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We build an effective field theory of multi-field inflationary fluctuations based on the adiabatic perturbation and on any number of matter fluctuations in the non-adiabatic sector, without imposing extra symmetries on the latter. Focusing on terms with at most two derivatives in fields' fluctuations, we argue that taking the decoupling limit -- in which gravitational interactions are neglected -- is justified in a quasi de Sitter spacetime with slow-varying Hubble scale. With these working hypotheses, we find simple forms of multi-field mixings (quadratic order) and interactions (cubic order). We explain how to break degeneracies amongst various terms, and we compare the predictions of the effective field theory to those of non-linear sigma models of inflation and more general multi-field Lagrangian in the traditional model approach. We stress that several multi-field cubic interactions are dictated by non-linearly realised spacetime symmetries and are therefore given in terms of parameters already present in the quadratic action. We propose various directions to systematically explore the phenomenology generic to multi-field inflation and beyond the lamppost of known models., Comment: 6 pages + appendices, no figure

Stationary processes do not accurately describe the diffuse backgrounds of relic gravitons whose correlations are homogeneous in space (i.e. only dependent upon the distance between the two spatial locations) but not in time. The symmetries of the autocorrelations ultimately reflect the quantum mechanical origin of the diffuse backgrounds and lead to non-stationary observables at late time. In particular, large oscillations are believed to arise in the spectral energy density that is customarily (but approximately) related to the tensor power spectrum. When the full expression of the spectral energy density is employed the amplitudes of oscillation are instead suppressed in the large-scale limit and the non-stationary features of the late-time signal practically disappear. For similar reasons the relations between the spectral energy density and the spectral amplitude are ambiguous in the presence of non-stationary features. While it is debatable if the non-stationary features are (or will be) directly detectable, we argue that the spectral amplitude following from the Wiener-Khintchine theorem is generally inappropriate for a consistent description of the relic signal. Nevertheless the strong oscillatory behaviour of the late-time observables is naturally smeared out provided the spectral energy density is selected as pivotal variable., Comment: 28 pages, 3 figures

We present the first fully and inherently relativistic derivation of the thermal Sunyaev-Zel'dovich effect. This work uses the formalism historically used to compute radiation spectra emerging from inverse Thomson/Compton sources of x-ray radiation. Comparing our results to the traditional approach based on relativistically-corrected classical Kompaneets equation, we find small, but systematic differences. Most notable are the modest (< 10 %) differences in the crossover frequency where the spectral distortion due to the Sunyaev-Zel'dovich effect vanishes, and the energy increase of the distribution at high electron cloud temperatures., Comment: 6 pages, 5 figures

The bubble wall velocity in the first order phase transition plays an important role in determining both the amplitude and the pivot frequency of stochastic gravitational wave background. In the framework of the minimal left-right symmetric model, we study the wall velocity when the first order phase transition can occur. The wall velocity can be determined by matching the distribution functions in the free particle approximation and the local thermal equilibrium approximation. It is found that the wall velocity can be determined in the range $ 0.2 < v_w < 0.5 $ for the parameter space with the first order phase transition. It is also found that for the case when the wall velocity is close to the speed of sound, the peak amplitude of gravitational wave spectrum can be larger than that in the runaway case. Moreover, It is also found that there exists an approximate power law between the wall velocity and pressure difference between broken and symmetry phases, and the power index is equal to 0.41 or so., Comment: 22 pages, 12 figures

Joint gravitational-wave and $\gamma$-ray bursts (GRB) observations are among the best prospects for standard siren cosmology. However, the strong selection effect for the coincident GRB detection, which is possible only for sources with small inclination angles, induces a systematic uncertainty that is currently not accounted for. We show that this severe source of bias can be removed by inferring the a-priori unknown electromagnetic detection probability directly from multimessenger data. This leads at the same time to an unbiased measurement of the Hubble constant, to constrain the properties of GRB emission, and to accurately measure the viewing angle of each source. Our inference scheme is applicable to real data already in the small-statistics regime, a scenario that might become reality in the near future. Additionally, we introduce a novel likelihood approximant for GW events which treats the dependence on distance and inclination as exact., Comment: 5+6 pages, 4 figures

The application of Horndeski theory/ Galileons for late time cosmology is heavily constrained by the strict coincidence in the speed of propagation of gravitational and electromagnetic waves. These constraints presuppose that the minimally coupled photon is not modified, not even at the scales where General Relativity (GR) may need modification. We find that the 4D Galileon obtained from a Kaluza-Klein compactification of its higher dimensional version is a natural unified modification of GR and electromagnetism with automatically "luminal" gravitational waves. This property follows without any fine tuning of Galileon potentials for a larger class of theories than previously thought. In particular, the $G_4$ potential is not constrained by the speed test and $G_5$ may also be present. In other words, some Galileon models that have been ruled out since the event GW170817 are, in fact, not necessarily constrained if they arise in 4D from compactifications of their higher dimensional Galileon counterparts. Besides their compelling luminality, the resulting vector Galileons are naturally $U(1)$ gauge invariant., Comment: 4 pages

Millisecond pulsars are extremely precise celestial clocks: as they rotate, the beamed radio waves emitted along the axis of their magnetic field can be detected with radio telescopes, which allows for tracking subtle changes in the pulsars' rotation periods. A possible effect on the period of a pulsar is given by a potential coupling to dark matter, in cases where it is modeled with an "ultralight" scalar field. In this paper, we consider a universal conformal coupling of the dark matter scalar to gravity, which in turn mediates an effective coupling between pulsars and dark matter. If the dark matter scalar field is changing in time, as expected in the Milky Way, this effective coupling produces a periodic modulation of the pulsar rotational frequency. By studying the time series of observed radio pulses collected by the European Pulsar Timing Array experiment, we present constraints on the coupling of dark matter, improving on existing bounds. These bounds can also be regarded as constraints on the parameters of scalar-tensor theories of the Fierz-Jordan-Brans-Dicke and Damour-Esposito-Far\`{e}se types in the presence of a (light) mass potential term., Comment: 17 pages, 5 figures

In this work, we systematically investigate the inflationary complexity of the two-mode squeezed state with thermal effect for the single field inflation, modified dispersion relation, and non-trivial sound speed with the method of closed system and open system, respectively, which our analysis is valid for most inflationary models. First, the numeric of Krylov complexity in the method of the closed system indicates that the evolution of Krylov complexity highly depends on the squeezed angle parameter once taking the thermal effect into account, which will decay into some very tiny values, but the Krylov complexity will always enhance without thermal effect. For comparison, the numeric of circuit complexity shows that the evolution is always increasing no matter whether there are thermal effects or not which is independent of the evolution of squeezed angle parameter. By utilizing the method of open system, we first construct the wave function. As for the Krylov complexity with the method of open system, our investigations show the evolution of Krylov complexity will enhance upon some peaks factoring in the thermal effects. For completeness, we also calculate the Krylov entropy in the method of closed system and open system, which indicates that the hotter universe, the more chaotic the universe. Furthermore, our derivation for the Krylov complexity and Krylov entropy could nicely recover into the case of closed system under weak dissipative approximation, which confirms the validity of construction for the wave function. Finally, our numeric of Lanczos coefficient shows that the non-trivial sound speed has minimal chaos compared to the other two cases., Comment: 47 pages, 18 figures

We review the kinematic effects on a gravitational wave due to either a peculiar motion of the astrophysical source emitting it or a local motion of the observer. We show, at fully non-linear order in velocity, that the amplitude of the wave is amplified by the Doppler factor in the case in which the source moves with respect to a reference frame, while it is invariant if the observer moves (with respect to a reference observer). However, the observed specific intensity transforms in the same way under a boost of the source or of the observer. We also show at fully non-linear order that under a boost (of either source or observer), the polarization tensor is rotated in the same way the wave direction is rotated by aberration, such that the only net effect of a boost on polarization is to change the phase of the helicity components. We apply these results to a wave emitted by a binary system of compact objects in the cosmological context., Comment: 38 pages, 5 figures

In this paper, we investigate the gravitational collapse to form the black hole in the acceleratingly expanding universe in the frame of Einstein--Gauss-Bonnet theory having two scalar fields and we study the propagation of the gravitational wave (GW). The collapsing spacetime can be obtained by using the formulation of the ``reconstruction'', that is, we find a model that realises the desired or given geometry. In the reconstructed models, ghosts often appear, which could be eliminated by imposing constraints. We show that the standard cosmological solutions or self-gravitating objects such as a planet, the Sun, various types of stars, etc., in Einstein's gravity, are also solutions in this model. Using the dynamical value of Gauss-Bonnet coupling, the propagation of the high-frequency GW is investigated. The propagating speed changes due to the coupling during the period of the black hole formation. The speed at which the GW propagates The speed at which the GW propagates going into the black hole is different from that of the wave going out., Comment: 21 pages, no figure. arXiv admin note: text overlap with arXiv:2312.02889

The kinetic Sunyaev Zel'dovich (kSZ) effect is a blackbody cosmic microwave background (CMB) temperature anisotropy induced by Thomson scattering off free electrons in bulk motion with respect to the CMB rest frame. The statistically anisotropic cross-correlation between the CMB and galaxy surveys encodes the radial bulk velocity (more generally, the remote dipole field), which can be efficiently reconstructed using a quadratic estimator. Here, we develop and implement a quadratic estimator for the remote dipole field to data from the Planck satellite and the unWISE galaxy redshift catalog. With this data combination, we forecast a $\sim 1$-$\sigma$ detection within $\Lambda$CDM assuming a simple model for the distribution of free electrons. Using reconstructions based on individual frequency temperature maps, we characterize the impact of foregrounds, concluding that they can be effectively mitigated by masking and removing the estimator monopole. We demonstrate that reconstructions based on component-separated CMB maps have no detectable biases from foregrounds or systematics at the level of the expected statistical error. We use these reconstructions to constrain the multiplicative optical depth bias to $b_v < 1.40$ at $68 \%$ confidence. Our fiducial signal model with $b_v =1$ is consistent with this measurement. Our results support an optimistic future for kSZ velocity reconstruction with near-term datasets., Comment: 26 pages, 18 figures, comments welcome

A new degravitation mechanism within the framework of scalar tensor gravity is proposed. The mechanism eliminates all constant contributions from the potential to the Friedmann equation, leaving only the kinematic and the dynamic terms of the potential to drive cosmic acceleration. We explore a scenario involving a density-triggered phase transition in the late-time universe, and argue that the resulting effective energy density and equation of state parameter can explain late-time cosmology when extrapolated to a region of the parameter space., Comment: 5 pages, 2 figures

In this letter we investigate new constraints on $f(T)$ gravity using the recent Baryon Acoustic Oscillation (BAO) data released by the Dark Energy Spectroscopic Instrument (DESI) and the Type Ia supernovae (SNIa) catalog from the full 5-years of the Dark Energy Survey Supernova Program (DES-SN5YR). The $f(T)$ cosmological models considered are characterised by power law late-time accelerated expansion. Our results show that the combination DESI BAO +$r_d$ CMB Planck suggests a Bayesian preference for late-time $f(T)$ cosmological models over $\Lambda$CDM, obtaining a value of $H_0=72.4\pm 2.9$[km/s/Mpc] in agreement with SH0ES collaboration., Comment: 5 pages, 3 tables and 1 figure

We use a combination of Planck cosmic microwave background (CMB) anisotropy data and non-CMB data that include Pantheon+ type Ia supernovae, Hubble parameter [$H(z)$], growth factor ($f\sigma_8$) measurements, and a collection of baryon acoustic oscillation (BAO) data, but not recent DESI 2024 BAO measurements, to confirm the DESI 2024 (DESI+CMB+PantheonPlus) data compilation support for dynamical dark energy with an evolving equation of state parameter $w(z) = w_0 + w_a z/(1+z)$. From our joint compilation of CMB and non-CMB data, in a spatially-flat cosmological model, we obtain $w_0 = -0.850 \pm 0.059$ and $w_a = -0.59^{+0.26}_{-0.22}$ and find that this dynamical dark energy is favored over a cosmological constant by $\sim 2\sigma$. Our data constraints on the flat $w_0w_a$CDM model are slightly more restrictive than the DESI 2024 constraints, with the DESI 2024 and our values of $w_0$ and $w_a$ differing by $-0.27\sigma$ and $0.44\sigma$, respectively. Our data compilation slightly more strongly favors the flat $w_0w_a$CDM model over the flat $\Lambda$CDM model than does the DESI 2024 data compilation., Comment: 9 pages, 3 figures

Photon propagator for power-law inflation is considered in the general covariant gauges within the canonical quantization formalism. Photon mode functions in covariant gauges are considerably more complicated than their scalar counterparts, except for the special choice of the gauge-fixing parameter we call the simple covariant gauge. We explicitly construct the position space photon propagator in the simple covariant gauge, and find the result considerably more complicated than its scalar counterpart. This is because of the need for explicitly inverting the Laplace operator acting on the scalar propagator, which results in Appell's fourth function. Our propagator correctly reproduces the de Sitter and flat space limits. We use this propagator to compute two simple observables: the off-coincident field strength-field strength correlator and the energy-momentum tensor, both of which yield consistent results. As a spinoff of our computation we also give the exact expression for the Coulomb gauge propagator in power-law inflation in arbitrary dimensions., Comment: 77 pages (including 25 pages of appendices)

Gravitational lensing is a crucial tool for exploring cosmic phenomena, providing insights into galaxy clustering, dark matter, and dark energy. Given the substantial computational demands of $N$-body simulations, approximate methods like $\texttt{PINOCCHIO}$ and $\texttt{turboGL}$ offer viable alternatives for simulating lensing probability density functions (PDFs). This paper evaluates these methods in contexts where baryonic effects are negligible, focusing on dark matter-dominated models and assessing their effectiveness across both weak and strong lensing regimes. Our comparative analysis reveals that these methods are particularly effective for applications involving electromagnetic and gravitational wave point sources, where strong lensing events are infrequent. Both $\texttt{PINOCCHIO}$ and $\texttt{turboGL}$ perform well in modeling the weak-lensing region influenced by mildly nonlinear structures. However, they lose accuracy in capturing small-scale nonlinear matter fields, owing to oversimplified assumptions about internal halo structures and reliance on perturbation theory. The analysis shows that $\texttt{PINOCCHIO}$ achieves an 8-15% agreement with $N$-body simulations for the second-to-fourth moments of lensing PDFs. These findings aim to inform future studies on gravitational lensing of point sources, which are increasingly relevant with upcoming supernova and gravitational wave datasets., Comment: 14 pages, 12 figures and 3 tables

Gravitational chiral anomaly connects the topological charge of spacetime and the chirality of fermions. It has been known that the chirality is carried by the particles (or the excited states) and also by vacuum. While the gravitational anomaly equation has been applied to cosmology, distinction between these two contributions has been rarely discussed. In the study of gravitational leptogenesis, for example, lepton asymmetry associated with the chiral gravitational waves sourced during inflation is evaluated only by integrating the anomaly equation. How these two contributions are distributed has not been seriously investigated. Meanwhile, a dominance of vacuum contribution is observed in some specific types of Bianchi spacetime with parity-violating gravitational fields, whose application to cosmology is not straightforward. One may wonder whether such a vacuum dominance takes place also in the system with chiral gravitational waves around the flat background, which is more suitable for application to realistic cosmology. In this work, we apply an analogy between U(1) electromagnetism and the weak gravity to the spacetime that resembles the one considered in the gravitational leptogenesis scenario. This approach allows us to obtain intuitive understanding of the fermion chirality generation under the parity-violating spin-2 gravitational field. By assuming the emergence of Landau level-like dispersion relation in our setup, we conjecture that level-crossing does not seem to be efficient while the charge accumulation in the vacuum likely takes place. Phenomenological implication is also discussed in the context of gravitational leptogenesis., Comment: 34 pages, 5 figures

We study how Abelian-gauge-field production during inflation affects scalar perturbations in the case when the gauge field interacts with the inflaton directly (by means of generic kinetic and axial couplings) and via gravity. The homogeneous background solution is defined by self-consistently taking into account the backreaction of the gauge field on the evolution of the inflaton and the scale factor. For the perturbations on top of this background, all possible scalar contributions coming from the inflaton, the metric, and the gauge field are considered. We derive a second-order differential equation for the curvature perturbation, $\zeta$, capturing the impact of the gauge field, both on the background dynamics and on the evolution of scalar perturbations. The latter is described by a source term in the $\zeta$-equation, which is quadratic in the gauge-field operators and leads to non-Gaussianities in the curvature perturbations. We derive general expressions for the induced scalar power spectrum and bispectrum. Finally, we apply our formalism to the well-known case of axion inflation without backreaction. Numerical results show that, in this example, the effect of including metric perturbations is small for values of the gauge-field production parameter $\xi> 3$. This is in agreement with the results of previous studies in the literature. However, in the region of smaller values, $\xi\lesssim 2$, our new results exhibit order-of-unity deviations when compared to previous results., Comment: 36 pages, 5 figures

In this work, we explore the capability of future gravitational wave (GW) standard siren observations to constrain the total neutrino mass in some typical interacting dark energy (IDE) models. We examine the combined potential of the third-generation ground-based GW detector network and a short $\gamma$-ray burst (GRB) detector similar to the THESEUS telescope for cosmological analysis. Our findings suggest that future GW standard siren observations could modestly refine the upper limit on the total neutrino mass, enhancing it by $5\%$ to $10\%$ over the existing limit given by the CMB+BAO+SN data. Additionally, the future observations are expected to significantly improve the constraints on $\Omega_{\rm m}$ and $H_0$. Moreover, the measurements could enhance the precision of the coupling strength $\beta$ by $23\%$ to $42\%$., Comment: 8 pages, 2 figures

We study the cosmology of the complete quadratic (in torsion and nonmetricity) metric-affine gravity. Namely, we add to the scalar-curvature gravitational Lagrangian, the 17 independent quadratic (parity-even and parity-odd) torsion and nonmetricity invariants. Sticking to a homogeneous and isotropic Friedmann-Robertson-Walker spacetime and assuming a perfect hyperfluid source, we explore the new effects that torsion and nonmetricity bring into play. It is shown that the inclusion of these invariants offers rich phenomenology. In particular, some well-known examples of exotic matter like cosmic strings, domain walls, stiff matter, etc., emerge quite naturally as manifestations of the fluid's intrinsic structure (hypermomentum). By studying the extended Friedmann equations in the complete quadratic theory and isolating the various parts of the hypermomentum, we find a plethora of solutions with interesting features., Comment: 29 pages, 2 figures, PDF with matrix coefficients included

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) \cite{DESI:2024mwx} 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., Comment: 10 pages, 3 figures

The idea of composite dark energy (DE) is quite natural since on general grounds we expect that the vacuum energy (associated to the cosmological term $\Lambda$) may appear in combination with other effective forms of DE, collectively denoted $X$. This was indeed the old proposal from 2006, (cf. Ref.[41]) called the `$\Lambda$XCDM model', which was primordially designed to explain the cosmic coincidence problem. We now find that it can also have far reaching consequences on the current cosmological tensions on $H_0$ and the growth of large scale structure (LSS). The $\Lambda$XCDM may involve both a phantom-like component $X$ and a constant cosmological term $\Lambda$ (positive or negative) or even a running one, $\Lambda=\Lambda(H)$. In the current work, we deal with a simplified version of the model and exploit the possibility that $X$ behaves as `phantom matter' (PM). The latter appears in stringy versions of the running vacuum model (RVM). Unlike phantom DE, it satisfies the strong energy condition like usual matter, hence bringing to bear positive pressure at the expense of negative energy. Bubbles of PM may appear in the manner of a transitory `phantom vacuum' tunneled into the late universe before it heads towards a new de Sitter era, thereby offering a crop field for the growing of structures earlier than expected. Using SNIa, cosmic chronometers, transversal BAO, LSS data and the full CMB likelihood from Planck 2018, we find that the tensions virtually disappear in this stringy RVM scenario characterized by axionic dark matter. The value of $H_0$ emerging from our analysis proves compatible with SH0ES to within less than $0.25\sigma$ and the LSS growth tension is nonexistent. The statistical information criteria point to very strong evidence in favor of the PM solution., Comment: LaTeX, 22 pages, 4 Figures and 2 Tables

Recent analysis of quantum cosmology has focused on the Lorentzian path integral formulations of both the no-boundary and tunneling proposals. However, it has been criticized that the wave function for linearized perturbations around a homogeneous and isotropic background leads to an inverse Gaussian distribution. This results in divergent correlation functions and cosmological inconsistencies. In this paper we explore these perturbation problems in Lorentzian quantum cosmology, focusing in particular on the quantum creation of closed, flat, and open universes from no spacetime and the beginning of primordial inflation. We show that most quantum cosmological scenarios have serious perturbation problems. We also study the effects of trans-Planckian physics on quantum cosmology, using the generalized Corley-Jacobson dispersion as a case study of modified dispersion relations. Our findings indicate that resolving perturbation problems in Lorentzian quantum cosmology with modified dispersion relations remains a challenge. However, the perturbations can be Gaussian in the quantum creation of the flat or open universe within the confines of the saddle-point approximation and the generalized Corley-Jacobson dispersion., Comment: 24 pages, 3 figures

It might be necessary to access the impact of recent released Dark Energy Spectroscopic Instrument (DESI) data on the state equation of dark energy in the Hubble-tension-free cosmologies. In this paper, we report the MCMC analysis for the $w_0w_a$CDM model with pre-recombination early dark energy (EDE) using Planck+DESI+Pantheon+SH0ES dataset. The results reveal that $H_0=72.43\pm 0.75$, $w_0=-0.971\pm0.035$, $w_a=-0.347\pm0.120$ for axion-like EDE, while $H_0=73.32\pm 0.64$, $w_0=-0.923\pm0.054$, $w_a=-0.435\pm0.132$ for AdS-EDE, and also not surprisingly the spectral index of primordial scalar perturbation moves towards $n_s=1$. It looks like that in corresponding models the bestfit $H_0$ are higher than those with pre-DESI BAO data, but without the further exacerbation of $S_8$ tension., Comment: 5 pages, 1 figure

A popular science article designed to introduce people familiar with basic cosmological nomenclature with models alternative to cosmological inflation. The paper briefly discusses the modern view of the Big Bang model, inflation (both its advantages and potential deficiencies). This is followed by a discussion of historical alternative models and modern approaches such as matter bounce, ekpyrotic Universe, Conformal Cyclic Cosmology, Hartle-Hawking state and loop quantum cosmology. The final aspect of the paper is to present the advantages and potential problems associated with alternative models and to present the conceptual challenges associated with the uniqueness of cosmology as a specific domain of physics., Comment: Popular science article created as part of the COST Action CA21136 ("Addressing observational tensions in cosmology with systematics and fundamental physics") CosmoVerse website: https://cosmoversetensions.eu/learn-cosmology/did-the-big-bang-and-cosmic-inflation-really-happen/

Explaining the origin of supermassive black holes via a primordial origin is severely challenged by the tight spectral distortion constraints on the amplitude of the primordial perturbations. Following the first calculation of how the $\mu$ constraints are modified by non-Gaussianity in a companion paper, we here make the first robust constraints on primordial black hole formation under large non-Gaussianity. Even the infinite $f_{\rm NL}$ limit is insufficiently non-Gaussian but much higher-order non-Gaussianity of the form ${\cal R}={\cal R}_{\rm G}^5$ may allow the formation of any mass primordial black hole without conflicting with distortion constraints. We caution that such extreme models face other challenges., Comment: 24 pages, 6 figures

We formulate the convenient and mimetic $f(Q)$ gravities in terms of the metric and four scalar fields with the $Q$ being the non-metricity scalar. As a result, it is shown that the obtained field equations are well-defined. By using the field equations, we show how the $f(Q)$ models which realise any given FLRW spacetime may be reconstructed. We construct convenient $f(Q)$ gravity and mimetic $f(Q)$ gravity, which describe the inflation and dark energy epochs and even unify the inflation and dark energy. Moreover, a radiation-dominated epoch and early dark energy may be easily included in the above theories as is explicitly shown. It is shown that the inflationary spectral index $n_s$ and the tensor-to-scalar ratio $r$ are consistent with Planck data for some models of $f(Q)$ gravity. Corresponding asymptotic forms of $f(Q)$ and mimetic $f(Q)$ are given. Finally, some remarks on possible reconstruction for spherically symmetric spacetime are given., Comment: 16 pages, no figure

We study 6 LCDM models, with 4 allowing for non-flat geometry and 3 allowing for a non-unity lensing consistency parameter $A_L$. We also study 6 XCDM models with a dynamical dark energy density X-fluid with equation of state $w$. For the non-flat models we use two different primordial power spectra, Planck $P(q)$ and new $P(q)$. These models are tested against: Planck 2018 CMB power spectra (P18) and lensing potential power spectrum (lensing), and an updated compilation of BAO, SNIa, $H(z)$, and $f\sigma_8$ data [non-CMB data]. P18 data favor closed geometry for the LCDM and XCDM models and $w<-1$ (phantom-like dark energy) for the XCDM models while non-CMB data favor open geometry for the LCDM models and closed geometry and $w>-1$ (quintessence-like dark energy) for the XCDM models. When P18 and non-CMB data are jointly analyzed there is weak evidence for open geometry and moderate evidence for quintessence-like dark energy. Regardless of data used, $A_L>1$ is always favored. The XCDM model constraints obtained from CMB data and from non-CMB data are incompatible, ruling out the 3 $A_L = 1$ XCDM models at $> 3\sigma$. In the 9 models not ruled out, for the P18+lensing+non-CMB data set we find little deviation from flat geometry and moderate deviation from $w=-1$. In all 6 non-flat models (not ruled out), open geometry is mildly favored, and in all 3 XCDM+$A_L$ models (not ruled out) quintessence-like dark energy is moderately favored (by at most $1.6 \sigma$). In the $A_L = 1$ non-flat LCDM cases, we find for P18+lensing+non-CMB data $\Omega_k = 0.0009 \pm 0.0017$ [$0.0008 \pm 0.0017$] for the Planck [new] $P(q)$ model, favoring open geometry. The flat LCDM model remains the simplest (largely) observationally-consistent cosmological model. Our cosmological parameter constraints obtained for the flat LCDM model (and other models) are the most restrictive results to date (Abridged)., Comment: 71 pages, 33 figures

We extend the earlier linear studies of cosmological peculiar velocities to Friedmann universes with nonzero spatial curvature. In the process, we also compare our results with those obtained in cosmologies with Euclidean spatial sections. Employing relativistic cosmological perturbation theory, we first provide the differential formulae governing the evolution of peculiar velocities on all Friedmann backgrounds. The technical complexities of the curved models, however, mean that analytic solutions are possible only in special, though characteristic, moments in the lifetime of these universes. Nevertheless, our solutions exhibit persistent patterns that make us confident enough to generalise them. Thus, we confirm earlier claims that, compared to the Newtonian studies, the relativistic analysis supports considerably stronger linear growth-rates for peculiar-velocity perturbations. This result holds irrespective of the background curvature. Moreover, for positive curvature, the peculiar growth-rate is found to be faster than that obtained in a spatially flat Friedman universe. In contrast, linear peculiar velocities appear to grow at a slower pace when their Friedmann host is spatially open. Extrapolating them to the present, our results seem to suggest faster bulk peculiar motions in overdense, rather than in underdense, regions of the universe., Comment: 15 pages, 1 figure

Recently Tsallis cosmology has been presented as a novel proposal for alleviating both $H_0$ and $\sigma_8$ tensions. Hence a universe filled with matter and radiation as perfect fluids and considering the Tsallis entropy is confronted using recent cosmological measurements coming from cosmic chronometers, type Ia supernovae, hydrogen II galaxies, quasars, and baryon acoustic oscillations. Following a Bayesian Markov Chain Monte Carlo analysis and combining the samples, we constrain the main characteristic parameters $\alpha = 1.031^{+0.054}_{-0.051}$ and $\delta = 1.005^{+0.001}_{-0.001}$ where the uncertainties are $1\sigma$ confidence level. Additionally, we estimate the today deceleration parameter $q_0=-0.530^{+0.018}_{-0.017}$, the deceleration-acceleration transition redshift $z_T=0.632^{+0.028}_{-0.028}$ and the age of the universe $\tau_U = 12.637^{+0.067}_{-0.066}\,\rm{Gyrs}$ which are in agreement with the standard cosmology ($\Lambda$CDM) within $1.5\sigma$. Furthermore, we find that the dark energy equation of state is consistent with both phantom and quintessence behaviors within $1\sigma$ in the past and converging to $\Lambda$CDM in the future. Finally, Tsallis cosmology is preferred over $\Lambda$CDM by the combined data, suggesting further studies at the perturbation level., Comment: 9 pages, 2 figures, 2 tables

Ultralight electrophilic scalar field can mediate a long-range force or radiate from a pulsar or a magnetar if the scalar field has a coupling with the Goldreich-Julian charge density or the net electron charge density of the star. The interaction of the electron with the long-range scalar profile results in a spatial variation of the electron mass. A scalar induced magnetic field is created due to such interaction. The mass of the scalar in such cases is constrained by the radius of the star. The scalar field can also radiate from a binary system or an isolated star if the mass of the scalar is less than the orbital frequency and the spin frequency respectively. The electrophilic scalar radiation can contribute to the orbital period loss of binary systems and pulsar spin-down. Comparing with existing and projected experimental sensitivities, we obtain constraints on scalar coupling with ultralight mass. Some of these bounds are stronger than the existing fifth force constraints. The constraints on the scalar coupling can be significantly screened if the scalar has a coupling with the ubiquitous cosmic neutrino background. Improvements in experimental sensitivity and observations of compact objects with stronger magnetic fields and higher angular velocities could further refine these bounds., Comment: 35 pages, 10 figures, and comments are welcome

Multi-band gravitational-wave (GW) standard siren observations are poised to herald a new era in the study of cosmic evolution. These observations offer higher signal-to-noise ratios and improved localizations compared to those achieved with single-band GW detection, which are crucial for the cosmological applications of dark sirens. In this work, we explore the role multi-band GW synergetic observations will play in measuring cosmological parameters, particularly in comparison with single GW observatory data. We used mock multi-band dark siren data from third-generation GW detectors and the baseline Decihertz Interferometer Gravitational-Wave Observatory to infer cosmological parameters. Our analysis was conservative, involving only the 89 actual GW events from the current Gravitational Wave Transient Catalogs in our data simulation, facilitating a direct comparison with existing dark siren results. Multi-band GW observations significantly improve sky localization accuracy by two to three orders of magnitude over single-band observations, although their impact on luminosity distance error remains limited. This results in a substantial improvement in the constraints on matter density and the Hubble constant, enhancing them by $75\%$ to $85\%$ and $65\%$ to $82\%$, respectively. We conclude that the significant potential of multi-band GW synergistic observations for detecting GW signals and resolving the Hubble tension is highly promising and warrants anticipation., Comment: 11 pages, 4 figures

Every signal propagating through the universe is diffracted by the gravitational fields of intervening objects, aka gravitational lenses. Diffraction is most efficient when caused by compact lenses, which invariably produce additional images of a source. The signals associated with additional images are generically faint, but their collective effect may be detectable with coherent sources, such as gravitational waves (GWs), where both amplitude and phase are measured. Here, I describe lens stochastic diffraction (LSD): Poisson-distributed fluctuations after GW events caused by compact lenses. The amplitude and temporal distribution of these signals encode crucial information about the mass and abundance of compact lenses. Through the collective stochastic signal, LSD offers an order-of-magnitude improvement over single lens analysis for objects with mass $\gtrsim 10^3 M_\odot$. This gain can improve limits on compact dark-matter halos and allows next-generation instruments to detect supermassive black holes, given the abundance inferred from quasar luminosity studies., Comment: 5 pages, 4 figures. Comments welcome!

We analyze the effective four-dimensional dynamics of the extra-dimensional moduli fields in curved braneworlds having nested warping, with particular emphasis on the doubly warped model which is interesting in the light of current collider constraints on the mass of the Kaluza-Klein graviton. The presence of a non-zero brane cosmological constant ($\Omega$) naturally induces an effective moduli potential in the four-dimensional action, which shows distinct features in dS ($\Omega>0$) and AdS ($\Omega<0$) branches. For the observationally interesting case of dS 4-branes, a metastable minimum in the potential arises along the first modulus, with no minima along the higher moduli. The underlying nested geometry also leads to interesting separable forms of the non-canonical kinetic terms in the Einstein frame, where the brane curvature directly impacts the kinetic properties of only the first modulus. We subsequently explore the ability of curved multiply warped geometries to drive inflation with an in-built exit mechanism, by assuming predominant slow roll along each modular direction on a case-by-case basis. We find slow roll on top of the metastable plateau along the first modular direction to be the most viable scenario, with the higher-dimensional moduli parametrically tuning the height of the potential without significant impact on the inflationary observables. On the other hand, while slow roll along the higher moduli can successfully inflate the background and eventually lead to an exit, consistency with observations seemingly requires unphysical hierarchies among the extra-dimensional radii, thus disfavouring such scenarios., Comment: 22 pages, 7 sets of figures, 1 table, comments welcome

A hypothetical photon mass, $m_{\gamma}$, can produce a frequency-dependent vacuum dispersion of light, which leads to an additional time delay between photons with different frequencies when they propagate through a fixed distance. The dispersion measure--redshift measurements of fast radio bursts (FRBs) have been widely used to constrain the rest mass of the photon. However, all current studies analyzed the effect of the frequency-dependent dispersion for massive photons in the standard $\Lambda$CDM cosmological context. In order to alleviate the circularity problem induced by the presumption of a specific cosmological model based on the fundamental postulate of the masslessness of photons, here we employ a new model-independent smoothing technique, Artificial Neural Network (ANN), to reconstruct the Hubble parameter $H(z)$ function from 34 cosmic-chronometer measurements. By combining observations of 32 well-localized FRBs and the $H(z)$ function reconstructed by ANN, we obtain an upper limit of $m_{\gamma} \le 3.5 \times 10^{-51}\;\rm{kg}$, or equivalently $m_{\gamma} \le 2.0 \times 10^{-15}\;\rm{eV/c^2}$ ($m_{\gamma} \le 6.5 \times 10^{-51}\;\rm{kg}$, or equivalently $m_{\gamma} \le 3.6 \times 10^{-15}\;\rm{eV/c^2}$) at the $1\sigma$ ($2\sigma$) confidence level. This is the first cosmology-independent photon mass limit derived from extragalactic sources., Comment: 8 pages, 3 figures, 3 tables. Accepted for publication in Chinese Physics Letters. Invited article to special issue "FAST"

Recent surveys have been reporting bulk peculiar flows considerably faster than expected. Bulk flows are moving matter and matter in motion implies nonzero energy flux. In relativity, as opposed to Newtonian physics, matter fluxes gravitate as well, since they also contribute to the energy-momentum tensor. The gravitational input of the "peculiar" flux survives at the linear level and it can drastically change our understanding of the way bulk flows have evolved in time. By default, the Newtonian analysis of peculiar motions bypasses the relativistic flux-contribution to the gravitational field. The problem is that there are also studies, with an otherwise relativistic profile, which inadvertently do the same. As result, these treatments reduce to Newtonian and they misleadingly reproduce the slow Newtonian growth-rate of linear peculiar velocities. In contrast, by accounting for the flux effects, the proper relativistic analysis arrives at a considerably stronger growth. We show that it is the flux input of the moving matter to gravity that separates the relativistic studies of peculiar motions from the rest and, in so doing, it could provide an answer to the bulk-flow question., Comment: 9 pages, no figures

The Event Horizon Telescope (EHT) has revolutionized our ability to study black holes by providing unprecedented spatial resolution and unveiling horizon-scale details. With advancements leading to the next-generation EHT, there is potential to probe even deeper into the black hole's dark region, especially the inner shadow characterized by low-intensity foreground emissions from the jet, thanks to a significant enhancement in dynamic range by two orders of magnitude. We demonstrate how such enhanced observations could transform supermassive black holes into powerful probes for detecting annihilating dark matter, which can form a dense profile in the vicinity of supermassive black holes, by examining the morphology of the black hole image., Comment: 19 pages, 6 figures, references updated

Gravitational waves from condensates of ultra-light particles, such as axion, around rotating black holes are a promising probe to search for unknown physics. For this purpose, we need to characterize the signal to detect the gravitational waves, which requires tracking the evolution of the condensates, including various effects. The axion self-interaction causes the non-linear coupling between the superradiant modes, resulting in complicated branching of evolution. Most studies so far have considered evolution under the non-relativistic approximation or the two-mode approximation. In this paper, we numerically investigate the evolution of the axion condensate without these approximations, taking higher multipole modes into account. We also investigate the possible signature in gravitational waves from the condensate. We show that the higher multipole modes are excited, leading to the gravitational wave signal by the transition of the axion between different levels. The most prominent signal of gravitational waves arises from the transition between modes with their angular quantum numbers different by two. The gravitational wave signal is emitted in the deci-Hz band for stellar mass black holes, which might be observable with the future gravitational wave detectors., Comment: 19 pages, 17 figures

We analyze a model for Dark Energy - Dark Matter interaction, based on a decaying process of the former constituents into the latter ones. The dynamical equations are constructed following a kinetic formulation, which separates the interacting fluctuations from equilibrium distribution of the both the species. The emerging dynamical picture consists of coupled equations, which are specialized in the case of a Dark Energy equation of state parameter: we deal with a modified Lambda Cold Dark Matter model, which is investigated versus a possible interpretation of the Hubble tension. We compare our model with data corresponding to 6 points of the expansion rate from Type Ia Supernovae. We show that, the proposed model suitably fits data according to a value of the Hubble constant compatible with the SHOES Collaboration measurement. The tension is solved because, essentially for redshift greater than one, the correction to the Lambda Cold Dark Matter model vanishes and its presence does not affect the Planck measurements., Comment: 6 pages, 2 figures

We examine local physics in the presence of global variables: variables associated with the whole of the spacelike surfaces of a foliation. These could be the (pseudo-)constants of nature and their conjugate times, but our statements are more general. Interactions between the local and the global (for example, dependence of the local action on global times dual to constants) degrades full space-time diffeomorphism invariance down to spatial diffeomorphism invariance, and so an extra degree of freedom appears. When these presumably primordial global interactions switch off, the local action recovers full invariance and so the usual two gravitons, but a legacy matter component is left over, bearing the extra degree of freedom. Under the assumption that the preferred foliation is geodesic, this component behaves like dark matter, except that 3 of its 4 local degrees of freedom are frozen, forcing its rest frame to coincide with the preferred foliation. The non-frozen degree of freedom (the number density of the effective fluid) is the survivor of the extra "graviton" present in the initial theory, and keeps memory of all the past global interactions that took place in a given location in the preferred foliation. Such "painted-on" dark matter is best distinguished from the conventional one in situations where the preferred frame would be preposterous if all 4 degrees of freedom of dark matter were available. We provide one example: an outflowing halo of legacy matter with exact escape speed at each point and a very specific profile, surrounding a condensed structure made of normal matter.

In our quest to understand the generation of cosmological perturbations, we face two serious obstacles: we do not have direct information about the environment experienced by primordial perturbations during inflation, and our observables are practically limited to correlators of massless fields, heavier fields and derivatives decaying exponentially in the number of e-foldings. The flexible and general framework of open systems has been developed precisely to face similar challenges. Building on previous work, we develop a Schwinger-Keldysh path integral description for an open effective field theory of inflation, describing the possibly dissipative and non-unitary evolution of the Goldstone boson of time translations interacting with an unspecified environment, under the key assumption of locality in space and time. Working in the decoupling limit, we study the linear and interacting theory in de Sitter and derive predictions for the power spectrum and bispectrum that depend on a finite number of effective couplings organised in a derivative expansion. The smoking gun of interactions with the environment is an enhanced but finite bispectrum close to the folded kinematical limit. We demonstrate the generality of our approach by matching our open effective theory to an explicit model. Our construction provides a standard model to simultaneously study phenomenological predictions as well as quantum information aspects of the inflationary dynamics., Comment: 56 pages without appendices (81 pages in total), 12 figures, 2 tables

We show that the simplest, and currently favoured, theoretical realizations of cosmic inflation yield a sharp prediction for the running of the spectral index $\alpha_\mathrm{S}$. Using latest cosmological data, we compute its marginalized posterior probability distribution over the space of nearly 300 models of single-field slow-roll inflation. The most probable value is $\alpha_\mathrm{S}=-6.3 \times 10^{-4}$, lying within the $98\%$ credible interval $-1.8 \times 10^{-3}< \alpha_\mathrm{S}< -9.1 \times 10^{-5}$. Within the landscape of all the proposed slow-roll inflationary models, positive values for the running are therefore disfavoured at more than three-sigma., Comment: 5 pages, 4 figures, uses RevTeX

The formation and evolution of supermassive black holes (SMBHs) remains an open question in the field of modern cosmology. The detection of nanohertz (n-Hz) gravitational waves via pulsar timing arrays (PTAs) in the form of individual events and the stochastic gravitational wave background (SGWB) offers a promising avenue for studying SMBH formation across cosmic time, with SGWB signal being the immediately detectable signal with the currently accessible telescope sensitivities. By connecting the galaxy properties in the large scale (Gpc scale) cosmological simulation such as \texttt{MICECAT} with the small scale ($\sim$ Mpc scale) galaxy simulations from \texttt{ROMULUS}, we show that different scenarios of galaxy--SMBHs evolution with redshift leads to a frequency-dependent spatial anisotropy in the SGWB signal. The presence of slow evolution of the SMBHs in the Universe leads to a pronounced blue anisotropic spectrum of the SGWB. In contrast, if SMBHs grow faster in the Universe in lighter galaxies, the frequency-dependent spatial anisotropy exhibits a more flattened anisotropic spectrum. This additional aspect of the SGWB signal on top of the monopole SGWB signal, can give insight on how the SMBHs form in the high redshift Universe and its interplay with the galaxy formation from future measurements., Comment: 19 page, 27 figures

It has been shown that a three-point correlation function of tensor perturbations from a bounce model in general relativity with a minimally-coupled scalar field is highly suppressed, and the resultant three-point function of cosmic microwave background (CMB) B-mode polarizations is too small to be detected by CMB experiments. On the other hand, bounce models in a more general class with a non-minimal derivative coupling between a scalar field and gravity can predict the three-point correlation function of the tensor perturbations without any suppression, the amplitude of which is allowed to be much larger than that in general relativity. In this paper, we evaluate the three-point function of the B-mode polarizations from the general bounce cosmology with the non-minimal coupling and show that a signal-to-noise ratio of the B-mode auto-bispectrum in the general class can reach unity for $\ell_{\rm max}\geq9$ and increase up to $5.39$ for $\ell_{\rm max}=100$ in the full-sky case. We also discuss the possibility to test the general class of bounce models by upcoming CMB experiments., Comment: 13 pages, 5 figures

In this study, we present an analysis of the fine-tuning required in various inflationary models in order to explain the production of Primordial Black Holes (PBHs). We specifically examine the degree of fine-tuning necessary in two prominent single field inflationary models: those with an inflection point and those with step-like features in the potential. Our findings indicate that models with step-like features generally require less fine-tuning compared to those with an inflection point, making them more viable for consistent PBH production. An interesting outcome of these models is that, in addition to improved fine-tuning, they may also predict low-frequency signals that can be detected by pulsar timing array (PTA) collaborations. Additionally, we extend our analysis to multifield inflationary models to assess whether the integration of additional fields can further alleviate the fine-tuning demands. The study also explores the role of a spectator field and its impact on the fine-tuning process. Through a comparative analysis across these models, we evaluate their parametric sensitivities and alignment with the constraints from Cosmic Microwave Background (CMB) observations. Our results indicate that although mechanisms involving a spectator field can circumvent the issue of fine-tuning parameters for PBH production, both multifield models and models with step-like features present promising alternatives. While fine-tuning involves multiple considerations, our primary objective is to evaluate various inflationary models to identify the one that most naturally explains the formation of PBHs. Hence, this study aims to the development of less constrained inflationary scenarios that align with observational data and support the theoretical possibility of PBH production., Comment: 18 pages, 6 figures

The next generation of very long baseline interferometry (VLBI) is stepping into the era of microarcsecond ($\mu$as) astronomy, and pushing astronomy, especially astrometry, to new heights. VLBI with the Square Kilometre Array (SKA), SKA-VLBI, will increase current sensitivity by an order of magnitude, and reach astrometric precision routinely below 10 $\mu$as, even challenging 1 $\mu$as. This advancement allows precise parallax and proper motion measurements of various celestial objects. Such improvements can be used to study objects (including isolated objects, and binary or multiple systems) in different stellar stages (such as star formation, main-sequence stars, asymptotic giant branch stars, pulsars, black holes, white dwarfs, etc.), unveil the structure and evolution of complex systems (such as the Milky Way), benchmark the international celestial reference frame, and reveal cosmic expansion. Furthermore, the theory of general relativity can also be tested with SKA-VLBI using precise measurements of light deflection under the gravitational fields of different solar system objects and the perihelion precession of solar system objects., Comment: 41 pages, 12 figures, 4 tables. Accepted to RAA (Review)

We present the first constraints on tidal heating for the binary systems detected in the LIGO-Virgo-KAGRA (LVK) gravitational wave data. Tidal heating, also known as tidal dissipation, characterizes the viscous nature of an astrophysical body and provides a channel for exchanging energy and angular momentum with the tidal environment. Using the worldline effective field theory formalism, we introduce a physically motivated and easily interpretable parametrization of tidal heating valid for an arbitrary compact astrophysical object. We then derive the imprints of the spin-independent and linear-in-spin tidal heating effects of generic binary components on the waveform phases and amplitudes of quasi-circular orbits. Notably, the mass-weighted spin-independent tidal heating coefficient derived in this work, $\mathcal{H}_0$, is the dissipative analog of the tidal Love number. We constrain the tidal heating coefficients using the public LVK O1-O3 data. Our parameter estimation study includes two separate analyses: the first treats the catalog of binary events as binary black holes (BBH), while the second makes no assumption about the nature of the binary constituents and can therefore be interpreted as constraints for exotic compact objects. In the former case, we combine the posterior distributions of the individual BBH events and obtain a joint constraint of $-13 < \mathcal{H}_0 < 20$ at the $90\%$ credible interval for the BBH population. This translates into a bound on the fraction of the emitted gravitational wave energy lost due to tidal heating (or gained due to radiation enhancement effects) at $|\Delta E_H/\Delta E_{\infty}|\lesssim 3\cdot 10^{-3}$. Our work provides the first robust framework for deriving and measuring tidal heating effects in merging binary systems, demonstrating its potential as a powerful probe of the nature of binary constituents and tests of new physics., Comment: 30+18 pages, 7 figures

Dark energy is one of the potential strategies for preventing compact objects from gravitationally collapsing into singularities. Because it is the cause of the accelerated expansion of our universe, it has the greatest impact on the cosmos. Thus, it is plausible that dark energy will interact with any stellar object that is compact in the universe [\textit{Phys. Rev. D} \textbf{103}, 084042 (2021)]. Our main goal in this work is to create a simplified model, in the Rastall gravitational framework, of a charged strange star coupled to anisotropic dark energy in Krori-Barua spacetime [\textit{J. Phys. A, Math. Gen.} \textbf{8}:508, 1975]. Here, we consider a specific strange star object, Her X-1, with observed values of mass $=(0.85 \pm 0.15)M_{\odot}$ and radius $= 8.1_{-0.41}^{+0.41}$ km., so that we can develop our model. In this context, we began by modeling dark energy using the equation of state (EoS), in which the dark energy density is proportional to the isotropic perfect fluid matter-energy density. The Darmois-Israel condition has been used to calculate the unknown constants that are present in the metric. We perform a detailed analysis of the model's physical properties, including the mass-radius relation, pressure, density, metric function, and dark energy parameters, by varying the Rastall coupling parameter. We also examine the stability and force equilibrium of our proposed stellar configuration. Following a comprehensive theoretical analysis, we discovered that our suggested model is both singularity-free and meets all stability requirements needed to be a stable, physically reasonable stellar model., Comment: 17 pages, 11 figures, 1 table. Prepared and submitted to EPJC on 08.04.2024

We demonstrate that the constraints on the evolution of dark energy implemented by the DESI collaboration may be insufficient or incomplete using their own BAO data. Using large enough prior ranges for the present-day equation of state of dark energy $\omega_0$ and amplitude of dark energy evolution $\omega_a$, we obtain the complete $1\,\sigma$ and $2\,\sigma$ constraints $\omega_0=1.04^{+0.91+2.00}_{-1.00-1.90}$ and $\omega_a=-7.4^{+3.8+6.8}_{-3.2-7.3}$ indicating a beyond $2\,\sigma$ preference of quintessence-like dark energy today and an evidence of evolving dark energy at beyond $2\,\sigma$ CL, respectively. Our results are different from $\omega_0=-0.55^{+0.39}_{-0.21}$ and the $2\,\sigma$ upper limit $\omega_a<-1.32$ reported by the DESI collaboration \cite{DESI:2024mwx}. Employing a data combination of cosmic microwave background, DESI BAO and type Ia supernova, we obtain the $1\,\sigma$, $2\,\sigma$ and $3\,\sigma$ constraints $\omega_0=-0.707^{+0.089+0.18+0.24}_{-0.089-0.17-0.22}$ and $\omega_a=-1.09^{+0.38+0.67+0.82}_{-0.31-0.72-1.00}$, which reveals a $\sim4\,\sigma$ evidence of dynamical dark energy when the redshift $z\lesssim0.1$. We verify that the BAO data point from luminous red galaxies at the effective redshift $z_{\rm eff}=0.51$ hardly affects the joint constraint from the data combination of cosmic microwave background, DESI BAO and type Ia supernova. We also point out the shortcomings and advantages of the binning method widely used in cosmological analyses., Comment: 8 pages, 7 figures

We propose a methodology to measure the cosmological spatial curvature by employing the deviation from statistical isotropy due to the Alcock-Paczy\'nski effect of large scale galaxy clustering. This approach has a higher degree of model independence than most other proposed methods, being independent of calibration of standard candles, rulers, or clocks, of the power spectrum shape (and thus also of the pre-recombination physics), of the galaxy bias, of the theory of gravity, of the dark energy model and of the background cosmology in general. We find that a combined DESI-Euclid galaxy survey can achieve $\Delta \Omega_{k0}=0.057$ at 1$\sigma$ C.L. in the redshift range $z<2$ by combining power-spectrum and bispectrum measurements., Comment: 5 pages. Comments are welcome