the criterion for their palindromicity). Finally, we discuss the connection to the conjecture of Kantarc{\i} O\u{g}uz on circular fence posets.

math.CO↗

arXiv2025

Gaussian-process reconstructions and model building of quintom dark energy from latest cosmological observations

In this article we use the latest cosmological observations, including SNe, BAO, CC and RSD, to reconstruct the cosmological evolution via the Gaussian process. At the background level, we find consistency with the quintom dynamics for different data combinations and divide the characteristics of dark energy into three different categories, which are negative-energy dark energy, late-dominated dark energy and oscillating dark energy, respectively. Considering the effect of modified gravity on the growth of matter perturbations, the reconstruction results at the perturbative level show that we only need minor corrections to general relativity. Furthermore, we provide theoretical interpretation for the three different types of dynamical dark-energy behavior, in the framework of modified gravity, scalar fields, and dark-energy equation-of-state parametrizations. Finally, we show that all of these models can be unified in the framework of effective field theory.

astro-ph.CO↗

arXiv2024

Background-dependent and classical correspondences between $f(Q)$ and $f(T)$ gravity

$f(Q)$ and $f(T)$ gravity are based on fundamentally different geometric frameworks, yet they exhibit many similar properties. This article provides a comprehensive summary and comparative analysis of the various theoretical branches of torsional gravity and non-metric gravity, which arise from different choices of affine connection. We identify two types of background-dependent and classical correspondences between these two theories of gravity. The first correspondence is established through their equivalence within the Minkowski spacetime background. To achieve this, we develop the tetrad-spin formulation of $f(Q)$ gravity and derive the corresponding expression for the spin connection. The second correspondence is based on the equivalence of their equations of motion. Utilizing a metric-affine approach, we derive the general affine connection for static and spherically symmetric spacetime in $f(Q)$ gravity and compare its equations of motion with those of $f(T)$ gravity. Among others, our results reveal that, $f(T)$ solutions are not simply a subset of $f(Q)$ solutions; rather, they encompass a complex solution beyond $f(Q)$ gravity in black hole background.

gr-qc↗

arXiv2024

Multiple Kernel Clustering via Local Regression Integration

Multiple kernel methods less consider the intrinsic manifold structure of multiple kernel data and estimate the consensus kernel matrix with quadratic number of variables, which makes it vulnerable to the noise and outliers within multiple candidate kernels. This paper first presents the clustering method via kernelized local regression (CKLR). It captures the local structure of kernel data and employs kernel regression on the local region to predict the clustering results. Moreover, this paper further extends it to perform clustering via the multiple kernel local regression (CMKLR). We construct the kernel level local regression sparse coefficient matrix for each candidate kernel, which well characterizes the kernel level manifold structure. We then aggregate all the kernel level local regression coefficients via linear weights and generate the consensus sparse local regression coefficient, which largely reduces the number of candidate variables and becomes more robust against noises and outliers within multiple kernel data. Thus, the proposed method CMKLR avoids the above two limitations. It only contains one additional hyperparameter for tuning. Extensive experimental results show that the clustering performance of the proposed method on benchmark datasets is better than that of 10 state-of-the-art multiple kernel clustering methods.

cs.LG↗

arXiv2024

Observational test for $f(Q)$ gravity with weak gravitational lensing

In this article we confront a class of $f(Q)$ gravity models with observational data of galaxy-galaxy lensing. Specifically, we consider the $f(Q)$ gravity models containing a small quadratic correction when compared with General Relativity (GR), and quantify this correction by a model parameter $\alpha$. To derive the observational constraints, we start by extracting the spherically symmetric solutions which correspond to the deviations from the Schwarzschild solution that depends on the model parameter in a two-fold way, i.e., a renormalized mass and a new term proportional to $r^{-2}$. Then, we calculate the effective lensing potential, the deflection angle, the shear component, and the effective Excess Surface Density (ESD) profile. After that, we employ the group catalog and shape catalog from the SDSS DR7 for the lens and source samples respectively. Moreover, we handle the off-center radius as a free parameter and constrain it using the MCMC. Concerning the deviation parameter from GR we derive $\alpha=1.202^{+0.277}_{-0.179}\times 10^{-6} {\rm Mpc}^{-2}$ at 1 $\sigma$ confidence level, and then compare the fitting efficiency with the standard $\Lambda$CDM paradigm by applying the AIC and BIC information criteria. Our results indicate that the $f(Q)$ corrections alongside off-center effects yield a scenario that is slightly favored.

astro-ph.CO↗

arXiv2024

Testing Cotton gravity as dark matter substitute with weak lensing

Harada proposed a modified theory of gravity called Cotton gravity, and argued that it successfully explains the rotation curves of $84$ galaxies without the need of dark matter. In this work we use galaxy-galaxy lensing technique to test whether the modification effect of Cotton gravity can indeed be a viable substitute for dark matter. Using the spherically symmetric solution of Cotton gravity, we obtain the deflection angle via Gauss-Bonnet theorem and the weak lensing shear. We use five galaxy catalogs divided in 5 stellar mass bins from the Sloan Digital Sky Survey Data Release 7 (SDSS DR7), each of which is further divided into blue star forming galaxy and red passive galaxy sub-catalogs. We find that Cotton gravity on its own has significant deviation from the measured galaxy-galaxy lensing signals, thus it cannot replace the role of dark matter. If we consider the combination of dark matter and Cotton gravity, the modification is tightly constrained. Our analysis also applies to other modified gravity theories whose an additional linear term appears in the Schwarzschild solution.

astro-ph.CO↗

arXiv2024

Constrain the linear scalar perturbation theory of Cotton gravity

We perform a cosmological test of Cotton gravity, which describes gravity by cotton tensor. We assume in Cotton gravity the background evolution is the same as the flat FLRW background. We derive the cosmological perturbation theory of the scalar mode at the linear level, where the difference from the $\Lambda$CDM model is characterized by the parameter $\beta$. We incorporate Cotton gravity with a neutrino model and perform a Monte Carlo Markov Chain (MCMC) analysis using data from the Cosmic Microwave Background (CMB) and Sloan Digital Sky Survey (SDSS). The analysis constrains parameter $\beta=-0.00008^{+0.00080}_{-0.00104}$ at the 1-$\sigma$ confidence level. We conclude that currently, there is no obvious deviation between Cotton gravity and the $\Lambda$CDM model in the linear cosmological perturbation level for observations.

astro-ph.CO↗

arXiv2024

Quintom cosmology and modified gravity after DESI 2024

We reconstruct the cosmological background evolution under the scenario of dynamical dark energy through the Gaussian process approach, using the latest Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillations (BAO) combined with other observations. Our results reveal that the reconstructed dark-energy equation-of-state (EoS) parameter $w(z)$ exhibits the so-called quintom-B behavior, crossing $-1$ from phantom to quintessence regime as the universe expands. We investigate under what situation this type of evolution could be achieved from the perspectives of field theories and modified gravity. In particular, we reconstruct the corresponding actions for $f(R)$, $f(T)$, and $f(Q)$ gravity, respectively. We explicitly show that, certain modified gravity can exhibit the quintom dynamics and fit the recent DESI data efficiently, and for all cases the quadratic deviation from the $\Lambda$CDM scenario is mildly favored.

astro-ph.CO↗

arXiv2024

Data reconstruction of the dynamical connection function in $f(Q)$ cosmology

We employ Hubble data and Gaussian Processes in order to reconstruct the dynamical connection function in $f(Q)$ cosmology beyond the coincident gauge. In particular, there exist three branches of connections that satisfy the torsionless and curvatureless conditions, parameterized by a new dynamical function $\gamma$. We express the redshift dependence of $\gamma$ in terms of the $H(z)$ function and the $f(Q)$ form and parameters, and then we reconstruct it using 55 $H(z)$ observation data. Firstly, we investigate the case where ordinary conservation law holds, and we reconstruct the $f(Q)$ function, which is very well described by a quadratic correction on top of Symmetric Teleparallel Equivalent of General Relativity. Proceeding to the general case, we consider two of the most studied $f(Q)$ models of the literature, namely the square-root and the exponential one. In both cases we reconstruct $\gamma(z)$, and we show that according to AIC and BIC information criteria its inclusion is favoured compared to both $\Lambda$CDM paradigm, as well as to the same $f(Q)$ models under the coincident gauge. This feature acts as an indication that $f(Q)$ cosmology should be studied beyond the coincident gauge.

astro-ph.CO↗

arXiv2024

Arithmetic on $q$-deformed rational numbers

Recently, Morier-Genoud and Ovsienko introduced a $q$-deformation of rational numbers. More precisely, for an irreducible fraction $\frac{r}s>0$, they constructed coprime polynomials $\mathcal{R}_{\frac{r}s}(q),~ \mathcal{S}_{\frac{r}s}(q) \in {\mathbb Z}[q]$ with $\mathcal{R}_{\frac{r}s}(1)=r,~\mathcal{S}_{\frac{r}s}(1)=s$. Their theory has a rich background and many applications. By definition, if $r \equiv r' \pmod{s}$, then $\mathcal{S}_{\frac{r}s}(q)=\mathcal{S}_{\frac{r'}s}(q)$. We show that $rr'{\equiv} -1 \pmod{s}$ implies $\mathcal{S}_{\frac{r}s}(q)=\mathcal{S}_{\frac{r'}s}(q)$, and it is conjectured that the converse holds if $s$ is prime (and $r \not \equiv r' \pmod{s}$). We also show that $s$ is a multiple of 3 (resp. 4) if and only if $\mathcal{S}_{\frac{r}s}(\zeta)=0$ for $\zeta=(-1+\sqrt{-3})/2$ (resp. $\zeta=i$). We give applications to the representation theory of quivers of type $A$ and the Jones polynomials of rational links.

math.CO↗

arXiv2024

Exploring $f(T)$ Gravity via strongly lensed fast radio bursts

This study aims to investigate the strong gravitational lensing effects in $f(T)$ gravity. We present the theoretical analytic expressions for the lensing effects in $f(T)$ gravity, including deflection angle, magnification, and time delay. On this basis, we also take the plasma lensing effect into consideration. We compare the lensing effects between the General Relativity in a vacuum environment and the $f(T)$ gravity in a plasma environment. From a strongly lensed fast radio burst, the results indicate that in a plasma environment, General Relativity and $f(T)$ gravity can generate indistinguishable image positions, but the magnification and time delay on these positions are significantly different, which can be distinguished by current facilities in principle. Therefore, the discrepancies between observational results and theoretical expectations can serve as clues for a modified gravity theory and provide constraints on $f(T)$ gravity.

gr-qc↗