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Modified Gravity Approaches to the Tensions of ΛCDM

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A special issue of Universe (ISSN 2218-1997). This special issue belongs to the section "Gravitation".

Deadline for manuscript submissions: closed (29 February 2024) | Viewed by 29414

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Special Issue Editors

Dr. Eleonora Di Valentino

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Guest Editor

School of Mathematics and Statistics, University of Sheffield, Hounsfield Road, Sheffield S3 7RH, UK
Interests: cosmology; gravitation; astroparticle physics; high-energy physics
Special Issues, Collections and Topics in MDPI journals

Prof. Dr. Leandros Perivolaropoulos

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Guest Editor

Department of Physics, University of Ioannina, 45110 Ioannina, Greece
Interests: cosmology; modified gravity; dark energy; field theory
Special Issues, Collections and Topics in MDPI journals

Dr. Jackson Levi Said

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Guest Editor

Institute of Space Sciences and Astronomy, University of Malta, MSD 2080 Msida, Malta
Interests: cosmology; astrophysics; theories beyond general relativity
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The standard cosmological model ΛCDM is based on three main assumptions: the validity of General Relativity, the existence of a fine-tuned Cosmological Constant Λ that drives the accelerating expansion of the Universe, and the large-scale isotropy and homogeneity of the Universe (Cosmological Principle). Despite its simplicity and its relatively small number of parameters, this model is consistent with the vast majority of cosmological data. A range of statistically significant inconsistencies (tensions) with specific cosmological observations have been reported in the literature during the past few years. These inconsistencies include the measurement of the Hubble parameter which appears to be conflicting among different probes in the context of ΛCDM, the measurement of the growth rate of cosmological perturbations which are found to be slower than the ΛCDM predictions, and measurements of cosmological anisotropies (dipoles) which appear to persist on scales larger than allowed by the cosmological principle in the context of ΛCDM. If these tensions are not due to systematics, they may be the first hints for the requirements of a new theoretical framework beyond the standard model.

A well-physically motivated class of theoretical models that may address this problem is the one based on extensions of General Relativity (Modified Gravity). General Relativity, despite its fundamental nature and beauty, is an incomplete theory because it generically includes singularities and also requires finetuning to explain the accelerating cosmological expansion. Thus, Modified Gravity theories constitute a fundamentally interesting approach for the resolution of the standard model tensions.

The present Special Issue aims to provide a platform for the discussion of some of the main Modified Gravity approaches to the resolution of standard model tensions. In this context, we invite you to present your latest and main results on Modified Gravity theories, pointing out the models and references that you consider most promising in successfully addressing this important cosmological problem.

A selected group of leaders in the field have agreed to contribute to the Special Issue as Invited Authors.

We hope that you will also choose to represent your work in this Special Issue, thus promoting your ideas while at the same time enriching its content. We kindly ask the authors wishing to represent their work in the Special Issue to fill the 'Title-abstract registration form' which may be found here. This will help us to properly organize the Special Issue.

An indicative list of Modified Gravity approaches that are especially encouraged is as follows:

Scalar-tensor theories;
Scalar-tensor-vector Modified Gravity;
Modified teleparallel gravity;
Extra-dimensional theories of gravity;
f(R,T) theories;
Yang-Mills gravity;
Weyl invariant gravity;
Quantum gravity;
Conformal gravity;
Gauss-Bonnet gravity;
Non-metricity gravity f(Q,T).

Dr. Eleonora Di Valentino
Prof. Dr. Leandros Perivolaropoulos
Dr. Jackson Levi Said
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Universe is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

Hubble tension
modified gravity
cosmological parameters
standard cosmological model ΛCDM
cosmological observations
growth tension
general relativity
cosmic dipoles

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Published Papers (12 papers)

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Editorial

Jump to: Research, Review, Other

6 pages, 210 KiB

Open AccessEditorial

Special Issue on Modified Gravity Approaches to the Tensions of ΛCDM: Goals and Highlights

by Eleonora Di Valentino, Leandros Perivolaropoulos and Jackson Levi Said

Universe 2024, 10(4), 184; https://doi.org/10.3390/universe10040184 - 18 Apr 2024

Cited by 3 | Viewed by 1188

Abstract

The standard cosmological model, known as

Λ

CDM, has been remarkably successful in providing a coherent and predictive framework for understanding the Universe’s evolution, its large-scale structure, and cosmic microwave background (CMB) radiation [...] Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

Research

Jump to: Editorial, Review, Other

13 pages, 396 KiB

Open AccessEditor’s ChoiceArticle

Alleviating the H₀ Tension in Scalar–Tensor and Bi-Scalar–Tensor Theories

by Maria Petronikolou and Emmanuel N. Saridakis

Universe 2023, 9(9), 397; https://doi.org/10.3390/universe9090397 - 30 Aug 2023

Cited by 12 | Viewed by 1414

Abstract

Herein, we investigate scalar–tensor and bi-scalar–tensor modified theories of gravity that can alleviate the

H_{0}

tension. In the first class of theories, we show that by choosing particular models with a shift-symmetric friction term we are able to alleviate the tension by [...] Read more.

Herein, we investigate scalar–tensor and bi-scalar–tensor modified theories of gravity that can alleviate the

H_{0}

tension. In the first class of theories, we show that by choosing particular models with a shift-symmetric friction term we are able to alleviate the tension by obtaining a smaller effective Newton’s constant at intermediate times, a feature that cannot be easily obtained in modified gravity. In the second class of theories, which involve two extra propagating degrees of freedom, we show that the

H_{0}

tension can be alleviated, and the mechanism behind this is the phantom behavior of the effective dark-energy equation-of-state parameter. Hence, scalar–tensor and bi-scalar–tensor theories have the ability to alleviate the

H_{0}

tension with both known sufficient late-time mechanisms. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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14 pages, 3906 KiB

Open AccessArticle

Untying the Growth Index to Relieve the σ₈ Discomfort

by Ziad Sakr

Universe 2023, 9(8), 366; https://doi.org/10.3390/universe9080366 - 8 Aug 2023

Cited by 9 | Viewed by 1204

Abstract

The matter fluctuation parameter

σ_{8}

is, by model construction, degenerate with the growth index

γ

. Here, we study the effect on the cosmological parameter constraints by treating each independently from one another, considering

σ_{8}

as a free and non-derived parameter [...] Read more.

The matter fluctuation parameter

σ_{8}

is, by model construction, degenerate with the growth index

γ

. Here, we study the effect on the cosmological parameter constraints by treating each independently from one another, considering

σ_{8}

as a free and non-derived parameter along with a free

γ

. We then try to constrain all parameters using three probes that span from deep to local redshifts, namely the CMB spectrum, the growth measurements from redshift space distortions

f σ_{8}

, and the galaxy cluster counts. We also aim to assess the impact of this relaxation on the

σ_{8}

tension between its inferred CMB value in comparison to that obtained from local cluster counts. We also propose a more sophisticated correction, along with the classical one, that takes into account the impact of cosmology on the growth measurements when the parameters are varied in the Monte Carlo process, which consist in adjusting the growth to keep the observed power spectrum, integrated over all angles and scales, as invariant with the background evolution. We found by using the classical correction that untying the two parameters does not shift the maximum likelihood of either

σ_{8}

γ

, but it rather enables larger bounds with respect to when

σ_{8}

is a derived parameter, and that when considering CMB +

f σ_{8}

, or when further combining with cluster counts albeit with tighter bounds. Precisely, we obtain

σ_{8} = 0.809 \pm 0.043

and

γ = 0.613 \pm 0.046

in agreement with Planck’s constraint for the former and compatible with ΛCDM for the latter but with bounds wide enough to accommodate both values subject to the tensions. Allowing for massive neutrinos does not change the situation much. On the other hand, considering a tiered correction yields

σ_{8} = 0.734 \pm 0.013

close to ∼1

σ

for the inferred local values albeit with a growth index of

γ = 0.636 \pm 0.022

at ∼2

σ

from its ΛCDM value. Allowing for massive neutrinos in this case yielded

σ_{8} = 0.756 \pm 0.024

, still preferring low values but with much looser constraints on

γ = 0.549 \pm 0.048

and a slight preference for

Σ m_{ν} \sim 0.19

. We conclude that untying

σ_{8}

and

γ

helps in relieving the discomfort on the former between the CMB and local probes, and that careful analysis should be followed when using data products treated in a model-dependent way. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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40 pages, 942 KiB

Open AccessEditor’s ChoiceArticle

Running Vacuum in the Universe: Phenomenological Status in Light of the Latest Observations, and Its Impact on the σ₈ and H₀ Tensions

by Joan Solà Peracaula, Adrià Gómez-Valent, Javier de Cruz Pérez and Cristian Moreno-Pulido

Universe 2023, 9(6), 262; https://doi.org/10.3390/universe9060262 - 30 May 2023

Cited by 36 | Viewed by 2063

Abstract

A substantial body of phenomenological and theoretical work over the last few years strengthens the possibility that the vacuum energy density (VED) of the universe is dynamical, and in particular that it adopts the ‘running vacuum model’ (RVM) form, in which the VED [...] Read more.

δ ρ_{vac} (H) \sim ν_{eff} m_{Pl}^{2} O (H^{2})

, where H is the Hubble rate and

ν_{eff}

is a (small) free parameter. This dynamical scenario is grounded on recent studies of quantum field theory (QFT) in curved spacetime and also on string theory. It turns out that what we call the ‘cosmological constant’,

Λ

, is no longer a rigid parameter but the nearly sustained value of

8 π G (H) ρ_{vac} (H)

around any given epoch

H (t)

, where

G (H)

is the gravitational coupling, which can also be very mildly running (logarithmically). Of particular interest is the possibility suggested in past works that such a running may help to cure the cosmological tensions afflicting the

Λ

CDM. In the current study, we reanalyze the RVM in full and we find it becomes further buttressed. Using modern cosmological data, namely a compilation of the latest SNIa+BAO+

H (z)

+LSS+CMB observations, we probe to what extent the RVM provides a quality fit better than the concordance

Λ

CDM model, with particular emphasis on its impact on the

σ_{8}

and

H_{0}

tensions. We utilize the Einstein–Boltzmann system solver CLASS and the Monte Carlo sampler MontePython for the statistical analysis, as well as the statistical DIC criterion to compare the running vacuum against the rigid vacuum (

ν_{eff} = 0

). On fundamental grounds,

ν_{eff}

receives contributions from all the quantized matter fields in FLRW spacetime. We show that with a tiny amount of vacuum dynamics (

ν_{eff} ≪ 1

) the global fit can improve significantly with respect to the

Λ

CDM and the mentioned tensions may subside to inconspicuous levels. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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13 pages, 1068 KiB

Open AccessArticle

Dynamical Systems Analysis of f(Q) Gravity

by Christian Böhmer, Erik Jensko and Ruth Lazkoz

Universe 2023, 9(4), 166; https://doi.org/10.3390/universe9040166 - 29 Mar 2023

Cited by 16 | Viewed by 1678

Abstract

Modified gravity theories can be used for the description of homogeneous and isotropic cosmological models through the corresponding field equations. These can be cast into systems of autonomous differential equations because of their sole dependence on a well-chosen time variable, be it the cosmological time, or an alternative. For that reason, a dynamical systems approach offers a reliable route to study those equations. Through a model-independent set of variables, we are able to study all

f (Q)

modified gravity models. The drawback of the procedure is a more complicated constraint equation. However, it allows the dynamical system to be formulated in fewer dimensions than using other approaches. We focus on a recent model of interest, the power-exponential model, and generalize the fluid content of the model. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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20 pages, 903 KiB

Open AccessArticle

Generic Modification of Gravity, Late Time Acceleration and Hubble Tension

by Mayukh R. Gangopadhyay, Shibesh K. Jas Pacif, Mohammad Sami and Mohit K. Sharma

Universe 2023, 9(2), 83; https://doi.org/10.3390/universe9020083 - 3 Feb 2023

Cited by 17 | Viewed by 1856

Abstract

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 realised 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 intact and gives rise to late time acceleration in the Jordan frame, which necessarily includes phantom crossing, which, in the standard framework, can be realised using at least two scalar fields. This scenario is embodied by two distinguished features, namely, acceleration in the Jordan frame and deceleration in the Einstein frame, and the possibility of resolution of the Hubble tension thanks to the emergence of the phantom phase at late times. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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20 pages, 535 KiB

Open AccessEditor’s ChoiceArticle

Addressing Cosmological Tensions by Non-Local Gravity

by Filippo Bouché, Salvatore Capozziello and Vincenzo Salzano

Universe 2023, 9(1), 27; https://doi.org/10.3390/universe9010027 - 30 Dec 2022

Cited by 10 | Viewed by 2020

Abstract

Alternative cosmological models have been under deep scrutiny in recent years, aiming to address the main shortcomings of the

Λ

CDM model. Moreover, as the accuracy of cosmological surveys improved, new tensions have risen between the model-dependent analysis of the Cosmic Microwave Background [...] Read more.

Alternative cosmological models have been under deep scrutiny in recent years, aiming to address the main shortcomings of the

Λ

CDM model. Moreover, as the accuracy of cosmological surveys improved, new tensions have risen between the model-dependent analysis of the Cosmic Microwave Background and lower redshift probes. Within this framework, we review two quantum-inspired non-locally extended theories of gravity, whose main cosmological feature is a geometrically driven accelerated expansion. The models are especially investigated in light of the Hubble and growth tension, and promising features emerge for the Deser–Woodard one. On the one hand, the cosmological analysis of the phenomenological formulation of the model shows a lowered growth of structures but an equivalent background with respect to

Λ

CDM. On the other hand, the study of the lensing features at the galaxy cluster scale of a new formulation of non-local cosmology, based on Noether symmetries, makes room for the possibility of alleviating both the

H_{0}

and

σ_{8}

tension. However, the urgent need for a screening mechanism arises for this non-local theory of gravity. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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14 pages, 976 KiB

Open AccessArticle

H₀ Tension on the Light of Supermassive Black Hole Shadows Data

by Celia Escamilla-Rivera and Rubén Torres Castillejos

Universe 2023, 9(1), 14; https://doi.org/10.3390/universe9010014 - 26 Dec 2022

Cited by 10 | Viewed by 1766

Abstract

Cosmological tensions in current times have opened a wide door to study new probes to constrain cosmological parameters, specifically, to determine the value of the Hubble constant

H_{0}

through independent techniques. The two standard methods to measure/infer

H_{0}

rely on: (i) [...] Read more.

Cosmological tensions in current times have opened a wide door to study new probes to constrain cosmological parameters, specifically, to determine the value of the Hubble constant

H_{0}

through independent techniques. The two standard methods to measure/infer

H_{0}

rely on: (i) anchored observables for the distance ladder, and (ii) establishing the relationship of the

H_{0}

to the angular size of the sound horizon in the recombination era assuming a standard Cosmological Constant Cold Dark Matter (

Λ

CDM) cosmology. However, the former requires a calibration with observables at nearby distances, while the latter is not a direct measurement and is model-dependent. The physics behind these aspects restrains our possibilities in selecting a calibration method that can help minimise the systematic effects or in considering a fixed cosmological model background. Anticipating the possibility of deeply exploring the physics of new nearby observables such as the recently detected black hole shadows, in this paper we propose standard rules to extend the studies related to these observables. Supermassive black hole shadows can be characterised by two parameters: the angular size of the shadow and the black hole mass. We found that it is possible to break the degeneracy between these parameters by forecasting and fixing certain conditions at high(er) redshifts, i.e., instead of considering the ≈10% precision from the EHT array, our results reach a

\approx 4 %

, a precision that could be achievable in experiments in the near future. Furthermore, we found that our estimations provide a value of

H_{0} = 72.89 \pm 0.12

km/s/Mpc and, for the baryonic mass density,

Ω_{m} = 0.275 \pm 0.002

, showing an improvement in the values reported so far in the literature. We anticipate that our results can be a starting point for more serious treatments of the physics behind the SMBH shadow data as cosmological probes to relax tension issues. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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14 pages, 3174 KiB

Open AccessArticle

DE Models with Combined H₀ · r_d from BAO and CMB Dataset and Friends

by Denitsa Staicova

Universe 2022, 8(12), 631; https://doi.org/10.3390/universe8120631 - 28 Nov 2022

Cited by 7 | Viewed by 1594

Abstract

It has been theorized that dynamical dark energy (DDE) could be a possible solution to Hubble tension. To avoid degeneracy between Hubble parameter

H_{0}

and sound horizon scale

r_{d}

, in this article, we use their multiplication as one parameter [...] Read more.

It has been theorized that dynamical dark energy (DDE) could be a possible solution to Hubble tension. To avoid degeneracy between Hubble parameter

H_{0}

and sound horizon scale

r_{d}

, in this article, we use their multiplication as one parameter

c / (H_{0} r_{d})

, and we use it to infer cosmological parameters for 6 models—

Λ

CDM and 5 DDE parametrizations—the Chevallier–Polarski–Linder (CPL), the Barboza–Alcaniz (BA), the low correlation (LC), the Jassal–Bagla–Padmanabhan (JBP) and the Feng–Shen–Li-Li models. We choose a dataset that treats this combination as one parameter, which includes the baryon acoustic oscillation (BAO) data

0.11 \leq z \leq 2.40

and additional points from the cosmic microwave background (CMB) peaks (

z ≃ 1090

). To them, we add the marginalized Pantheon dataset and GRB dataset. We see that the tension is moved from

H_{0}

and

r_{d}

c / (H_{0} r_{d})

and

Ω_{m}

. There is only one model that satisfies the Planck 2018 constraints on both parameters, and this is LC with a huge error. The rest cannot fit into both constraints.

Λ

CDM is preferred, with respect to the statistical measures. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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Review

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24 pages, 617 KiB

Open AccessReview

The Effective Fluid Approach for Modified Gravity and Its Applications

by Savvas Nesseris

Universe 2023, 9(1), 13; https://doi.org/10.3390/universe9010013 - 24 Dec 2022

Cited by 6 | Viewed by 1347

Abstract

In this review, we briefly summarize the so-called effective fluid approach, which is a compact framework that can be used to describe a plethora of different modified gravity models as general relativity (GR) and a dark energy (DE) fluid. This approach, which is complementary to the cosmological effective field theory, has several benefits, as it allows for the easier inclusion of most modified gravity models into the state-of-the-art Boltzmann codes that are typically hard-coded for GR and DE. Furthermore, it can also provide theoretical insights into their behavior since in linear perturbation theory it is easy to derive physically motivated quantities such as the DE anisotropic stress or the DE sound speed. We also present some explicit applications of the effective fluid approach with

f (R)

, Horndeski and scalar–vector–tensor models, namely, how this approach can be used to easily solve the perturbation equations and incorporate the aforementioned modified gravity models into Boltzmann codes so as to obtain cosmological constraints using Monte Carlo analyses. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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12 pages, 470 KiB

Open AccessReview

Probing Our Universe’s Past Using Earth’s Geological and Climatological History and Shadows of Galactic Black Holes

by V. K. Oikonomou, Pyotr Tsyba and Olga Razina

Universe 2022, 8(9), 484; https://doi.org/10.3390/universe8090484 - 14 Sep 2022

Cited by 11 | Viewed by 1735

Abstract

In this short review, we discuss how Earth’s climatological and geological history and also how the shadows of galactic black holes might reveal our Universe’s past evolution. Specifically we point out that a pressure singularity that occurred in our Universe’s past might have left its imprint on Earth’s geological and climatological history and on the shadows of cosmological black holes. Our approach is based on the fact that the

H_{0}

tension problem may be resolved if some sort of abrupt physics change occurred in our Universe 70–150 Myrs ago, an abrupt change that deeply affected the Cepheid parameters. We review how such an abrupt physics change might have been caused in our Universe by a smooth passage of it through a pressure finite-time singularity. Such finite-time singularities might occur in modified gravity and specifically in

F (R)

gravity, so we show how modified gravity might drive this type of evolution, without resorting to peculiar cosmic fluids or scalar fields. The presence of such a pressure singularity can distort the elliptic trajectories of bound objects in the Universe, causing possible geological and climatological changes on Earth, if its elliptic trajectory around the Sun might have changed. Also, such a pressure singularity affects directly the circular photon orbits around supermassive galactic black holes existing at cosmological redshift distances, thus the shadows of some cosmological black holes at redshifts

z \leq 0.01

, might look different in shape, compared with the SgrA* and M87* supermassive black holes. This feature however can be checked experimentally in the very far future. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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Other

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56 pages, 3425 KiB

Open AccessFeature PaperEditor’s ChoiceOpinion

Seven Hints That Early-Time New Physics Alone Is Not Sufficient to Solve the Hubble Tension

by Sunny Vagnozzi

Universe 2023, 9(9), 393; https://doi.org/10.3390/universe9090393 - 30 Aug 2023

Cited by 128 | Viewed by 9530

Abstract

The Hubble tension has now grown to a level of significance which can no longer be ignored and calls for a solution which, despite a huge number of attempts, has so far eluded us. Significant efforts in the literature have focused on early-time [...] Read more.

Λ

CDM, introducing new physics operating prior to recombination and reducing the sound horizon. In this opinion paper I argue that early-time new physics alone will always fall short of fully solving the Hubble tension. I base my arguments on seven independent hints, related to (1) the ages of the oldest astrophysical objects, (2) considerations on the sound horizon-Hubble constant degeneracy directions in cosmological data, (3) the important role of cosmic chronometers, (4) a number of “descending trends” observed in a wide variety of low-redshift datasets, (5) the early integrated Sachs-Wolfe effect as an early-time consistency test of

Λ

CDM, (6) early-Universe physics insensitive and uncalibrated cosmic standard constraints on the matter density, and finally (7) equality wavenumber-based constraints on the Hubble constant from galaxy power spectrum measurements. I argue that a promising way forward should ultimately involve a combination of early- and late-time (but non-local—in a cosmological sense, i.e., at high redshift) new physics, as well as local (i.e., at

z \sim 0

) new physics, and I conclude by providing reflections with regards to potentially interesting models which may also help with the

S_{8}

tension. Full article

(This article belongs to the Special Issue Modified Gravity Approaches to the Tensions of ΛCDM)

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