This article explores how modifications to gravity influence the structure of the brane, with the goal of identifying the gravitational model that most closely reflects the one governing our physical universe. To achieve this, we consider a generalization of standard General Relativity. The stability of the model is evaluated through probabilistic measurements, revealing minimum points that represent the most probable and stable configurations of the brane for different values of the gravitational terms. Furthermore, the location of fermions on the brane is affected by gravitational variations, with the presence of resonance modes and the possibility of leakage of massive fermions into the bulk. Numerical analyses are presented, showing that the increase in the influence of gravitational terms increases the certainty of the location of massless fermions on the brane. All these results provide important insights for understanding the dynamics of the braneworld universe.

China

Brazil

A.R.P. Moreira

Mexico

Shi-Hai Dong

Braneworld- <italic>f</italic>( <italic>R</italic>, <italic>T</italic>, <italic>G</italic>)

In this paper, we investigate pure geometric <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> cosmology branes embedded in five-dimensional spacetime. The form of <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo stretchy='false'>)</mo></math> is chosen as a polynomial. The Five-dimensional scalar curvature <italic>R</italic> is assumed to be constant. Based on the value of the four-dimensional cosmological constant <math altimg='si2.svg'><msub><mrow><mi>&#955;</mi></mrow><mrow><mn>4</mn></mrow></msub></math>, the branes can be classified into Minkowski, de Sitter, and de anti-de Sitter cases. Solutions for each case can be calculated. These solutions are stable against linear tensor perturbations in all cases. In the Minkowski brane case, the zero mode of gravity can be localized on the brane. In the de Sitter brane case, the zero mode and one massive Kaluza-Klein mode can be localized on the brane. In the anti-de Sitter brane case, all massive Kaluza-Klein modes can be localized on the brane. The results of the analysis of tensor fluctuations are the same in both the Einstein frame and the Jordan frame.

Heng Guo

Cai-Ling Wang

Yong-Tao Lu

Yue Sun

Lang-Lang Wang

Pure geometric <italic>f</italic>( <italic>R</italic>) branes

<p>Assuming that (1) the Universe underwent a postinflationary accelerated expansion phase driven by a fluid with equation of state <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mi>P</mi><mo>=</mo><mi>w</mi><mi>ρ</mi></mrow></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>−</mo><mn>1</mn><mo>&lt;</mo><mi>w</mi><mo>&lt;</mo><mo>−</mo><mn>1</mn><mo>/</mo><mn>3</mn></math>, that (2) the cosmic horizon in an accelerating, quasi–de Sitter Universe has a temperature inversely proportional to the proper size of the horizon, and that (3) we are static observers, we calculate the frozen-in density of a stable particle of mass <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>m</mi></math> produced by the cosmic horizon that does not undergo any number-changing processes in the late Universe. We find that, as a function of the equation of state and the temperature when radiation domination starts and the quasi–de Sitter phase ends, the mass of the dark matter producing the observed cosmological abundance via this mechanism ranges from 10 keV up to close to the Planck scale.</p>

United States

Stefano Profumo

Dark matter from quasi–de Sitter horizons

It is well known that the area of the de Sitter cosmological horizon is related to the entropy of the bulk spacetime. Recent work has however shown that the horizon encodes more information about the bulk spacetime than just the entropy. In this work, we show that the horizon contains all of the gauge invariant (diffeomorphism and U(1)) information about (static albeit unstable) configurations of charged and rotating objects placed deep inside the de Sitter spacetime. We study highly symmetric objects, such as dipoles and cubes, built of objects with electric charge and angular momentum at their vertices. We show how these configurations affect the geometry of the cosmological horizon and imprint detailed information about the objects in the bulk onto the cosmological horizon.

Willy Fischler

Hare Krishna

Sarah Racz

There is more to the de Sitter horizon than just the area

We propose a new formula for the entropy of a dynamical cosmological event horizon, which is valid to leading order for perturbations of a stationary asymptotically de Sitter spacetime. By introducing a nontrivial correction term, we generalize Gibbons and Hawking’s first law of event horizons to non-stationary eras. We also develop the non-stationary physical process first law between two arbitrary horizon cross-sections for the cosmological event horizon.

Jinan Zhao

The entropy of dynamical de Sitter horizons

<p>I demonstrate that soft graviton modes in de Sitter spacetimes are the Goldstone modes of the spontaneously broken asymptotic symmetry group of de Sitter space. I then show that any local measurement, including the effects of the environment, will collapse the symmetric state onto the broken state in the large volume limit. In any discussion involving observers, de Sitter spacetimes are, therefore, best described globally by the broken phase, while local observers, in the small volume limit, can not discriminate between different degenerate global vacuum states and are therefore best described by the symmetric state. As a consequence, a small Hubbled-sized local region initially in the symmetric state will, after a time-scale corresponding to the Page time of de Sitter space, have expanded to a large region in the broken state. This illuminates the physical nature of soft graviton modes in de Sitter spacetimes.</p>

Denmark

Martin S. Sloth

Soft gravitons as Goldstone modes of spontaneously broken asymptotic symmetries in de Sitter spacetimes

This study explores wormhole solutions within two distinct modified gravity theories, namely <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity and <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity, incorporating Bose-Einstein condensate (BEC) dark matter to analyze their geometric properties. The primary objective is to comprehensively compare wormhole characteristics in these frameworks under the influence of BEC matter. The derived shape functions satisfy all fundamental traversability conditions. Furthermore, we examine the energy conditions, revealing that the NEC holds in <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>R</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity but is violated in <math altimg='si2.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo>,</mo><mi>T</mi><mo stretchy='false'>)</mo></math> gravity, highlighting the contrasting nature of wormhole solutions in these theories. Additionally, we investigate the effects of anisotropy, active gravitational mass, and surface diagram of wormhole geometries. Our findings confirm the existence of physically viable and stable wormhole models within these modified gravity theories.

India

Chaitra Chooda Chalavadi

H. Aruna Kumara

V. Venkatesha

Probing the geometries of wormholes: A comparative study of <italic>f</italic>( <italic>R</italic>, <italic>T</italic>) and <italic>f</italic>( <italic>Q</italic>, <italic>T</italic>) theories in the presence of BEC matter

We study the causal structure of Schwarzschild-de Sitter (SdS), including shock wave perturbations, in $\textit{D >}$ 3 using reflected null ray trajectories, either through the interior black hole or the exterior de Sitter region. Specifically, we compute the quasinormal mode frequencies in the eikonal, high-frequency, limit, by identifying the ‘critical time’, for arbitrary values of the black hole mass. We emphasize the important role of the static sphere proper time normalization and related boundary conditions. The computed critical times indicate the presence of singularities in the late-time, large mass, scalar field correlator in SdS, which should be resolved by introducing complex geodesics consistent with interior black hole and exterior de Sitter effective thermofield double states. In addition we relate the critical time to a diverging holographic complexity observable and compute the ‘switchback’ delay by adding a pair of shock wave perturbations for arbitrary values of the mass of the black hole.

Canada

Mir Faruk

Netherlands

Facundo Rost

Jan Schaar

Quasinormal modes and the switchback effect in Schwarzschild-de Sitter

Gravitational particle production in cosmology is a mechanism through which particles of different natures are produced during the very early universe. It is a general mechanism that explains how the universe became populated with the particles of the Standard Model after cosmic inflation and may also account for the origin of dark matter. In this work, we study the non-perturbative production of massive scalar particles in the Higgs- $$R^2$$ inflation model, a two-field scalar inflation model within the Einstein frame. We consider spectator scalar fields that are conformally or minimally coupled to the gravitational field through the curvature scalar $\textit{R}$ which in turn is a time-dependent function determined by the fields driving inflationary dynamics. We numerically compute the production of these particles using the Bogolyubov transformation method for each scenario, aiming to assess the spectrum of the produced particles. For both scenarios, we consider light particles with masses $$m_\chi \ll H_{\textrm{end}}$$ and large masses that exceed the Hubble scale at the end of inflation $$m_\chi \gtrsim H_{\textrm{end}}.$$ We use these numerical results to calculate the relic abundance $$\Omega _\chi h^2$$ to find out if the model is viable as a dark matter candidate.

Flavio Pineda

Luis Pimentel

Non-perturbative approach for scalar particle production in Higgs- $$R^2$$ inflation

The hybrid metric-Palatini gravity with Lagrangian density $$L =R+f(\mathcal {R},\mathcal {R}_{\mu \nu }\mathcal {R}^{\mu \nu })$$ is considered, where $\textit{R}$ is the metric Ricci scalar and $$\mathcal {R}_{\mu \nu }$$ is the Palatini Ricci tensor. Contrary to the standard hybrid metric-Palatini theory, because of the term $$\mathcal {R}_{\mu \nu }\mathcal {R}^{\mu \nu }$$ in the action, the model can not be analytically transformed to a scalar-tensor theory. However, on top of a maximally symmetric space-times like the FRW universe, there is a way to solve for a metric compatible connection which we will follow in this paper. The cosmological implications of the resulting model will then be fully considered. The best fit values of the model and cosmological parameters will be obtained by confronting the model with the recent observational data on the Hubble parameter. We will see that the observational data can be explained very good in this model, but, significant deviations from the standard $$\Lambda $$ CDM model could be seen in derivatives of the Hubble parameter $\textit{q}$, $\textit{j}$ and $\textit{s}$. We will perform a statefinder analysis for the model and show that its behavior differs from that of the $$\Lambda $$ CDM model. Also, we will consider the recently proposed $\textit{Om}$ diagnostics to categorize the dark energy type of the model and obtain the $$\omega $$ -varying alternative of the model that mimics the Hubble flow.

Iran

Shahab Shahidi

Shiva Kayedi

Cosmological implications of hybrid metric-Palatini $$f(\mathcal {R},\mathcal {R}_{\mu \nu }\mathcal {R}^{\mu \nu })$$ gravity