The standard $Λ$-CDM predicts a growth of structures which tends to be higher than the values of redshift space distortion (RSD) measurements, if the cosmological parameters are fixed by the CMB data. In this paper we point out that this discrepancy can be resolved/understood if we assume that the graviton has a small but non-zero mass. In the context of the Minimal Theory of Massive Gravity (MTMG), due to infrared Lorentz violations measurable only at present cosmological scales, the graviton acquires a mass without being haunted by unwanted extra degrees of freedom. While the so-called self-accelerating branch of cosmological solutions in MTMG has the same phenomenology for the background as well as the scalar- and vector-type linear perturbations as the $Λ$-CDM in General Relativity (GR), it is possible to choose another branch so that the background is the same as that in GR but the evolution of matter perturbations gets modified by the graviton mass. On studying the fit of such modified dynamics to the above-mentioned RSD measurements, we find that the $Λ$-CDM model is less probable than MTMG by two orders of magnitude. With the help of the cross correlation between the integrated Sachs-Wolfe (ISW) effect and the large scale structure (LSS), the data also pin-down the graviton mass squared around $μ^2\approx - (3\times 10^{-33} \rm{eV})^2$, which is consistent with the latest bound $|μ^2|<(1.2\times 10^{-22} \rm{eV})^2$ set by the recent LIGO observation.
We analyze the properties that any late-time modification of the $Λ$CDM expansion history must have in order to consistently solve both the $H_0$ and the $σ_8$ tensions. Taking a model-independent approach, we obtain a set of necessary conditions that can be applied to generic late-time extensions. Our results are fully analytical and merely based on the assumptions that the deviations from the $Λ$CDM background remain small. For the concrete case of a dark energy fluid with equation of state $w(z)$, we derive the following general requirements: (i) Solving the $H_0$ tension demands $w(z)<-1$ …
Braneworld models with variable brane tension $λ$ introduce a new degree of freedom that allows for evolving gravitational and cosmological constants, the latter being a natural candidate for dark energy. We consider a thermodynamic interpretation of the varying brane tension models, by showing that the field equations with variable $λ$ can be interpreted as describing matter creation in a cosmological framework. The particle creation rate is determined by the variation rate of the brane tension, as well as by the brane-bulk energy-matter transfer rate. We investigate the effect of a variable …
In a model independent approach, we derive generic conditions that any late time modification of the $Λ$CDM expansion history must satisfy in order to consistently solve both the $H_0$ and the $σ_8$ tensions. Our results are fully analytical and the method is merely based on the assumption that the late-time deviations from $Λ$CDM remain small. For the concrete case of a dark energy fluid with deviations encoded in the expansion history and the gravitational coupling constant, we present necessary conditions on its equation of state. Solving both the $H_0$ and $σ_8$ tensions requires that $w(z…
We propose a one-parameter extension to $Λ$CDM, expected to strongly affect cosmological tensions. An effective dark radiation component in the early universe redshifts away as hot dark matter, then quintessence, tracking the dominant equation-of-state parameter and leaving a falsifiable torsion field in the current epoch. This picture results from a new Poincaré gauge theory (PGT), one of the most promising among the latest batch of 58 PGTs found to be both power-counting renormalisable and free from ghosts and tachyons. We systematically categorise the cosmologies of 33 of these PGTs, as spe…
For a large class of mass-varying massive gravity models, the graviton mass cannot provide the late-time cosmic expansion of the universe due to its vanishing at late time. In this work, we propose a new class of mass-varying massive gravity in which the graviton mass varies according to a kinetic term of a k-essence field. By using a more general form of the fiducial metric, we found a solution such that a non-vanishing graviton mass can drive the accelerated expansion of the universe at late time. We also perform dynamical analyses of such model and found that without introducing the k-essen…
In the framework of the minimal quartet-metric gravity/systogravity, a scalar graviton/systolon is stated as a universal dark component, with supplementary manifestations in the different contexts either as dark matter or dark energy. An ensuing extension to the standard ΛCDM model is developed. A modification of the late expansion of the Universe, with an attractor of a scalar master equation defining an effective cosmological constant, which supersedes the true one, is proposed. A new partial solution to the cosmological constant problem is discussed.
The Minimal theory of Massive Gravity (MTMG) is endowed non-linearly with only two tensor modes in the gravity sector which acquire a non-zero mass. On a homogeneous and isotropic background the theory is known to possess two branches: the self-accelerating branch with a phenomenology in cosmology which, except for the mass of the tensor modes, exactly matches the one of $Λ$CDM; and the normal branch which instead shows deviation from General Relativity in terms of both background and linear perturbations dynamics. For the latter branch we study using several early and late times data sets the…
We consider a quintessence field which transitions from a matter-like to a cosmological constant behavior between recombination and the present time. We aim at easing the tension in the measurement of the present Hubble rate, and we assess the $Λ$CDM model properly enlarged to include our quintessence field against cosmological observations. The model does not address the scope we proposed. This result allows us to exclude a class of quintessential models as a solution to the tension in the Hubble constant measurements.
Many late time approaches for the solution of the Hubble tension use late time smooth deformations of the Hubble expansion rate $H(z)$ of the Planck18/$Λ$CDM best fit to match the locally measured value of $H_0$ while effectively keeping the comoving distance to the last scattering surface and $Ω_{0m} h^2$ fixed to maintain consistency with Planck CMB measurements. A well known problem of these approaches is that they worsen the fit to low $z$ distance probes. Here we show that another problem of these approaches is that they worsen the level of the $Ω_{0m}-σ_8$ growth tension. We use the gene…
Cosmological tensions in the era of precision cosmology: Insights from Tensions in Cosmology 2025
University of Sheffield（谢菲尔德大学）；University of Malta（马耳他大学）；National Observatory of Athens（雅典国家天文台）；University of Science and Technology of China（中国科学技术大学）；Universidad Católica del Norte（天主教主教大学）
We consider a scenario of modified gravity, which is generic to late-time acceleration, namely, acceleration in the Jordan frame and no acceleration in the Einstein frame. The possibility is realized by assuming an interaction between dark matter and the baryonic component in the Einstein frame which is removed by going to the Jordan frame using a disformal transformation giving rise to an exotic effective fluid responsible for causing phantom crossing at late times. In this scenario, past evolution is not distinguished from $Λ$CDM but late time dynamics is generically different due to the pre…
We consider a scenario of large-scale modification of gravity that does not invoke extra degrees of freedom but includes coupling between baryonic matter and dark matter in the Einstein frame. The total matter energy density follows the standard conservation, and evolution has the character of deceleration in this frame. The model exhibits interesting features in the Jordan frame realized by virtue of a disformal transformation where individual matter components adhere to standard conservation but gravity is modified. A generic parametrization of disformal transformation leaves thermal history…
Braneworld models have been proposed as a possible solution to the problem of the accelerated expansion of the Universe. The idea is to dispense the dark energy (DE) and drive the late-time cosmic acceleration with a five-dimensional geometry. Here, we investigate a brane model with variable brane tension as a function of redshift called chrono-brane. We propose the polynomial $λ=(1+z)^{n}$ function inspired in tracker-scalar-field potentials. To constrain the $n$ exponent we use the latest observational Hubble data from cosmic chronometers, Type Ia Supernovae from the full JLA sample, baryon …
In this work we present a further investigation about Teleparallel Gravity Cosmology. We demonstrate that according the current astrophysical data (CC+Pantheon+BAO samplers with late universe measurements SH0ES+H0LiCOW), an $f(T,B)$ theory can provide another interpretation to the oscillatory behaviour of the dark energy equation of state when applied to late times. The four $f(T,B)$ cosmological viable models proposed here can undergo an epoch of late-time acceleration and reproduce quintessence and phantom regimes with a transition along the phantom-divided line, making this theory a good ap…
Early- and late-time constraints on Wald-Gauss-Bonnet topological dark energy and implications for the $H_0$ and $S_8$ tensions
National Observatory of Athens（雅典国家天文台）；University of Peloponnese（伯罗奔尼撒大学）；Academy of Athens, Research Center for Astronomy and Applied Mathematics（雅典科学院天文学与应用数学研究中心）；School of Sciences, European University Cyprus（塞浦路斯欧洲大学理学院）；Durban University of Technology（德班理工大学）；North-West University（西北大学）；Universidad Católica de Temuco（特木科天主教大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）；CAS Key Laboratory for Researches in Galaxies and Cosmology（中国科学院星系与宇宙学重点实验室）
The standard cosmological model successfully describes many observations from widely different epochs of the Universe, from primordial nucleosynthesis to the accelerating expansion of the present day. However, as the basic cosmological parameters of the model are being determined with increasing and unprecedented precision, it is not guaranteed that the same model will fit more precise observations from widely different cosmic epochs. Discrepancies developing between observations at early and late cosmological time may require an expansion of the standard model, and may lead to the discovery o…
The Hubble tension, if not caused by any systematics, could be relieved or even resolved from modifying either the early-time or late-time Universe. The early-time modifications are usually in tension with either galaxy clustering or galaxy lensing constraints. The late-time modifications are also in conflict with the constraint from the inverse distance ladder, which, however, is weakened by the dependence on a sound-horizon prior and some particular approximation for the late-time expansion history. To achieve a more general no-go argument for the late-time scenarios, we propose to use a glo…
An only early or only late time alteration to $Λ$CDM has been inadequate at resolving both the $H_0$ and $S_8$ tensions simultaneously; however, a combination of early and late time alterations to $Λ$CDM can provide a solution to both tensions. As an illustration, we examine a combined Early Dark Energy - Decaying Dark Matter model. While early dark energy has the ability to resolve the $H_0$ tension, it leads to a discrepancy in $S_8$ measurements. We show that the addition of decaying dark matter helps resolve the $S_8$ discrepancy that would otherwise be enhanced in an early dark energy mod…
We study the cosmological effects of two-body dark matter decays where the products of the decay include a massless and a massive particle. We show that if the massive daughter particle is slightly warm it is possible to relieve the tension between distance ladder measurements of the present day Hubble parameter with measurements from the cosmic microwave background.
A Friendly Phantom: Late-time AdS-to-dS transition and cosmological tensions
Istanbul Technical University（伊斯坦布尔理工大学）；University of Ioannina（约阿尼纳大学）；Deutsches Zentrum für Astrophysik（德国天体物理中心）；Odessa National University（敖德萨国立大学）
Quasidilaton massive gravity offers a physically well-defined gravitational theory with non-zero graviton mass. We present the full set of dynamical equations governing the expansion history of the universe, valid during radiation domination, matter domination, and a late-time self-accelerating epoch related to the graviton mass. The existence of self-consistent solutions constrains the amplitude of the quasi-dilaton field and the graviton mass, as well as other model parameters. We point out that the effective mass of gravitational waves can be significantly larger than the graviton mass, ope…
National Technical University of Athens（雅典国立技术大学）；Institute for Astronomy, Astrophysics, Space Applications and Remote Sensing, National Observatory of Athens（雅典国家天文台天体物理学、空间应用与遥感研究所）；Universidad Católica del Norte（北天主教学会大学）；CAS Key Laboratory for Researches in Galaxies and Cosmology, School of Astronomy and Space Science, University of Science and Technology of China（中国科学院星系与宇宙学重点实验室，中国科学技术大学天文与空间科学学院）
Focus Point on Tensions in Cosmology from Early to Late Universe: Part II: New Directions in the Light of Observations from the Most Modern Astronomical Facilities
It has been suggested that late-universe dark matter decays can alleviate the tension between measurements of $H_0$ in the local universe and its value inferred from cosmic microwave background fluctuations. It has been suggested that decaying dark matter can potentially account for this discrepancy as it reshuffles the energy density between matter and radiation and as a result allows dark energy to become dominant at earlier times. In this work, we show that the low multipole amplitude of the cosmic microwave background anisotropy power spectrum severely constrains the feasibility of late-ti…
The $Λ$CDM model provides a good fit to most astronomical observations but harbors large areas of phenomenology and ignorance. With the improvements in the precision and number of observations, discrepancies between key cosmological parameters of this model have emerged. Among them, the most notable tension is the 4$σ$ to 6$σ$ deviation between the Hubble constant ($H_{0}$) estimations measured by the local distance ladder and the cosmic microwave background (CMB) measurement. In this review, we revisit the $H_{0}$ tension based on the latest research and sort out evidence from solutions to th…
The Hubble tension seems to be a crisis with $\sim5σ$ discrepancy between the most recent local distance ladder measurement from type Ia supernovae calibrated by Cepheids and the global fitting constraint from the cosmic microwave background data. To narrow down the possible late-time solutions to the Hubble tension, we have used in a recent study [Phys. Rev. D 105, L021301 (2022)] an improved inverse distance ladder method calibrated by the absolute measurements of the Hubble expansion rate at high redshifts from the cosmic chronometer data, and found no appealing evidence for new physics at …
We investigate the Minimal Theory of Massive Gravity (MTMG) in the light of different observational data sets which are in tension within the $Λ$CDM cosmology. In particular, we analyze MTMG model, for the first time, with the Planck-CMB data, and how these precise measurements affect the free parameters of the theory. The MTMG model can affect the CMB power spectrum at large angular scales and cause a suppression on the amplitude of the matter power spectrum. We find that on adding Planck-CMB data, the graviton has a small, positive, but non-zero mass at 68\% confidence level, and from this p…
We investigate the cosmological viability of the generalized proca theory. We first implement the background and linear perturbation equations of motion in the Boltzmann code and then study the constraints on the parameters of the generalized proca theory after running MCMC against the cosmological data set. With Planck + HST data, we obtain the constraint $h=0.7334_{-0.0269}^{+0.0246}$, which indicates that the tension between early universe and late time universe within this theory is removed. By adding other late-time data sets (BAO, RSD, etc.) we show that the tension is reduced, as the 2$…
We investigate a mechanism for the production of self-interacting dark matter based on WIMP-like messenger state decays into dark matter and dark radiation occurring after recombination. Such a transition leads to a mild relaxation of the Hubble tension, and at the same time may resolve the small-scale structure problems of the $Λ$CDM. We illustrate this mechanism in the Higgs portal dark matter model, which we find to be a promising route.
We propose an analytical parametrization of the comoving distance and Hubble parameter to study the cosmic expansion history beyond the vanilla $Λ$CDM model. The parametrization is generalized enough to include the contribution of spatial curvature and to capture the higher redshift behaviors. With this parameterization, we study the late time cosmic behavior and put constraints on the cosmological parameters like present values of Hubble parameter ($H_{0}$), matter energy density parameter ($Ω_{m0}$), spatial curvature energy density parameter ($Ω_{k0}$) and baryonic matter energy density par…
There has been a significant interest in modifications of the standard $Λ$ Cold Dark Matter ($Λ$CDM) cosmological model prompted by tensions between certain datasets, most notably the Hubble tension. The late-time modifications of the $Λ$CDM model can be parametrized by three time-dependent functions describing the expansion history of the Universe and gravitational effects on light and matter in the Large Scale Structure. We perform the first joint Bayesian reconstruction of these three functions from a combination of recent cosmological observations, utilizing a theory-informed prior built o…
A current problem within the ΛCDM framework is the tension between late and early time measurements of the Hubble parameter today, H0. We entertain the possibility that dark energy modeled as multiple interacting axion-like-particle species can alleviate the current Hubble tension. We then test these parameters against the milder tension between the CMB and large scale structure (LSS) observations of σ8 to ensure that these models do not exacerbate the tension. We find that there exist parameter spaces for models of two and three axion-like-particles which can potentially alleviate the Hubble …
Hubble tension in k-essence: Evidence for robust tension alleviation
Botswana International University of Science and Technology（博茨瓦纳国际科学与技术大学）；University of Cape Town（开普敦大学）；North-West University（西北大学）；Omdurman Islamic University（恩图曼伊斯兰大学）
