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13 pages, 1400 KiB

Open AccessArticle

Propagation of Tensor Perturbation in Horndeski-like Gravity

by Fabiano F. Santos and Jackson Levi Said

Symmetry 2025, 17(5), 675; https://doi.org/10.3390/sym17050675 - 28 Apr 2025

Viewed by 448

Scalar–tensor theories have shown promise in many sectors of cosmology. However, recent constraints from the speed of gravitational waves have put severe limits on the breadth of models such classes of theories can realize. In this work, we explore the possibility of a [...] Read more.

Scalar–tensor theories have shown promise in many sectors of cosmology. However, recent constraints from the speed of gravitational waves have put severe limits on the breadth of models such classes of theories can realize. In this work, we explore the possibility of a Horndeski Lagrangian that is equipped with two dilaton fields. The evolution of a two-dilaton coupled cosmology is not well known in the literature. We explore the tensor perturbations in order to assess the behavior of the model against the speed of the gravitational wave constraint. Our main result is that this model exhibits a class of cosmological theories that is consistent with this observational constraint. Full article

(This article belongs to the Special Issue Gravitational Physics and Symmetry)

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49 pages, 491 KiB

Open AccessReview

FeynGrav and Recent Progress in Computational Perturbative Quantum Gravity

by Boris Latosh

Symmetry 2024, 16(1), 117; https://doi.org/10.3390/sym16010117 - 18 Jan 2024

Cited by 3 | Viewed by 1789

Abstract

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study [...] Read more.

This article reviews recent progress in computational quantum gravity caused by the framework that efficiently computes Feynman’s rules. The framework is implemented in the FeynGrav package, which extends the functionality of the widely used FeynCalc package. FeynGrav provides all the tools to study quantum gravitational effects within the standard model. We review the framework, provide the theoretical background for the efficient computation of Feynman rules, and present the proof of its completeness. We review the derivation of Feynman rules for general relativity, Horndeski gravity, Dirac fermions, Proca field, electromagnetic field, and

S U (N)

Yang–Mills model. We conclude with a discussion of the current state of the FeynGrav package and discuss its further development. Full article

(This article belongs to the Section Physics)

69 pages, 819 KiB

Open AccessFeature PaperReview

Recent Advances in Inflation

by Sergei D. Odintsov, Vasilis K. Oikonomou, Ifigeneia Giannakoudi, Fotis P. Fronimos and Eirini C. Lymperiadou

Symmetry 2023, 15(9), 1701; https://doi.org/10.3390/sym15091701 - 5 Sep 2023

Cited by 157 | Viewed by 8812

Abstract

We review recent trends in inflationary dynamics in the context of viable modified gravity theories. After providing a general overview of the inflationary paradigm emphasizing on what problems hot Big Bang theory inflation solves, and a somewhat introductory presentation of single-field inflationary theories [...] Read more.

We review recent trends in inflationary dynamics in the context of viable modified gravity theories. After providing a general overview of the inflationary paradigm emphasizing on what problems hot Big Bang theory inflation solves, and a somewhat introductory presentation of single-field inflationary theories with minimal and non-minimal couplings, we review how inflation can be realized in terms of several string-motivated models of inflation, which involve Gauss–Bonnet couplings of the scalar field, higher-order derivatives of the scalar field, and some subclasses of viable Horndeski theories. We also present and analyze inflation in the context of Chern–Simons theories of gravity, including various subcases and generalizations of string-corrected modified gravities, which also contain Chern–Simons correction terms, with the scalar field being identified with the invisible axion, which is the most viable to date dark matter candidate. We also provide a detailed account of vacuum

f (R)

gravity inflation, and also inflation in

f (R, ϕ)

and kinetic-corrected

f (R, ϕ)

theories of gravity. At the end of the review, we discuss the technique for calculating the overall effect of modified gravity on the waveform of the standard general relativistic gravitational wave form. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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44 pages, 1867 KiB

Open AccessReview

Modified Gravity Approaches to the Cosmological Constant Problem

by Foundational Aspects of Dark Energy (FADE) Collaboration, Heliudson Bernardo, Benjamin Bose, Guilherme Franzmann, Steffen Hagstotz, Yutong He, Aliki Litsa and Florian Niedermann

Universe 2023, 9(2), 63; https://doi.org/10.3390/universe9020063 - 20 Jan 2023

Cited by 13 | Viewed by 2635

Abstract

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein’s general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We [...] Read more.

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein’s general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We introduce a modern and concise language to describe the problems associated with its phenomenology, and inspect no-go theorems and their loopholes to motivate the approaches discussed here. Constrained gravity approaches exploit minimal departures from general relativity; massive gravity introduces mass to the graviton; Horndeski theories lead to the breaking of translational invariance of the vacuum; and models with extra dimensions change the symmetries of the vacuum. We also review screening mechanisms that have to be present in some of these theories if they aim to recover the success of general relativity on small scales as well. Finally, we summarize the statuses of these models in their attempts to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations. Full article

(This article belongs to the Special Issue Cosmological Constant)

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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 7 | Viewed by 1744

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 [...] Read more.

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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39 pages, 671 KiB

Open AccessFeature PaperReview

Measuring Gravity at Cosmological Scales

by Luca Amendola, Dario Bettoni, Ana Marta Pinho and Santiago Casas

Universe 2020, 6(2), 20; https://doi.org/10.3390/universe6020020 - 22 Jan 2020

Cited by 35 | Viewed by 3909

Abstract

This review is a pedagogical introduction to models of gravity and how they are constrained through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of assumptions. Alternatives or extensions of general [...] Read more.

This review is a pedagogical introduction to models of gravity and how they are constrained through cosmological observations. We focus on the Horndeski scalar-tensor theory and on the quantities that can be measured with a minimum of assumptions. Alternatives or extensions of general relativity have been proposed ever since its early years. Because of the Lovelock theorem, modifying gravity in four dimensions typically means adding new degrees of freedom. The simplest way is to include a scalar field coupled to the curvature tensor terms. The most general way of doing so without incurring in the Ostrogradski instability is the Horndeski Lagrangian and its extensions. Testing gravity means therefore, in its simplest term, testing the Horndeski Lagrangian. Since local gravity experiments can always be evaded by assuming some screening mechanism or that baryons are decoupled, or even that the effects of modified gravity are visible only at early times, we need to test gravity with cosmological observations in the late universe (large-scale structure) and in the early universe (cosmic microwave background). In this work, we review the basic tools to test gravity at cosmological scales, focusing on model-independent measurements. Full article

(This article belongs to the Section Cosmology)

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8 pages, 246 KiB

Open AccessReview

A Review on the Cosmology of the de Sitter Horndeski Models

by Nelson J. Nunes, Prado Martín-Moruno and Francisco S. N. Lobo

Universe 2017, 3(2), 33; https://doi.org/10.3390/universe3020033 - 31 Mar 2017

Cited by 7 | Viewed by 3220

Abstract

We review the most general scalar-tensor cosmological models with up to second-order derivatives in the field equations that have a fixed spatially flat de Sitter critical point independent of the material content or vacuum energy. This subclass of the Horndeski Lagrangian is capable [...] Read more.

We review the most general scalar-tensor cosmological models with up to second-order derivatives in the field equations that have a fixed spatially flat de Sitter critical point independent of the material content or vacuum energy. This subclass of the Horndeski Lagrangian is capable of dynamically adjusting any value of the vacuum energy of the matter fields at the critical point. We present the cosmological evolution of the linear models and the non-linear models with shift symmetry. We come to the conclusion that the shift symmetric non-linear models can deliver a viable background compatible with current observations. Full article

(This article belongs to the Special Issue Varying Constants and Fundamental Cosmology)

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14 pages, 265 KiB

Open AccessArticle

k-Essence Non-Minimally Coupled with Gauss–Bonnet Invariant for Inflation

by Ratbay Myrzakulov and Lorenzo Sebastiani

Symmetry 2016, 8(7), 57; https://doi.org/10.3390/sym8070057 - 28 Jun 2016

Cited by 7 | Viewed by 4672

Abstract

In this paper, we investigated inflationary solutions for a subclass of Horndeski models where a scalar field is non-minimally coupled with the Gauss–Bonnet invariant. Examples of canonical scalar field and k-essence to support the early-time acceleration are considered. The formalism to calculate [...] Read more.

In this paper, we investigated inflationary solutions for a subclass of Horndeski models where a scalar field is non-minimally coupled with the Gauss–Bonnet invariant. Examples of canonical scalar field and k-essence to support the early-time acceleration are considered. The formalism to calculate the perturbations in a Friedmann–Robertson–Walker (FRW) universe and to derive the spectral index and the tensor-to-scalar ratio is furnished. Full article

(This article belongs to the Special Issue Symmetry: Feature Papers 2016)

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