In this work, we analyze the Einstein-scalar-Gauss–Bonnet (EsGB) theory of gravity in a cosmological context using the formalism of dynamical systems. We obtain the equations of motion of the theory and introduce an appropriate set of dynamical variables to allow for a direct comparison with the results from General Relativity (GR). We observe that the cosmological phase space features the same set of fixed points as in standard GR, i.e., radiation-dominated, matter-dominated, curvature-dominated, and exponentially-accelerated solutions independently of the values of the coupling function and the scalar field. Furthermore, the radiation-dominated fixed points are repellers and the exponentially accelerated fixed points are attractors in the phase space, thus allowing for cosmological solutions behaving qualitatively similar to the $$\Lambda $$ CDM model, i.e., transitioning from a radiation-dominated phase into a matter-dominated phase, and later into a late-time cosmic acceleration phase supported by the scalar field potential. Following a reconstruction method through which we produce the cosmological solutions in the GR limit of the theory and introduce them into the general EsGB dynamical system, a numerical integration of the dynamical system shows that the EsGB theory provides cosmological solutions indistinguishable from those of the standard $$\Lambda $$ CDM model, compatible with the current observations from the Planck satellite and weak-field solar system dynamics, while maintaining the scalar field and the coupling function finite and regular throughout the entire time evolution.

Portugal

Miguel Pinto

Spain

Estonia

João Rosa

$$\Lambda $$ CDM-like evolution in Einstein-scalar-Gauss–Bonnet gravity

Motivated by the growing interest in the nonmetricity-matter couplings, we develop the scalar–tensor formulation of recently introduced ( , ) gravity, where is the nonmetricity and is the trace of the energy–momentum tensor. The main properties of the scalar–tensor formalism for the Friedmann–Lemaître–Robertson–Walker (FLRW) Universe are discussed, and we introduce an appropriate set of dynamical variables to analyze the cosmic evolution of the scalar–tensor ( , ) cosmology as a dynamical system. By considering two distinct cosmic fluids, namely matter and radiation, we have demonstrated that the cosmological phase space exhibits the typical curvature-dominated, radiation-dominated, matter-dominated, and exponentially accelerated fixed points. Furthermore, under an appropriate set of initial conditions compatible with the current observations from the Planck satellite, our analysis shows that the scalar–tensor ( , ) successfully yields models indistinguishable from the $$\Lambda $$ CDM cosmology and compatible with the weak-field solar system dynamics, without the inclusion of a cosmological constant $$\Lambda $$ . Thus, the theory introduced herein may be regarded as a suitable candidate to describe the cosmological dynamics of the Universe.

Poland

Adam Kaczmarek

Dominik Szczȩśniak

Dynamical reconstruction of the $$\Lambda $$ CDM model in the scalar–tensor representation of $$f\left( Q,T\right) $$ gravity

In this work, we apply the formalism of dynamical systems to analyze the viability of the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model in a generalized form of the hybrid metric-Palatini gravity theory written in terms of its dynamically equivalent scalar–tensor representation. Adopting a matter distribution composed of two relativistic fluids described by the equations of state of radiation and pressureless dust, one verifies that the cosmological phase space features the usual curvature-dominated, radiation-dominated, matter-dominated, and exponentially accelerated fixed points, even in the absence of a dark energy component. A numerical integration of the dynamical equations describing the system, subjected to initial conditions consistent with the cosmographic observations from the Planck satellite and weak-field solar system dynamics, shows that cosmological solutions mimicking the behavior of the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model in General Relativity (GR) are attainable in this theory, with the deviations from GR being exponentially suppressed at early-times and the scalar-field potential effectively playing the role of dark energy at late times.

Dynamical reconstruction of the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model in hybrid metric-Palatini gravity

We propose a method to determine the mass and spin of primordial black holes based on measuring the energy and emission rate at the dipolar and quadrupolar peaks in the primary photon Hawking spectrum, applicable for dimensionless spin parameters   <math> <mover> <mi>a</mi> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{a} $$  ≳ 0.6. In particular, we show that the ratio between the energies of the two peaks is only a function of the black hole spin, while the ratio between their emission rates depends also on the line-of-sight inclination. The black hole mass and distance from the Earth may then be inferred from the absolute values of the peak energies and emission rates. This method is relevant for primordial black holes born with large spin parameters that are presently still in the early stages of their evaporation process. While Hawking radiation from such black holes is somewhat below the reach of planned gamma-ray telescopes, we expect the required sensitivity to be attained in the not too distant future.

Marco Calzà

Determining the spin of light primordial black holes with Hawking radiation. Part II. High spin regime

In the string axiverse scenario, light primordial black holes may spin up due to the Hawking emission of a large number of light (sub-MeV) axions. We show that this may trigger superradiant instabilities associated with a heavier axion during the black holes’ evolution, and study the coupled dynamics of superradiance and evaporation. We find, in particular, that the present black hole mass-spin distribution should follow the superradiance threshold condition for black hole masses below the value at which the superradiant cloud forms, for a given heavy axion mass. Furthermore, we show that the decay of the heavy axions within the superradiant cloud into photon pairs may lead to a distinctive line in the black hole’s emission spectrum, superimposed on its electromagnetic Hawking emission.

Filipe Serrano

Primordial black hole superradiance and evaporation in the string axiverse

We show that warm inflation can be successfully realized in the high temperature regime through dissipative interactions between the inflaton and a single fermionic degree of freedom, provided that the latter’s mass is an oscillatory function of the inflaton field value. We demonstrate, in particular, that despite the consequent large amplitude oscillations of the eta slow-roll parameter, their effect is, on average, sufficiently suppressed to allow for a slow-roll trajectory. In addition, we demonstrate that, even though this also induces a parametric resonance that amplifies inflaton perturbations, this has a negligible effect on CMB scales in the relevant parametric range. Hence, the “Warm Little Inflaton” scenario can be realized with one less fermionic degree of freedom and no need of imposing an additional discrete interchange symmetry.

Paulo Ferraz

Shrinking the Warm Little Inflaton

We propose a method to determine the mass and spin of primordial black holes (PBHs) in the mass range 5 × 107–1012 kg (Hawking temperatures ~ 10 MeV–200 GeV), based on measuring the energy of specific features in the photon Hawking emission spectrum, including both primary and secondary components. This is motivated by scenarios where PBHs in this mass range spin up as they evaporate, namely the string axiverse, where dimensionless spin parameters   <math> <mover> <mi>a</mi> <mo>~</mo> </mover> </math>  $$ \overset{\sim }{a} $$  ~ 0.1–0.5 can be achieved through the Hawking emission of hundreds or even thousands of light axion-like particles. Measuring the present PBH mass-spin distribution may thus be an important probe of physics beyond the Standard Model. Since the proposed method relies on the energy of the photons emitted by a given PBH, rather than on the associated flux, it is independent of the PBH-Earth distance and, as a byproduct, can also be used to infer the latter.

Determining the spin of light primordial black holes with Hawking radiation

In this work, we study the possibility of finite-time future cosmological singularities appearing in f(R, T) gravity, where R is the Ricci scalar and T is the trace of the stress-energy tensor. We present the theory in both the geometrical and the dynamically equivalent scalar–tensor representation and obtain the respective equations of motion. In a background Friedmann–Lemaître–Robertson–Walker (FLRW) universe with an arbitrary curvature and for a generic  $$C^\infty $$  <math> <msup> <mi>C</mi> <mi>∞</mi> </msup> </math>   function f(R, T), we prove that the conservation of the stress-energy tensor prevents the appearance of sudden singularities in the cosmological context at any order in the time-derivatives of the scale factor. However, if this assumption is dropped, the theory allows for sudden singularities to appear at the level of the third time-derivative of the scale factor a(t), which are compensated by divergences in either the first time-derivatives of the energy density  $$\rho (t)$$  <math> <mrow> <mi>ρ</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </math>   or the isotropic pressure p(t). For these cases, we introduce a cosmological model featuring a sudden singularity that is consistent with the current measurements for the cosmological parameters, namely, the Hubble constant, deceleration parameter, and age of the universe, and provide predictions for the still unmeasured jerk and snap parameters. Finally, we analyse the constraints on a particular model of the function f(R, T) that guarantees that the system evolves in a direction favorable to the energy conditions at the divergence time.

Tiago Gonçalves

Francisco Lobo

Cosmological sudden singularities in f(R, T) gravity

In this work we study braneworld configurations in the scalar–tensor representation of the  $$f\left( R,T\right) $$  <math> <mrow> <mi>f</mi> <mfenced> <mi>R</mi> <mo>,</mo> <mi>T</mi> </mfenced> </mrow> </math>   gravity theory in the presence of a Cuscuton term in the source field matter Lagrangian. We start by deriving the scalar–tensor representation of the theory and obtaining its respective equations of motion. We then introduce the standard metric for a flat braneworld model with one extra dimension for the general case of a  $$f\left( R,T\right) $$  <math> <mrow> <mi>f</mi> <mfenced> <mi>R</mi> <mo>,</mo> <mi>T</mi> </mfenced> </mrow> </math>   theory and study two different models for the source field. Given the complexity of the field equations, these solutions are obtained numerically. In these cases, the Cuscuton term effectively amplifies the effect, by increasing the height of the stability potential barrier and, consequently, the depth of the minimum of the graviton zero-mode on the brane. Finally, we study the particular cases of  $$F(R)+T$$  <math> <mrow> <mi>F</mi> <mo>(</mo> <mi>R</mi> <mo>)</mo> <mo>+</mo> <mi>T</mi> </mrow> </math>   and  $$R+G\left( T\right) $$  <math> <mrow> <mi>R</mi> <mo>+</mo> <mi>G</mi> <mfenced> <mi>T</mi> </mfenced> </mrow> </math>  , for which only the scalar fields  $$\varphi $$  <math> <mi>φ</mi> </math>   or  $$\psi $$  <math> <mi>ψ</mi> </math>   are present, respectively, and we prove that the presence of the scalar field  $$\varphi $$  <math> <mi>φ</mi> </math>   is essential in the development of internal structure on the brane.

Brazil

D. Bazeia

A. Lobão

Effects of Cuscuton dynamics on braneworld configurations in the scalar–tensor representation of  $$f\left( R,T\right) $$  <math> <mrow> <mi>f</mi> <mfenced> <mi>R</mi> <mo>,</mo> <mi>T</mi> </mfenced> </mrow> </math>   gravity

In this work we study braneworld models in generalized     $$f\left( R,T\right) $$  <math> <mrow> <mi>f</mi> <mfenced> <mi>R</mi> <mo>,</mo> <mi>T</mi> </mfenced> </mrow> </math>   gravity theories where the action depends on a function of the Ricci scalar R and the trace of the stress–energy tensor T. We explore the so-called scalar–tensor representation of the theory, where the dependence on R and T are exchanged for two auxiliary real scalar fields. We introduce a first-order formalism to relate the auxiliary fields with the source field of brane and analyze four distinct possibilities of current interest regarding compactification and asymmetry of the brane. We investigate the behavior of the auxiliary fields and their stability in each one of the four cases. For the models where the solution of the source field engenders compact behavior, the auxiliary fields exhibit a hybrid structure, behaving differently inside and outside the compact region described by the source configuration. In particular, we found that the solutions of the auxiliary fields are significantly modified in models where the geometry is strongly influenced by the source field. Moreover, for the model capable of engendering asymmetric features, the two auxiliary fields also respond to modifications on the parameter that controls the asymmetry of the system.

Impact of compactlike and asymmetric configurations of thick branes on the scalar–tensor representation of     $$f\left( R,T\right) $$  <math> <mrow> <mi>f</mi> <mfenced> <mi>R</mi> <mo>,</mo> <mi>T</mi> </mfenced> </mrow> </math>   gravity