Search

We present the results from a series of analyses on two parametric tests of gravity that modify the growth of linear, sub-horizon matter perturbations in the $\Lambda$CDM model. The first test, known as the $(\mu,\Sigma)$ framework, modifies the Poisson and lensing equations from General Relativity (GR). The second test introduces the growth index $\gamma$, which directly affects the time evolution of matter density perturbations. Our study is motivated by results from the analysis of the Planck-PR3 2018 spectra, which indicate a preference for $\Sigma_0 \neq 0$ and $\gamma_0 > 0.55$, both of which deviate from the $\Lambda$CDM predictions at a significance level of $\sim 2.5\sigma$. To clarify the nature of these anomalous results and understand how the lensing anomaly fits into the picture, we analyze the most recent Planck-PR4 spectra extracted from the updated \texttt{NPIPE} maps. Overall, the Planck-PR4 data show better consistency with GR. The updated likelihood \texttt{Camspec} provides constraints on $\Sigma_0$ and $\gamma_0$ that are consistent with GR within $1.5\sigma$ and $2\sigma$, respectively. The updated likelihoods \texttt{HiLLiPoP} and \texttt{LoLLiPoP} show even closer agreement, with all parameter values consistent with a $\Lambda$CDM cosmology within $1\sigma$. This enhanced consistency is closely correlated with the lensing anomaly. Across the different likelihoods, the tendency of $\Sigma_0$ and $\gamma_0$ to drift towards non-standard values matches the observed preference for $A_L > 1$, both of which are significantly reduced or disappear within the Planck-PR4 data., Comment: 20 pages, 6 figures

We parameterize the Hubble function by adding Hermitian wavelets to the Hubble radius of $\Lambda$CDM. This allows us to build Hubble functions that oscillate around $\Lambda$CDM at late times without modifying its angular diameter distance to last scattering. We perform parameter inference and model selection procedures on these new Hubble functions at the background level. In our analyses consisting of a wide variety of cosmological observations, we find that baryon acoustic oscillations (BAO) data play a crucial role in determining the constraints on the wavelet parameters. In particular, we focus on the differences between SDSS- and DESI-BAO datasets and find that wavelets provide a better fit to the data when either of the BAO datasets is present. However, DESI-BAO has a preference for the center of the wavelets to be around $z \sim 0.7$, while SDSS-BAO prefers higher redshifts of $z > 1$. This difference appears to be driven by the discrepancies between these two datasets in their $D_H / r_{\rm d}$ measurements at $z = 0.51$ and $z \sim 2.3$. Finally, we also derive the consequences of the wavelets on a dark energy component. We find that the dark energy density oscillates by construction and also attains negative values at large redshifts ($z\gtrsim2$) as a consequence of the SDSS-BAO data. We conclude that while the early universe and the constraints on the matter density and the Hubble constant remain unchanged, wavelets are favored in the late universe by the BAO data. Specifically, there is a significant improvement at more than $3\sigma$ in the fit when new DESI-BAO data are included in the analysis., Comment: 20 pages, 11 figures, 4 tables

In recent years, Cosmic Microwave Background (CMB) observations, Weak Lensing surveys, and $f(z)\sigma_8(z)$ measurements from Redshift-Space Distortions (RSD) have revealed a significant ($\sim$3$-$5$\sigma$) discrepancy in the inferred value of the matter clustering parameter $S_8$. In this work, we investigate the implications of RSD for a cosmological framework postulating an interaction between Dark Energy (DE) and Dark Matter (DM). We explore scenarios where DM can transfer energy-momentum to DE or vice versa. The energy-momentum flow is characterized by the strength and the sign of the coupling parameter $\xi$. Our baseline analysis combines RSD measurements with the latest data from Baryon Acoustic Oscillations (BAO) observed by DESI, Type Ia Supernovae from the PantheonPlus sample, and CMB data from Planck. We demonstrate that RSD measurements provide significant additional information. When energy-momentum flows from DM to DE (i.e., $\xi < 0$), these measurements set stringent new bounds on the interaction strength. Conversely, when energy-momentum flows from DE to DM ($\xi > 0$), they favor interactions at more than the $2\sigma$ confidence level. Models with $\xi > 0$ can effectively resolve the tension in $S_8$, presenting them as compelling alternatives., Comment: 13 pages, 6 figures. Comments welcome and appreciated

We investigate a modified cosmological model aimed at addressing the Hubble tension, considering revised dynamics in the late Universe. The model introduces a parameter $c$ affecting the evolution equations, motivated by a modified Poisson algebra inspired by effective Loop Quantum Cosmology. Our analysis includes diverse background datasets such as Cosmic Chronometers, Pantheon+ Type Ia Supernovae (with and without the SH0ES calibration), SDSS, DESY6 and DESI Baryon Acoustic Oscillations, and background information of the Cosmic Microwave Background. We find that the model alleviates the Hubble tension in most of the dataset combinations, with cases reducing discrepancies to below $1\sigma$ when including SH0ES. However, the model exhibits minimal improvement in the overall fit when compared to $\Lambda$CDM, and Bayesian evidence generally favors the standard model. Theoretical foundations support this approach as a subtle adjustment to low-redshift dynamics, suggesting potential for further exploration into extensions of $\Lambda$CDM. Despite challenges in data fitting, our findings underscore the promise of small-scale modifications in reconciling cosmological tensions., Comment: 12 pages, 4 figures, 2 tables

The recent DESI Baryon Acoustic Oscillation measurements have led to tight upper limits on the neutrino mass sum, potentially in tension with oscillation constraints requiring $\sum m_{\nu} \gtrsim 0.06\,{\text{eV}}$. Under the physically motivated assumption of positive $\sum m_{\nu}$, we study the extent to which these limits are tightened by adding other available cosmological probes, and robustly quantify the preference for the normal mass ordering over the inverted one, as well as the tension between cosmological and terrestrial data. Combining DESI data with Cosmic Microwave Background measurements and several late-time background probes, the tightest $2\sigma$ limit we find without including a local $H_0$ prior is $\sum m_{\nu}<0.05\,{\text{eV}}$. This leads to a strong preference for the normal ordering, with Bayes factor relative to the inverted one of $46.5$. Depending on the dataset combination and tension metric adopted, we quantify the tension between cosmological and terrestrial observations as ranging between $2.5\sigma$ and $5\sigma$. These results are strenghtened when allowing for a time-varying dark energy component with equation of state lying in the physically motivated non-phantom regime, $w(z) \geq -1$, highlighting an interesting synergy between the nature of dark energy and laboratory probes of the mass ordering. If these tensions persist and cannot be attributed to systematics, either or both standard neutrino (particle) physics or the underlying cosmological model will have to be questioned., Comment: 17 pages, 7 figures, positive neutrino masses

Recent Baryon Acoustic Oscillation (BAO) measurements released by DESI, when combined with Cosmic Microwave Background (CMB) data from Planck and two different samples of Type Ia supernovae (Pantheon-Plus and DESY5) reveal a preference for Dynamical Dark Energy (DDE) characterized by a present-day quintessence-like equation of state that crossed into the phantom regime in the past. A core ansatz for this result is assuming a linear Chevallier-Polarski-Linder (CPL) parameterization $w(a) = w_0 + w_a (1-a)$ to describe the evolution of the DE equation of state (EoS). In this paper, we test if and to what extent this assumption impacts the results. To prevent broadening uncertainties in cosmological parameter inference and facilitate direct comparison with the baseline CPL case, we focus on 4 alternative well-known models that, just like CPL, consist of only two free parameters: the present-day DE EoS ($w_0$) and a parameter quantifying its dynamical evolution ($w_a$). We demonstrate that the preference for DDE remains robust regardless of the parameterization: $w_0$ consistently remains in the quintessence regime, while $w_a$ consistently indicates a preference for a dynamical evolution towards the phantom regime. This tendency is significantly strengthened by DESY5 SN measurements. By comparing the best-fit $\chi^2$ obtained within each DDE model, we notice that the linear CPL parameterization is not the best-fitting case. Among the models considered, the EoS proposed by Barboza and Alcaniz consistently leads to the most significant improvement., Comment: 44 pages, 7 figures, 7 tables. V2: additional references, more details and discussion on the results and their interpretation, added a new Appendix presenting additional constraints on interesting properties of the DE EoS across the different models analyzed. Version accepted for publication in JCAP

The measurements of the cosmic microwave background (CMB) have played a significant role in understanding the nature of dark energy. In this article, we investigate the dynamics of the dark energy equation of state, utilizing high-precision CMB data from multiple experiments. We begin by examining the Chevallier-Polarski-Linder (CPL) parametrization, a commonly used and recognized framework for describing the dark energy equation of state. We then explore the general Exponential parametrization, which incorporates CPL as its first-order approximation, and extensions of this parametrization that incorporate nonlinear terms. We constrain these scenarios using CMB data from various missions, including the Planck 2018 legacy release, the Wilkinson Microwave Anisotropy Probe (WMAP), the Atacama Cosmology Telescope (ACT), and the South Pole Telescope (SPT), as well as combinations with low-redshift cosmological probes such as Baryon Acoustic Oscillations (BAO) and the Pantheon sample. While the $\Lambda$CDM cosmology remains consistent within the 68\% confidence level, we observe that the extensions of the CPL parametrization are indistinguishable for Planck data. However, for ACT and SPT data, the inclusion of additional terms begins to reveal a peak in $w_{\rm a, DE}$ that was previously unconstrained., Comment: 14 pages, 6 tables and 4 captioned figures; version published in Phys. Dark. Univ

In this study, we investigate deviations from the Planck-$\Lambda$CDM model in the late universe ($z \lesssim 2.5$) using the Gaussian Processes method, with minimal assumptions. Our goal is to understand where exploring new physics in the late universe is most relevant. We analyze recent Cosmic Chronometers (CC), Type Ia Supernovae (SN), and Baryon Acoustic Oscillations (BAO) data. By examining reconstructions of the dimensionless parameter $\delta(z)$, which measures deviations of the Hubble parameter from the Planck-$\Lambda$CDM predictions, we identify intriguing features at low ($z \lesssim 0.5$) and high ($z \gtrsim 2$) redshifts. Deviations from the Planck-$\Lambda$CDM model were not significant between $0.5\lesssim z \lesssim2$. Using the combined CC+SN+BAO dataset, we gain insights into dark energy (DE) dynamics, resembling characteristics of omnipotent DE, extending beyond quintessence and phantom models. DE exhibits n-quintessence traits for $z\gtrsim2$, transitioning with a singularity around $z\sim2$ to usual phantom traits in $1\lesssim z\lesssim2$. DE characteristics differ between scenarios ($H_0$-SH0ES and $H_0$-$\Lambda$\&CMB), with $H_0$-SH0ES leaning towards phantom traits and $H_0$-$\Lambda$\&CMB towards quintessence. We suggest exploring new physics at $z\lesssim0.5$ and $1.5\lesssim z\lesssim2.5$, particularly around $z = 2$, to understand cosmological tensions such as $H_0$ and $S_8$., Comment: 15 pages, 11 figures. Accepted for publication in EPJC

It has recently been argued that the Hubble tension may call for a combination of both pre- and post-recombination new physics. Motivated by these considerations, we provide one of the first concrete case studies aimed at constructing such a viable combination. We consider models that have individually worked best on either end of recombination so far: a spatially uniform time-varying electron mass leading to earlier recombination (also adding non-zero spatial curvature), and a sign-switching cosmological constant inducing an AdS-to-dS transition within the $\Lambda_{\rm s}$CDM model. When confronted against Cosmic Microwave Background (CMB), Baryon Acoustic Oscillations, and Type Ia Supernovae data, we show that no combination of these ingredients can successfully solve the Hubble tension. We find that the matter density parameter $\Omega_m$ plays a critical role, driving important physical scales in opposite directions: the AdS-to-dS transition requires a larger $\Omega_m$ to maintain the CMB acoustic scale fixed, whereas the varying electron mass requires a smaller $\Omega_m$ to maintain the redshift of matter-radiation equality fixed. Despite the overall failure, we use our results to draw general model-building lessons, highlighting the importance of assessing tension-solving directions in the parameter space of new physics parameters and how these correlate with shifts in other standard parameters, while underscoring the crucial role of $\Omega_m$ in this sense., Comment: 22 pages, 7 figures, 4 tables. Fig. 7 is the summary Figure. The reason for the failure of this particular combination of models and the consequent general lessons we draw are discussed between Pages 10 and 14. v2: several additional references added, minor change to title, added Bayesian evidence computation. Version accepted for publication in Phys. Dark Univ

The idea of a rapid sign-switching cosmological constant (mirror AdS-dS transition) in the late universe at $z\sim1.7$, known as the $\Lambda_{\rm s}$CDM model, has significantly improved the fit to observational data and provides a promising scenario for alleviating major cosmological tensions, such as the $H_0$ and $S_8$ tensions. However, in the absence of a fully predictive model, implementing this fit required conjecturing that the dynamics of the linear perturbations are governed by general relativity. Recent work embedding the $\Lambda_{\rm s}$CDM model with the Lagrangian of a type-II minimally modified gravity known as VCDM has propelled $\Lambda_{\rm s}$CDM to a fully predictive model, removing the uncertainty related to the aforementioned assumption; we call this new model $\Lambda_{\rm s}$VCDM. In this work, we demonstrate that not only does $\Lambda_{\rm s}$CDM fit the data better than the standard $\Lambda$CDM model, but the new model, $\Lambda_{\rm s}$VCDM, performs even better in alleviating cosmological tensions while also providing a better fit to the data, including CMB, BAO, SNe Ia, and Cosmic Shear measurements. Our findings highlight the $\Lambda_{\rm s}$CDM framework, particularly the $\Lambda_{\rm s}$VCDM model, as a compelling alternative to the standard $\Lambda$CDM model, especially by successfully alleviating the $H_0$ tension. Additionally, these models predict higher values for $\sigma_8$, indicating enhanced structuring, albeit with lower present-day matter density parameter values and consequently reduced $S_8$ values, alleviating the $S_8$ tension as well. This demonstrates that the data are well fit by a combination of background and linear perturbations, both having dynamics differing from those of $\Lambda$CDM. This paves the way for further exploration of new ways for embedding the sign-switching cosmological constant into other models., Comment: 15 pages, 5 figures, 2 tables

In any cosmological model where spacetime is described by a pseudo-Riemannian manifold, photons propagate along null geodesics, and their number is conserved, upcoming Gravitational Wave (GW) observations can be combined with measurements of the Baryon Acoustic Oscillation (BAO) angular scale to provide model-independent estimates of the sound horizon at the baryon-drag epoch. By focusing on the accuracy expected from forthcoming surveys such as LISA GW standard sirens and DESI or Euclid angular BAO measurements, we forecast a relative precision of $\sigma_{r_{\rm d}} /r_{\rm d} \sim 1.5\%$ within the redshift range $z \lesssim 1$. This approach will offer a unique model-independent measure of a fundamental scale characterizing the early universe, which is competitive with model-dependent values inferred within specific theoretical frameworks. These measurements can serve as a consistency test for $\Lambda$CDM, potentially clarifying the nature of the Hubble tension and confirming or ruling out new physics prior to recombination with a statistical significance of $\sim 4\sigma$., Comment: 13 pages, 6 figures

Low-redshift probes, such as Baryon Acoustic Oscillations (BAO) and Supernovae Ia luminosity distances, have been shown to be crucial for improving the bounds on the total neutrino mass from cosmological observations, due to their ability to break degeneracies among the different parameters. Here, we expand background observations to include $H(z)$ measurements from cosmic chronometers, distance moduli from Gamma Ray Bursts (GRBs), and angular diameter distances from galaxy clusters. For the very first time, we find neutrino mass limits below the minimal expectations from neutrino oscillation probes, suggesting non-standard neutrino and/or cosmological scenarios. The tightening of the neutrino mass bound is due to the slightly higher value of the Hubble constant $H_0$ preferred by the former three background probes, and also due to the improved errors on $H_0$ and the matter mass-energy density $\Omega_{\rm m}$. All values of $H_0$ are however in agreement at the $1-2\sigma$ level. Interestingly, it is not only the combination of the three background probes that is responsible for the $\sum m_\nu <0.06$~eV limits, but also each of them independently. The tightest bound we find here is $\sum m_\nu<0.043$~eV at $2\sigma$ after combining Cosmic Microwave Background Planck data with DESI BAO, Supernovae Ia, GRBs, cosmic chronometers, and galaxy clusters, showing a clear tension between neutrino oscillation results and cosmological analyses. In general, removing either one of the two background probes still provides a limit $\sum m_\nu \lesssim 0.06$~eV, reassuring the enormous potential of these low-redshift observations in constraining the neutrino mass., Comment: 9 pages, 5 figures

Neutrinos are the least known particle in the Standard Model of elementary particle physics. They play a crucial role in cosmology, governing the universe's evolution and shaping the large-scale structures we observe today. In this chapter, we review crucial topics in neutrino cosmology, such as the neutrino decoupling process in the very early universe. We shall also revisit the current constraints on the number of effective relativistic degrees of freedom and the departures from its standard expectation of 3. Neutrino masses represent the very first departure from the Standard Model of elementary particle physics and may imply the existence of new unexplored mass generation mechanisms. Cosmology provides the tightest bound on the sum of neutrino masses, and we shall carefully present the nature of these constraints, both on the total mass of the neutrinos and on their precise spectrum. The ordering of the neutrino masses plays a major role in the design of future neutrino mass searches from laboratory experiments, such as neutrinoless double beta decay probes. Finally, we shall also present the futuristic perspectives for an eventual direct detection of cosmic, relic neutrinos., Comment: 11 pages, 1 figure. This is a pre-print of a chapter for the Encyclopedia of Astrophysics (edited by I. Mandel, section editor C. Howlett) to be published by Elsevier as a Reference Module

We analyze a model for Dark Energy - Dark Matter interaction, based on a decaying process of the former into the latter. The dynamical equations are constructed following a kinetic formulation, which separates the interacting fluctuations from an equilibrium distribution of both 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 ($\Lambda$CDM) model, which is investigated versus a possible interpretation of the Hubble tension. Using an optimized set of the model's free parameters, it can be shown that the obtained Hubble parameter can, in principle, address the tension. We then use the most recent datasets from late Universe sources and compressed information from the Cosmic Microwave Background data to constrain the free parameters and compare the addressed scenario to the standard $\Lambda$CDM model. The study outlines how our proposal is preferred by the data in all cases, based on fit quality, while also alleviating the tension., Comment: 10 pages, 3 figures

We investigate the implications of the Baryon Acoustic Oscillation measurements released by the Dark Energy Spectroscopic Instrument (DESI) for Interacting Dark Energy (IDE) models characterized by an energy-momentum flow from Dark Matter to Dark Energy. By combining Planck-2018 and DESI data, we observe a preference for interactions exceeding the 95% confidence level, yielding a present-day expansion rate $H_0=71.4\pm1.5$ km/s/Mpc, in agreement with SH0ES. This preference remains robust when including measurements of the expansion rate $H(z)$ obtained from the relative ages of massive, early-time, and passively-evolving galaxies, as well as when considering distance moduli measurements from Type-Ia Supernovae sourced from the Pantheon-plus catalog using the SH0ES Cepheid host distances as calibrators. Overall, high and low redshift data can be equally or better explained within the IDE framework compared to $\Lambda$CDM, while also yielding higher values of $H_0$ in better agreement with the local distance ladder estimate., Comment: 6 pages, 3 figures

The Special Issue on "Modified Gravity Approaches to the Tensions of $\Lambda$CDM"} in the Universe journal tackles significant challenges faced by the $\Lambda$CDM model, including discrepancies in the Hubble constant, growth rate of structures, and cosmological anisotropies. These issues suggest foundational cracks in the model, raising questions about the validity of General Relativity, dark energy, and cosmological principles at large scales. This collection brings together leading researchers to delve into Modified Gravity theories as potential solutions. Covering approaches from Scalar-Tensor theories to $f(R,T)$ gravity and beyond, each contribution presents innovative research aimed at addressing the limitations of the $\Lambda$CDM model. This Special Issue not only highlights the theoretical and empirical strengths of Modified Gravity models but also opens avenues for future investigations, emphasizing the synergy between theoretical advancements and observational evidence to deepen our cosmological understanding., Comment: 6 pages no figures Published in Universe in the Special Issue "Modified Gravity Approaches to the Tensions of $\Lambda$CDM" ( https://www.mdpi.com/journal/universe/special_issues/Gravit )

We present model-marginalized limits on the six standard $\Lambda$CDM cosmological parameters ($\Omega_{\rm c} h^2$, $\Omega_{\rm b} h^2$, $\theta_{\rm MC}$, $\tau_{\rm reio}$, $n_s$ and $A_s$), as well as on selected derived quantities ($H_0$, $\Omega_{\rm m}$, $\sigma_8$, $S_8$ and $r_{\rm drag}$), obtained by considering three independent Cosmic Microwave Background (CMB) experiments: the Planck satellite, the Atacama Cosmology Telescope, and South Pole Telescope. We also consider low redshift observations in the form of Baryon Acoustic Oscillation (BAO) data from the SDSS-IV eBOSS survey and Supernovae (SN) distance moduli measurements from the Pantheon-Plus catalog. The marginalized errors are stable against the different fiducial cosmologies explored in this study. The largest impact on the parameter accuracy is produced by varying the effective number of relativistic degrees of freedom ($N_{\rm eff}$) or the lensing amplitude ($A_{\rm lens}$). Nevertheless the marginalized errors on some derived parameters such as $H_0$ or $\Omega_{\rm m}$ can be up to two orders of magnitude larger than in the canonical $\Lambda$CDM scenario when considering only CMB data. In these cases, low redshift measurements are crucial for restoring the stability of the marginalized cosmological errors computed here. Overall, our results underscore remarkable stability in the mean values and precision of the main cosmological parameters, making irrelevant the choice of different possible cosmological scenarios once both high and low redshift probes are fully accounted for. The very same results should be understood as a tool to test exotic cosmological scenarios, as the marginalized values should be used in numerical analyses due to their robustness and slightly larger errors, providing a more realistic and conservative approach., Comment: 18 pages, 11 figures, 12 tables. Prepared for submission to PRD

We present a comprehensive reassessment of the state of Interacting Dark Energy (IDE) cosmology, namely models featuring a non-gravitational interaction between Dark Matter (DM) and Dark Energy (DE). To achieve high generality, we extend the dark sector physics by considering two different scenarios: a non-dynamical DE equation of state $w_0\neq-1$, and a dynamical $w(a)=w_0+w_a(1-a)$. In both cases, we distinguish two different physical regimes resulting from a phantom or quintessence equation of state. To circumvent early-time superhorizon instabilities, the energy-momentum transfer should occur in opposing directions within the two regimes, resulting in distinct phenomenological outcomes. We study quintessence and phantom non-dynamical and dynamical models in light of two independent Cosmic Microwave Background (CMB) experiments - the Planck satellite and the Atacama Cosmology Telescope. We analyze CMB data both independently and in combination with Supernovae (SN) distance moduli measurements from the Pantheon-Plus catalog and Baryon Acoustic Oscillations (BAO) from the SDSS-IV eBOSS survey. Our results update and extend the state-of-the-art analyses, significantly narrowing the parameter space allowed for these models and limiting their overall ability to reconcile cosmological tensions. Although considering different combinations of data leaves some freedom to increase $H_0$ towards the value measured by the SH0ES collaboration, our most constraining dataset (CMB+BAO+SN) indicates that fully reconciling the tension solely within the framework of IDE remains challenging., Comment: 21 pages, 4 figures, 9 tables. V2: additional references added, clarified some aspects of the results, their interpretation, and implications. Version accepted for publication in PRD

We explore the possibility of redshift-dependent deviations in the contribution of relativistic degrees of freedom to the radiation budget of the cosmos, conventionally parameterized by the effective number of neutrinos $N_{\rm eff}$, from the predictions of the standard model. We expand the deviations $\Delta N_{\rm eff}(z)$ in terms of top-hat functions and treat their amplitudes as the free parameters of the theory to be measured alongside the standard cosmological parameters by the Planck measurements of the cosmic microwave background (CMB) anisotropies and Baryonic Acoustic Oscillations, as well as performing forecasts for futuristic CMB surveys such as PICO and CMB-S4. We reconstruct the history of $\Delta N_{\rm eff}$ and find that with the current data the history is consistent with the standard scenario. Inclusion of the new degrees of freedom in the analysis increases $H_0$ to $68.71\pm 0.44$, slightly reducing the Hubble tension. With the smaller forecasted errors on the $\Delta N_{\rm eff}(z)$ parametrization modes from future CMB surveys, very accurate bounds are expected within the possible range of dark radiation models., Comment: 6 pages, 7 figures

The main aim of this work is to use a model-independent approach, along with late-time observational probes, to reconstruct the dark energy (DE) equation of state $w_{\rm DE}(z)$. Our analysis showed that, for a late time universe, $w_{\rm DE}$ deviates from being a constant but in contrast exhibits an oscillatory behavior, hence both quintessence ($w_{\rm DE}> -1$) and phantom ($w_{\rm DE} < -1$) regimes are equally allowed. In order to portray this oscillatory behavior, we explored various parametrizations for the equation of state and identified the closest approximation based on the goodness of fit with the data and the Bayesian evidence analysis. Our findings indicated that while all considered oscillating DE parametrizations provided a better fit to the data, compared to the cosmological constant, they are penalized in the Bayesian evidence analysis due to the additional free parameters. Overall, the present article demonstrates that in the low redshift regime, the equation of state of the DE prefers to be dynamical and oscillating. We anticipate that future cosmological probes will take a stand in this direction., Comment: 12 pages, 5 figures, 4 tables

Understanding the behavior of the matter power spectrum on non-linear scales beyond the $\Lambda$CDM model is crucial for accurately predicting the large-scale structure (LSS) of the Universe in non-standard cosmologies. In this work, we present an analysis of the non-linear matter power spectrum within the framework of interacting dark energy-dark matter cosmologies (IDE). We employ N-body simulations and theoretical models to investigate the impact of IDE on these non-linear scales. Beginning with N-body simulations characterized by a fixed parameter space delineated by prior observational research, we adeptly fit the simulated spectra with a simple parametric function, achieving accuracy within 5\%. Subsequently, we refine a modified halo model tailored to the IDE cosmology, exhibiting exceptional precision in fitting the simulations down to scales of approximately 1 h/Mpc. To assess the model's robustness, we conduct a forecast analysis for the Euclid survey, employing our refined model. We find that the coupling parameter $\xi$ will be constrained to $\sigma(\xi) = 0.0110$. This marks a significant improvement by an order of magnitude compared to any other current observational tests documented in the literature. These primary findings pave the way for a novel preliminary approach, enabling the utilization of IDE models for observational constraints concerning LSS data on non-linear scales., Comment: 15 pages, 6 figures and 1 table. Matches the version published in EPJC

This research investigates the impact of the nature of Dark Energy (DE) on structure formation, focusing on the matter power spectrum and the Integrated Sachs-Wolfe effect (ISW). By analyzing the matter power spectrum at redshifts $z = 0$ and $z = 5$, as well as the ISW effect on the scale of $\ell = 10-100$, the study provides valuable insights into the influence of DE equations of state (EoS) on structure formation. The findings reveal that dynamical DE models exhibit a stronger matter power spectrum compared to constant DE models, with the JBP model demonstrating the highest amplitude and the CPL model the weakest. Additionally, the study delves into the ISW effect, highlighting the time evolution of the ISW source term $\mathcal{F}(a)$ and its derivative $d\mathcal{F}(a)/da$, and demonstrating that models with constant DE EoS exhibit a stronger amplitude of $\mathcal{F}(a)$ overall, while dynamical models such as CPL exhibit the highest amplitude among the dynamical models, whereas JBP has the lowest. The study also explores the ISW auto-correlation power spectrum and the ISW cross-correlation power spectrum, revealing that dynamical DE models dominate over those with constant DE EoS across various surveys. Moreover, it emphasizes the potential of studying the non-linear matter power spectrum and incorporating datasets from the small scales to further elucidate the dynamical nature of dark energy. This comprehensive analysis underscores the significance of both the matter power spectrum and the ISW signal in discerning the nature of dark energy, paving the way for future research to explore the matter power spectrum at higher redshifts and in the non-linear regime, providing deeper insights into the dynamical nature of dark energy.

In this study, we introduce a novel late-time effective dark energy model characterized by a quadratic equation of state (EoS) and rigorously examine its observational constraints. Initially, we delve into the background dynamics of this model, tracing the evolution of fluctuations in linear order. Our approach involves substituting the conventional cosmological constant with a dynamically effective dark energy fluid. Leveraging a diverse array of observational datasets encompassing the Planck 2018 Cosmic Microwave Background (CMB), Type Ia Supernovae (SNe), Baryon Acoustic Oscillations (BAO), and a prior on the Hubble constant $H_0$ (R21), we constrain the model parameters. We establish the model's consistency by comparing the Hubble parameter as a function of redshift against observational Hubble data (OHD), benchmarking its performance against the Standard $\Lambda$CDM model. Additionally, our investigation delves into studies of the model's dynamical behavior by computing cosmological parameters such as the deceleration parameter, relative Hubble parameter, and the evolution of the Hubble rate. Furthermore, employing Bayesian analysis, we determine the Bayesian Evidence for our proposed model compared to the reference $\Lambda$CDM model. While our analysis unveils the favorable behavior of the model in various observational tests, the well-known cosmological tensions persist when the full dataset combination is explored., Comment: 19 pages, 12 figures, Appendix added

We investigated a possible interaction between cold dark matter and dark energy, corresponding to a well-known interacting dark energy model discussed in the literature within the context of resolving the Hubble tension. We put constraints on it in a novel way, by creating new likelihoods with an analytical marginalization over the Hubble parameter $H_0$, the sound horizon $r_d$, and the supernova absolute magnitude $M_B$. Our aim is to investigate the impacts on the coupling parameter of the interacting model, $\xi$, and the equation of state of dark energy $w$ and the matter density parameter $\Omega_{m,0}$. The late-time cosmological probes used in our analysis include the PantheonPlus (calibrated and uncalibrated), cosmic chronometers, and baryon acoustic oscillation samples and the Pantheon for comparison. Through various combinations of these datasets, we demonstrate hints of an up to $2\sigma$ deviation from the standard $\Lambda$ cold dark matter model., Comment: published in Astronomy & Astrophysics

We have successfully integrated $\Lambda_{\rm s}$CDM, a promising model for alleviating cosmological tensions, into a theoretical framework by endowing it with a specific Lagrangian from the VCDM model, a type-II minimally modified gravity. In this theory, we demonstrate that an auxiliary scalar field with a linear potential induces an effective cosmological constant, enabling the realization of an abrupt mirror AdS-dS transition in the late universe through a piecewise linear potential. To eliminate the sudden singularity in this setup and ensure stable transitions, we smooth out this potential. Realized within the VCDM theory, the $\Lambda_{\rm s}$CDM model facilitates two types of rapid smooth mirror AdS-dS transitions: (i) the agitated transition, associated with a smooth jump in the potential, where $\Lambda_{\rm s}$, and consequently $H$, exhibits a bump around the transition's midpoint; and (ii) the quiescent transition, associated with a smooth change in the slope of the potential, where $\Lambda_{\rm s}$ transitions gracefully. These transitions are likely to leave distinct imprints on the background and perturbation dynamics, potentially allowing the observational data to distinguish between them. This novel theoretical framework propels $\Lambda_{\rm s}$CDM into a fully predictive model capable of exploring the evolution of the Universe including the late-time AdS-dS transition epoch, and extends the applicability of the model. We believe further research is crucial in establishing $\Lambda_{\rm s}$CDM as a leading candidate or guide for a new concordance cosmological model., Comment: 9 pages (including appendices), 4 figures, and no tables

Due to universality and attractor properties, $\alpha$-attractor quintessential inflation establishes direct relations between inflationary observables such as the scalar tilt $n_s$ and the tensor-to-scalar ratio $r$, and late-time dark energy equation of state parameters $w_0$ and $w_a$. In this work, we examine three different physically motivated regimes, considering complete freedom in the parameter $\alpha$, models inspired by supergravity where $\alpha$ takes on values up to $\alpha=7/3$, and Starobinsky inflation ($\alpha=1$). We investigate the consistency and constraints imposed by Cosmic Microwave Background measurements from the Planck satellite, B-mode polarization data from the BICEP/Keck collaboration, and low-redshift observations. Additionally, we consider small-scale CMB measurements released by the Atacama Cosmology Telescope, which give results approaching the Harrison-Zel'dovich spectrum ($n_s \approx 1$). Here $\alpha$-attractors lead to an improved fit over $\Lambda$CDM. For the large-scale CMB measurements, $\alpha\gtrsim2$ models can provide equally good fits as $\Lambda$CDM., Comment: 25 pages, 6 figures, 9 tables

Although the Lambda Cold Dark Matter model is the most accredited cosmological model, information at intermediate redshifts (z) between type Ia Supernovae (z = 2.26) and the Cosmic Microwave Background (z = 1100) is crucial to validate this model further. Here, we present a detailed and reliable methodology for binning the quasars (QSO) data that allows the identification of a golden sample of QSOs to be used as standard candles. This procedure has the advantage of being very general. Thus, it can be applied to any astrophysical sources at cosmological distances. This methodology allows us to avoid the circularity problem since it involves a flux-flux relation and includes the analysis of removing selection biases and the redshift evolution. With this method, we have discovered a sample of 1253 quasars up to z = 7.54 with reduced intrinsic dispersion of the relation between Ultraviolet and X-ray fluxes, with $\delta_{int} = 0.096\pm 0.003$ (56\% less than the original sample where $\delta_{int} =0.22$). Once the luminosities are corrected for selection biases and redshift evolution, this `gold' sample allows us to determine the matter density parameter to be $\Omega_M=0.240 \pm 0.064$. This value is aligned with the results of the $\Lambda CDM$ model obtained with SNe Ia., Comment: accepted in Physics of the Dark Universe, 16 figures and 1 table