Weyl geometric gravity theory, in which gravitational action is constructed from the square of the Weyl curvature scalar and the strength of the Weyl vector, has been intensively investigated recently. The theory admits a scalar–vector–tensor representation, obtained by introducing an auxiliary scalar field, and can therefore be reformulated as a scalar–vector–tensor theory in a Riemann space in the presence of a non-minimal coupling between the Ricci scalar and the scalar field. By assuming that the Weyl vector has only a radial component, an exact spherically symmetric vacuum solution of the field equations can be obtained, depending on three integration constants. As compared to the Schwarzschild solution, the Weyl geometric gravity solution contains two new terms, linear and quadratic, in the radial coordinate, respectively. We consider the possibility of testing and obtaining observational restrictions on the Weyl geometric gravity black hole at the scale of the Solar System, by considering six classical tests of general relativity (gravitational redshift, the Eötvös parameter and the universality of free fall, the Nordtvedt effect, the planetary perihelion precession, the deflection of light by a compact object, and the radar echo delay effect) for an exact spherically symmetric black hole solution of the Weyl geometric gravity. These gravitational effects can be fully explained, and are consistent with the vacuum solution of the Weyl geometric gravity. Moreover, the study of the classical general relativistic tests also allows us to constrain the free parameter of the solution.

Iran

Azerbaijan

Mohsen Khodadi

Romania

Tiberiu Harko

Weyl geometric gravity black holes in light of the Solar System tests

We consider the implications of modified dispersion relations, due to the noncommutativity of spacetime, for a photon gas filling the early Universe in the framework of the Big Bang nucleosynthesis (BBN) processes, during the period of light element formation. We consider three types of deformations present in the dispersion relations for radiation gas, from which we obtain low-temperature corrections to the energy density and pressure. The cosmological implications of the modified equations of state in the BBN era are explored in detail for all radiation models. Effects on the nucleosynthesis process induced by spacetime noncommutativity are investigated by evaluating the abundance of relic nuclei (hydrogen, deuterium, helium-3, helium-4, and lithium-7). Primordial mass fraction estimates and their deviations due to changes in the freezing temperature impose an upper limit on the energy density of deformed photon gas, which follows from the modified Friedmann equations. Deviations from the standard energy density of the radiative plasma are therefore constrained by the abundance of helium-4 nuclei. Upper limits on the free parameters of spacetime noncommutativity are obtained via a numerical analysis performed using the software package. The primordial abundance of light elements is obtained by evaluating thermonuclear reaction rates for the considered noncommutative spacetime models. A Markov chain Monte Carlo (MCMC) analysis allows us to obtain restrictions on the free parameters of the modified dispersion relations. The numerical and statistical approach is implemented in Python code , available on GitHub.

Teodora Matei

Cristian Croitoru

Big Bang Nucleosynthesis constraints on space-time noncommutativity

We investigate the effects that arise from the inclusion of boundary terms in the Einstein gravitational field equations in the Big Bang Nucleosynthesis (BBN) framework. In particular, we consider the possibility that the boundary of the Universe is described by a Weyl type geometry. With the help of the generalized Friedmann equations for a Universe with a Weylian boundary, obtained for a Friedmann–Lemaitre–Robertson–Walker FLRW metric, three distinct cosmological models can be constructed. The cosmological evolution is determined by a dissipative scalar field, and by the Weyl vector coming from the boundary. Several cosmological scenarios are obtained via the appropriate splitting of the generalized energy conservation equation. In the present work we obtain relevant constraints on these models by using the BBN data. In particular, the effects on the BBN that arise in the post warm-inflationary era will be examined by theoretically evaluating the measured abundances of relic nuclei (Hydrogen, Deuterium, Helium-3, Helium-4, and Lithium-7). We consider firstly the primordial mass fraction estimates, and their deviations due to changes in the freezing temperature, which impose an upper limit on the effective energy density obtained from the modified Friedmann equations. The deviation from the standard energy density of the radiative plasma is therefore constrained by the abundances of the Helium-4 nuclei. Secondly, an upper limit will be considered in a numerical analysis performed through the usage of the software package, with the help of which we calculate the primordial abundances of the light elements by evaluating the thermonuclear rates within the considered modified gravity framework. Finally, an MCMC analysis will validate the cosmological model with Weylian boundary contributions, imposing relevant constraints on the initial conditions of the cosmos. The methodology is implemented in the python code , which is available on GitHub.

Big Bang Nucleosynthesis constraints on the cosmological evolution in a Universe with a Weylian boundary

We investigate the properties of compact objects in the f(Q, T) theory, where  $$\mathcal {Q}$$  <math> <mi>Q</mi> </math>   is the non-metricity scalar and  $${ \mathcal {T}}$$  <math> <mi>T</mi> </math>   is the trace of the energy–momentum tensor. We derive an interior analytical solution for anisotropic perfect-fluid spheres in hydrostatic equilibrium using the linear form of  $$f(\mathcal {Q}, { \mathcal {T}})=\mathcal {Q}+\psi { \mathcal {T}}$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mi>ψ</mi> <mi>T</mi> </mrow> </math>  , where  $$\psi $$  <math> <mi>ψ</mi> </math>   represents a dimensional parameter. Based on the observational constraints related to the mass and radius of the pulsar SAX J1748.9-2021,  $$\psi $$  <math> <mi>ψ</mi> </math>   is set to a maximum negative value of  $$\psi _1=\psi / \kappa ^2=-0.04$$  <math> <mrow> <msub> <mi>ψ</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>ψ</mi> <mo>/</mo> <msup> <mi>κ</mi> <mn>2</mn> </msup> <mo>=</mo> <mo>-</mo> <mn>0.04</mn> </mrow> </math>  , where  $$\kappa ^2$$  <math> <msup> <mi>κ</mi> <mn>2</mn> </msup> </math>   is the gravitational coupling constant. The solution results in a stable compact object, which does not violate the speed of sound condition  $$c_s^2\le \frac{c^2}{3}$$  <math> <mrow> <msubsup> <mi>c</mi> <mi>s</mi> <mn>2</mn> </msubsup> <mo>≤</mo> <mfrac> <msup> <mi>c</mi> <mn>2</mn> </msup> <mn>3</mn> </mfrac> </mrow> </math>  . The effective equation of state is similar to the quark matter equation of state, and involves the presence of an effective bag constant. When  $$\psi $$  <math> <mi>ψ</mi> </math>   is negative, the star has a slightly larger size as compared to GR stars with the same mass. The difference in the predicted star size between the theory with a negative  $$\psi $$  <math> <mi>ψ</mi> </math>   and GR for the same mass is attributed to an additional force appearing in the hydrodynamic equilibrium equation. The maximum compactness allowed by the strong energy condition for  $$f(\mathcal {Q}, { \mathcal {T}})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   theory and for GR is  $$C = 0.514$$  <math> <mrow> <mi>C</mi> <mo>=</mo> <mn>0.514</mn> </mrow> </math>   and 0.419, respectively, with the  $$f(\mathcal {Q}, { \mathcal {T}})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mi>Q</mi> <mo>,</mo> <mi>T</mi> <mo>)</mo> </mrow> </math>   prediction about  $$10\%$$  <math> <mrow> <mn>10</mn> <mo>%</mo> </mrow> </math>   higher than the GR one. Assuming a surface density at saturation nuclear density of  $$\rho _{\text {nuc}} = 4\times 10^{14}~\hbox {g}/\hbox {cm}^3$$  <math> <mrow> <msub> <mi>ρ</mi> <mtext>nuc</mtext> </msub> <mo>=</mo> <mn>4</mn> <mo>×</mo> <msup> <mn>10</mn> <mn>14</mn> </msup> <mspace width="3.33333pt"></mspace> <mtext>g</mtext> <mo>/</mo> <msup> <mtext>cm</mtext> <mn>3</mn> </msup> </mrow> </math>  , the maximum mass of the star is  $$4.66 M_\odot $$  <math> <mrow> <mn>4.66</mn> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>  , with a radius of 14.9 km.

Egypt

G. Nashed

Structure, maximum mass, and stability of compact stars in  $$f(\mathcal {Q,T})$$  <math> <mrow> <mi>f</mi> <mo>(</mo> <mrow> <mi>Q</mi> <mo>,</mo> <mi>T</mi> </mrow> <mo>)</mo> </mrow> </math>   gravity

We consider Klein–Gordon equation in the Dyonic Kerr–Sen black hole background, which is the charged rotating axially symmetric solution of the Einstein–Maxwell–Dilaton–Axion theory of gravity. The black hole incorporates electric, magnetic, dilatonic and axionic charges and is constructed in 3+1 dimensional spacetime. We begin our investigations with the construction of the scalar field’s governing equation, i.e., the covariant Klein–Gordon equation. With the help of the ansatz of separation of variables, we successfully separate the polar part, and find the exact solution in terms of Spheroidal Harmonics, while the radial exact solution is obtained in terms of the Confluent Heun function. The quantization of the quasibound state is done by applying the polynomial condition of the Confluent Heun function that gives rise to discrete complex-valued energy levels for massive scalar fields. The real part is the scalar field relativistic quantized energy, while the imaginary part represents the quasibound states’s decay. We present all of the sixteen possible exact energy solutions for both massive and massless scalars. We also present the investigation the Hawking radiation of the Dyonic Kerr–Sen black hole’s apparent horizon, via the Sigurd–Sannan method by making use of the obtained exact scalar wave functions. The radiation distribution function, and the Hawking temperature are also obtained.

Thailand

David Senjaya

Piyabut Burikham

The exact relativistic scalar quasibound states of the dyonic Kerr–Sen black hole: quantized energy, and Hawking radiation

This article describes the configuration of strange quark stars composed of three flavour quarks in hydrostatic equilibrium considering the energy density profile of Mak and Harko and non-zero strange quark mass ( $$m_s\ne {0}$$  <math> <mrow> <msub> <mi>m</mi> <mi>s</mi> </msub> <mo>≠</mo> <mn>0</mn> </mrow> </math>  ). A suitable stellar model is proposed assuming equation of state of interior matter as modified MIT equation of state in bag model  $$p=\frac{1}{3}(\rho -4B_g)$$  <math> <mrow> <mi>p</mi> <mo>=</mo> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mrow> <mo>(</mo> <mi>ρ</mi> <mo>-</mo> <mn>4</mn> <msub> <mi>B</mi> <mi>g</mi> </msub> <mo>)</mo> </mrow> </mrow> </math>  , where  $$B_g$$  <math> <msub> <mi>B</mi> <mi>g</mi> </msub> </math>   is known as bag constant, to predict the viability of strange stars. The interior of such compact stars is mainly composed of quarks and electrons to establish charge neutrality condition. We have checked the various stability windows depending on the energy per baryon for different values of bag constant  $$B_g$$  <math> <msub> <mi>B</mi> <mi>g</mi> </msub> </math>   and mass of strange quark  $$m_s$$  <math> <msub> <mi>m</mi> <mi>s</mi> </msub> </math>  . We have studied the effect of non-zero mass of the strange quark ( $$m_s$$  <math> <msub> <mi>m</mi> <mi>s</mi> </msub> </math>  ) on the physical properties of the strange star in the context of the modified MIT bag equation of state. We note that the maximum stellar mass decreases with increasing  $$m_s$$  <math> <msub> <mi>m</mi> <mi>s</mi> </msub> </math>  . The model is suitable for predicting the radius, central density and other properties of compact stars having mass  $$\le 2.01M_{\odot }$$  <math> <mrow> <mo>≤</mo> <mn>2.01</mn> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>  , such as  $$4U~1820-30$$  <math> <mrow> <mn>4</mn> <mi>U</mi> <mspace width="3.33333pt"></mspace> <mn>1820</mn> <mo>-</mo> <mn>30</mn> </mrow> </math>  ,  $$PSR~J1614-2230$$  <math> <mrow> <mi>P</mi> <mi>S</mi> <mi>R</mi> <mspace width="3.33333pt"></mspace> <mi>J</mi> <mn>1614</mn> <mo>-</mo> <mn>2230</mn> </mrow> </math>   etc, which are supposed to be strange stars. The radius of few recently observed compact stars are predicted in our model and they are found to be compatible with the value as predicted from observation. The model is found to be suitable in view of all the necessary criterion along with fulfilment of stability of the stellar configuration as well as stable in view of small radial perturbations.

India

R. Roy

K. Goswami

A. Saha

A. Hakim

P. Chattopadhyay

Stellar model with non-zero strange quark mass ( $$m_s\ne 0$$  <math> <mrow> <msub> <mi>m</mi> <mi>s</mi> </msub> <mo>≠</mo> <mn>0</mn> </mrow> </math>  ) and Mak–Harko density profile admitting observational results

We consider the cosmological implications of the Weyl geometric gravity theory. The basic action of the model is obtained from the simplest conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and a matter term, respectively. The total action is linearized in the Weyl scalar by introducing an auxiliary scalar field. To maintain the conformal invariance of the action the trace condition is imposed on the matter energy–momentum tensor, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the theory, and we obtain first the cosmological evolution equations for a flat, homogeneous and isotropic geometry, described by Friedmann–Lemaitre–Robertson–Walker metric, which generalize the Friedmann equations of standard general relativity. In this context we consider two cosmological models, corresponding to the vacuum state, and to the presence of matter described by a linear barotropic equation of state. In both cases we perform a detailed comparison of the predictions of the theory with the cosmological observational data, and with the standard  $$\Lambda $$  <math> <mi>Λ</mi> </math>   CDM model. By assuming that the presence of the Weyl geometric effects induce small perturbations in the homogeneous and isotropic cosmological background, and that the anisotropy parameter is small, the equations of the cosmological perturbations due to the presence of the Weyl geometric effects are derived. The time evolution of the metric and matter perturbations are explicitly obtained. Therefore, if Weyl geometric effects are present, the Universe would acquire some anisotropic characteristics, and its geometry will deviate from the standard FLRW one.

Shahab Shahidi

Cosmological implications of the Weyl geometric gravity theory

In modern cosmology, the curiosity of ultimately understanding the nature of the dark energy controlling the recent acceleration of the Universe motivates us to explore its properties by using some novel approaches. In this work, to explore the properties of dark energy we adopt the modified f(Q) gravity theory, where the non-metricity scalar Q, emerging from Weyl geometry, plays the dynamical role. For the function f(Q) we adopt the functional form  $$f(Q)=Q+ 6\gamma \,H_0^2(Q/Q_0)^n$$  <math> <mrow> <mi>f</mi> <mrow> <mo>(</mo> <mi>Q</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>Q</mi> <mo>+</mo> <mn>6</mn> <mi>γ</mi> <mspace width="0.166667em"></mspace> <msubsup> <mi>H</mi> <mn>0</mn> <mn>2</mn> </msubsup> <msup> <mrow> <mo>(</mo> <mi>Q</mi> <mo>/</mo> <msub> <mi>Q</mi> <mn>0</mn> </msub> <mo>)</mo> </mrow> <mi>n</mi> </msup> </mrow> </math>  , where  $$n,\, \gamma ,\, H_0$$  <math> <mrow> <mi>n</mi> <mo>,</mo> <mspace width="0.166667em"></mspace> <mi>γ</mi> <mo>,</mo> <mspace width="0.166667em"></mspace> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </math>   and  $$Q_0$$  <math> <msub> <mi>Q</mi> <mn>0</mn> </msub> </math>   are constants. Then, we test our constructed model against the various observational datasets, such as the Hubble, and the Pantheon+SHOES samples, and their combined sample, through the Markov Chain Monte Carlo (MCMC) statistical analysis. We also employ the parameter estimation technique to constrain the free parameters of the model. In addition, we use the constrained values of the model parameters to explore a few implications of the cosmological model. A detailed comparison of the predictions of our model with the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM model is also performed. In particular, we discuss in detail some cosmographic parameters, like the deceleration, the jerk, and the snap parameters, as well as the behavior of the dark energy and matter energy densities to see the evolution of various energy/matter profiles. The Om diagnostics is also presented to test the dark energy nature of our model, as compared to the standard  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM paradigm. Our findings show that the considered version of the non-metric f(Q) type modified gravity theory, despite some differences with respect to the  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM paradigm, can still explain the current observational results on the cosmological parameters, and provide a convincing and consistent account for the accelerating expansion of the Universe.

Sanjay Mandal

Sneha Pradhan

P. Sahoo

Cosmological observational constraints on the power law f(Q) type modified gravity theory

We consider dark energy models obtained from the general conformal transformation of the Kropina metric, representing an  $$(\alpha , \beta )$$  <math> <mrow> <mo>(</mo> <mi>α</mi> <mo>,</mo> <mi>β</mi> <mo>)</mo> </mrow> </math>  -type Finslerian geometry, constructed as the ratio of the square of a Riemannian metric  $$\alpha $$  <math> <mi>α</mi> </math>   and the one-form  $$\beta $$  <math> <mi>β</mi> </math>  . Conformal symmetries appear in many fields of physics, and they may play a fundamental role in our understanding of the Universe. We investigate the possibility of obtaining conformal theories of gravity in the osculating Barthel–Kropina geometric framework, where gravitation is described by an extended Finslerian-type model, with the metric tensor depending on both the base space coordinates and a vector field. We show that it is possible to formulate a family of conformal Barthel–Kropina theories in an osculating geometry with second-order field equations, depending on the properties of the conformal factor, whose presence leads to the appearance of an effective scalar field of geometric origin in the gravitational field equations. The cosmological implications of the theory are investigated in detail by assuming a specific relation between the component of the one-form of the Kropina metric and the conformal factor. The cosmological evolution is thus determined by the initial conditions of the scalar field and a free parameter of the model. We analyze in detail three cosmological models corresponding to different values of the theory parameters. Our results show that the conformal Barthel–Kropina model can provide an acceptable description of the observational data, and may represent a theoretically attractive alternative to the standard  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM cosmology.

Rattanasak Hama

Japan

Sorin Sabau

Conformal gravitational theories in Barthel–Kropina-type Finslerian geometry, and their cosmological implications

The astrophysical consequences of the presence of a quintessence scalar field on the evolution of the horizon and on the accretion disk surrounding a static black hole, in the scalar–vector–tensor version of modified gravity (MOG), are investigated. The positions of the stable circular orbits of the massive test particles, moving around the central object, are obtained from the extremum of the effective potential. Detailed calculations are also presented to investigate the light deflection, shadow and Shapiro effect for such a black hole. The electromagnetic properties of the accretion disks that form around such black holes are considered in detail. The energy flux and efficiency parameter are estimated analytically and numerically. A comparison with the disk properties in Schwarzschild geometry is also performed. The quantum properties of the black hole are also considered, and the Hawking temperature and the mass loss rate due to the Hawking radiation are considered. The obtained results may lead to the possibility of direct astrophysical tests of black hole type objects in modified gravity theories.

South Africa

Canada

Haidar Sheikhahmadi

Saheb Soroushfar

S. Sajadi

Astrophysical and electromagnetic emissivity properties of black holes surrounded by a quintessence type exotic fluid in the scalar–vector–tensor modified gravity