Some novel regular spacetimes are considered that show a non-stationary wormhole structure. A Simpson-Visser-like procedure is applied to reconstruct these regular spacetimes, free of time-like and space-like singularities. Such a procedure is also applied to describe a regular cosmological expansion, where the universe reaches a minimum scale and then rebounds. This type of regular spacetime is achieved by considering some scalar fields as sources, with the appropriate kinetic term and scalar potential. We show that all these sources become ghosts due to the wrong sign of the kinetic term. Nevertheless, these ghosts can be eliminated by constraints. The same procedure is also explored in the framework of modified gravities, particularly within the so-called f(R) gravity, where a new wormhole spacetime is also obtained that does not require a ghost scalar field.

We study wormhole geometries embedded in an expanding universe within a four-scalar non-linear σ model, where the target-space metric is identified with the spacetime Ricci tensor. In this framework, wormholes can remain stable even when conventional energy conditions are violated. However, once cosmological expansion is included, the effective energy density and pressure are modified by the cosmological fluid, enabling the energy conditions to be satisfied. We further present intriguing geometries in which a finite future singularity appears in our universe but not in another universe connected by the wormhole. Near the throat, the hypersurface becomes timelike, allowing trajectories to traverse to the other universe before the singularity and return afterwards. We also construct wormhole solutions motivated by galactic dark-matter halo profiles, where the required non-vanishing pressure arises naturally from the four-scalar non-linear σ model.

Within the framework of generalised entropic cosmology and its equivalent f(Q) gravity, we construct inflationary scenarios consistent with recent Atacama Cosmology Telescope (ACT) observations combined with Planck-BAO data. We work with f(Q) gravity and use the reconstruction scheme from which one can obtain an arbitrary cosmological evolution consistent with desirable theoretical or observational considerations. Explicit inflationary cosmologies of the above theory, which pass ACT-Data Release 6 (DR6) data combined with Planck and BAO, are obtained. For f(Q) gravity coupled with scalar, we obtain ACT inflation for large classes of f(Q) via the choice of the scalar potentials. The entropic cosmology based on generalised entropy, which includes most of the known entropies like Tsallis, Rényi, Barrow, etc as a particular case, is investigated. The corresponding FRW equations, depending on the parameters of generalised entropy, are presented. Using the correspondence between the generalised entropy and f(Q) gravity, we obtain generalised entropic inflation, which is consistent with the ACT-DR6. At the next step, the entropic gravity coupled with scalar is considered. It is demonstrated how one can obtain ACT-DR6-consistent inflation for such a theory based on any generalised entropy considered in this paper via the choice of scalar potentials. These findings may point towards the correct unifying entropy of the early universe.

Abstract Systems containing objects with negative mass (NMOs) are considered. Such a system consists of one object with positive mass and one NMO, where a bound state exists even though the force exerted by the NMO on the object with positive-mass is repulsive. Unlike standard binaries composed of positive-mass objects, the emitted gravitational waves exhibit decreasing frequency and amplitude over time. We propose a model that removes the ghost appearing in the construction of the Ellis–Bronnikov wormhole, a candidate for a NMO. Furthermore, we perform numerical simulations to obtain the optical appearance of such NMOs. The observed luminosity is also compared with the Schwarzschild black hole and with the Simpson–Visser wormhole, revealing clear differences in the photon ring substructure around the central object.

The recent observations of the Dark Energy Spectroscopic Instrument (DESI) indicated the possibility that the dark energy equation of state parameter w might change from w<-1 to w>-1 when the redshift z∼ 0.5 , which is called the inverse phantom crossing. In this paper, we investigate the possibility of the phantom crossing, and we construct realistic models realizing the crossing in the framework of the scalar–Einstein–Gauss-Bonnet gravity and ghost-free f(𝒢) gravity. We also investigate the scenario of the apparent phantom crossing, where dark matter energy density decreases more slowly than usually expected, which might explain the DESI observations. In the scenarios developed, the energy conditions are not violated by any component of the cosmic fluid. In the framework of the apparent phantom crossing, we also propose a new scenario, where the particle corresponding to the scalar field in the scalar–Einstein–Gauss-Bonnet gravity is dark matter. The mass of the particle might increase due to the coupling with the Gauss-Bonnet invariant, which makes the decrease of the dark matter energy density slower. This last scenario may suggest that the inverse phantom crossing might be related to the transition from the decelerating expansion of the Universe to the accelerating expansion.

The present work reveals a direct correspondence between modified theories of gravity (cosmology) and entropic cosmology based on the thermodynamics of apparent horizon. It turns out that due to the total differentiable property of entropy, the usual thermodynamic law (used for Einstein gravity) needs to be generalized for modified gravity theories having more than one thermodynamic degree of freedom (d.o.f.). For the modified theories having n number of thermodynamic d.o.f., the corresponding horizon entropy is given by Sh similar to SBH+ terms containing the time derivatives of SBH up to (n-1)-th order, and moreover, the coefficient(s) of the derivative term(s) are proportional to the modification parameter of the gravity theory (compared to the Einstein gravity; SBH is the Bekenstein-Hawking entropy). By identifying the independent thermodynamic variables from the first law of thermodynamics, we show that the equivalent thermodynamic description of modified gravity naturally allows the time derivative of the Bekenstein-Hawking entropy in the horizon entropy.

The present work shows that the second law of thermodynamics gets naturally satisfied during the entire cosmic evolution of the Universe starting from inflation to the late dark energy era, without imposing any exotic condition. This makes the interconnection between cosmology and thermodynamics more concrete. Consequently, it also depicts that why the matter fields are not in thermal equilibrium with the apparent horizon during most of the cosmic era of the Universe, except for the fluids with omega 1/4 -1/3 leading to the transitions of the Universe from an accelerating to a decelerating era and vice-versa.

We investigate the correspondence between modified gravity theories and general entropic cosmology theory. Such a theory is proposed by an analogy with Jacobson's work, where the Einstein equation was derived from the Bekenstein-Hawking entropy. We compare FLRW equations obtained in entropic gravity with those in modified gravity theories. It is found the correspondence of F(T) and F(Q) gravities and general entropic gravity. We regard the F(T) and F(Q) gravity theories as effective local theories corresponding to the entropic gravity theories and we investigate the gravitational waves. The obtained equation of the gravitational wave is identical to that in Einstein's gravity except that the gravitational coupling is modified by the functional form of the functions F(T) and F(Q). It is interesting that in the case of the Tsallis entropic cosmology, the gravitational coupling becomes small or large, which may suppress or enhance the emission of the gravitational wave.

The first part of this work provides a review of recent research on generalised entropies and their origin, as well as its application to black hole thermodynamics. To start, it is shown that the Hawking temperature and the Bekenstein–Hawking entropy are, respectively, the only possible thermodynamical temperature and entropy of the Schwarzschild black hole. Moreover, it is investigated if the other known generalised entropies, which include Rényi’s entropy, Tsallis entropy, and the four- and five-parameter generalised entropies, could correctly yield the Hawking temperature and the ADM mass. The possibility that generalised entropies could describe hairy black hole thermodynamics is also considered, both for the Reissner–Nordström black hole and for Einstein’s gravity coupled with two scalar fields. Two possibilities are investigated, namely, the case when the ADM mass does not yield the Bekenstein–Hawking entropy, and the case in which the effective mass expressing the energy inside the horizon does not yield the Hawking temperature. For the model with two scalar fields, the radii of the photon sphere and of the black hole shadow are calculated, which gives constraints on the BH parameters. These constraints are seen to be consistent, provided that the black hole is of the Schwarzschild type. Subsequently, the origin of the generalised entropies is investigated, by using their microscopic particle descriptions in the frameworks of a microcanonical ensemble and canonical ensemble, respectively. Finally, the McLaughlin expansion for the generalised entropies is used to derive, in each case, the microscopic interpretation of the generalised entropies, via the canonical and the grand canonical ensembles.

This talk is based on the collaboration with Sergei D. Odintsov. We investigate the correspondence between modified gravity theories and general entropic cosmology theory. Such a theory is proposed by an analogy with Jacobson's work, where the Einstein equation was derived from the Bekenstein-Hawking entropy. We compare FLRW equations obtained in entropic gravity with those in modified gravity theories. It is found the correspondence of $F(T)$ and $F(Q)$ gravities and general entropic gravity. We regard the $F(T)$ and $F(Q)$ gravity theories as effective local theories corresponding to the entropic gravity theories and we investigate the gravitational waves. The obtained equation of the gravitational wave is identical to that in Einstein's gravity except that the gravitational coupling is modified by the functional form of the functions $F(T)$ and $F(Q)$. It is interesting that in the case of the Tsallis entropic cosmology, the gravitational coupling becomes small or large, which may suppress or enhance the emission of the gravitational wave.

We investigate the observational viability of non-minimally coupled scalar-Einstein-Gauss-Bonnet (GB) gravity, during inflation and post-inflationary reheating dynamics, from the perspective of the latest ACT-DR6 combined with the Planck 2018 and BAO data. It turns out that the ACT result considerably affects the inflationary e-fold number compared to the case where only Planck 2018 data is taken into account. The viable parameter spaces corresponding to the inflationary ACT-DR6+Planck18+BAO substantially influence the reheating phenomenology via the reheating equation of state (w_eff) and the reheating temperature. In particular, the ACT-DR6+Planck18+BAO data seems to disfavor w_eff < 1/3 during the reheating stage, which is unlike to that of only Planck 2018 case. These reveal how the ACT-DR6 data hits the early universe phenomenology from inflation to reheating in the context of higher curvature like scalar-Einstein-GB theory of gravity.

Several models within the framework of Einstein-Gauss-Bonnet gravities are considered with regard their late-time phenomenological viability. The models contain a non-minimally coupled scalar field and satisfy a constraint on the scalar field Gauss-Bonnet coupling, that guarantees that the speed of the tensor perturbations is equal to the speed of light. The late-time cosmological evolution of these Einstein-Gauss-Bonnet models is confronted with the observational data including the Pantheon plus Type Ia supernovae catalogue, the Hubble parameter measurements (cosmic chronometers), data from cosmic microwave background radiation (CMB) and baryon acoustic oscillations (BAO) including the latest measurements from Dark Energy Spectroscopic Instrument (DESI). Among the considered class of models some of them do not fit the CMB and BAO data. However, there exists some models that generate a viable Einstein-Gauss-Bonnet scenario with well-behaved late-time cosmological evolution that fits the observational data essentially better in comparison to the standard $\Lambda$-Cold-Dark-Matter model.

Over the last decades, tests on the standard model of cosmology, the so-called $$\Lambda $$ Λ CDM model, have been widely analysed and compared with many different models for describing dark energy. Modified gravities have played an important role in this sense as an alternative to $$\Lambda $$ Λ CDM model. Previous observational data has been always favouring $$\Lambda $$ Λ CDM model in comparison to any other model. While statistically speaking, alternative models have shown their power, fitting in some cases the observational data slightly better than $$\Lambda $$ Λ CDM, the significance and goodness of the fits were not significantly relevant to exclude the standard model of cosmology. In this paper, a generalisation of exponential F ( R ) gravity is considered and compared with $$\Lambda $$ Λ CDM model by using the latest observational data. Also some well-known model independent parameterisations for the equation of state (EoS) of dark energy are explored. These scenarios are confronted with the renewed observational data involving the Pantheon plus datasets of supernovae type Ia, the Hubble parameter estimations, data from the cosmic microwave background and baryon acoustic oscillations, where the latter includes the data provided by Dark Energy Spectroscopic Instrument Collaboration. Results of this analysis suggest that standard exponential F ( R ) models provide much better fits than $$\Lambda $$ Λ CDM model, which is excluded at 4 $$\sigma $$ σ . Moreover, the parameterisations of the equation of state suggest a non-constant EoS parameter for dark energy, where $$\Lambda $$ Λ CDM model is also excluded at 4 $$\sigma $$ σ .

We propose a pseudo-scalar quantity, which is an analogue of the Chern-Simons invariant, in the framework of non-metricity gravity. By considering the coupling between the pseudo-scalar quantity and the axion, we give scenarios which may solve the problems of the axion misalignment, the S_8 problem, and the beginning of inflation. When the phase transition associated with the spontaneous breaking of the gauge symmetry of the electroweak theory or grand unified theories (GUTs) occurs, the pseudo-scalar quantity has a non-trivial value, which induces the misalignment of the axion field and axion particles are produced. If the gradient of the potential is small, the S_8 problem might be solved. We also propose a mechanism which induces inflation by the misalignment of the axion field generated by the phase transition of the GUTs.

In the realm of thermodynamics of apparent horizon, we construct a dark energy (DE) model from 4-parameter generalized entropy of apparent horizon in a spatially non-flat universe. In particular, considering a non-zero spatial curvature of the universe, we determine the dark energy fractional density and the dark energy equation of state (EoS) parameter (corresponding to the 4-parameter generalized entropy) in closed analytic forms. It turns out that the scenario can describe the correct thermal history of the universe, with the sequence of matter and dark energy epochs. Comparing with the ACDM model, the proposed generalized entropic DE model provides a higher value of present Hubble parameter for certain range of entropic parameter(s) leading to a possible resolution of Hubble tension issue. This in turn leads to a positive spatial curvature of the universe. We confront the scenario with CC & BAO, Pantheon+ & SH0ES and joint analysis of the CC & BAO & Pantheon+ & SH0ES datasets, which clearly depicts the phenomenological viability of the present model for some best fitted values of entropic parameter(s) that are indeed consistent with the resolution of Hubble tension.

We propose a new dark energy (DE) model from four parameter generalized entropy function of apparent horizon in a spatially flat universe. Such kind of generalized entropy is able to generalize all the known entropies proposed so far, for suitable representations of the entropic parameters. It turns out that the scenario can describe the correct thermal history of the universe, with the sequence of matter and dark energy epochs. Comparing with the ΛCDM model, the proposed generalized entropic DE model provides a higher value of present Hubble parameter for certain range of entropic parameter(s) leading to a possible resolution of Hubble tension issue. We confront the scenario with CC, PantheonPlus+SH0ES, DESI DR1 and compressed Planck likelihood datasets, which clearly depicts the phenomenological viability of the present model for some best fitted values of entropic parameter(s) that are indeed consistent with the resolution of Hubble tension.

We investigate the radii of the photon sphere and the black hole shadow in the framework of () gravity. For this purpose, we derive the field equation for the corresponding theory when the general spherically symmetric and static configuration is considered. This equation is the third-order differential equation with respect to ()- ( ) ||| = ( ) , where is the radial coordinate. Solving the equation, we find () as a function of , = (). By using the assumed and obtained geometry, one can calculate the scalar curvature as a function of , = ( ) , which could be solved with respect to as = ( ) . Then one finds the functional form of as a function of the scalar curvature , = () = (= ( )) . We then solve the corresponding equation perturbatively by assuming the variation of the geometry from the Schwarzschild spacetime could be small and also the deviation of () gravity from Einstein's gravity is small. As a result, we obtain an inhomogeneous linear differential equation and solve the equation in the region around the radius of the photon sphere. This is a quite general approach which maybe adopted for any modified gravity. With the help of the obtained solutions, we calculate the radii of the photon sphere and the black hole shadow and find the parameter regions consistent with the observations of M87* and Sgr A*.

We construct and investigate the dynamical black hole spacetime embedded in the expanding universe filled with cosmic fluid, such as dark energy. When the equation of state (EoS) parameter of the fluid is a constant, we find exact solutions of the Einstein equation where the Schwarzschild black hole is embedded in the expanding universe. This solution differs from the well-known McVittie metric, where the EoS parameter is not a constant but rather depends on the radial coordinate. It is shown that a dynamical black hole grows with the expansion of the universe. If primordial black holes are created before or during inflation, above dynamical black holes might be the origin of the supermassive black holes at the centre of galaxies, massive black holes suggested by the GW231123 event, and also the dark matter. The case where the cosmic fluid EoS is more general is also considered so that the universe enters the epoch of finite-time future singularity. Thermodynamics and the behaviour of black holes around different future singularities are carefully investigated. It is then demonstrated that the black hole horizon enhances the tidal force, but near the horizon, the tidal force works to press the extended object, which is in contrast with a massive body near to future singularity. We also propose a new type of future singularity where the singularity inside the black hole is a sphere with a finite radius. When the radius of the spherical singularity becomes larger than the radius of the black hole horizon, it becomes naked. The universe may end up with a cosmic doomsday when the radius of the singularity becomes infinite.

We construct models of two exotic objects: (i) a wormhole whose throat is hidden by a stellar object like a neutron star; and (ii) a wormhole inside a black hole. We work within Einstein's gravity coupled to two scalar fields with a specific choice of the scalar field Lagrangian. In general, the model contains ghosts, but they are eliminated using the constraints given by the Lagrange multiplier fields. The constraints are a generalization of the mimetic constraint, where non-dynamical dark matter effectively appears. As a result, in our model, instead of the non-dynamical dark matter, non-dynamical exotic matter like a phantom effectively arises. For the mixed wormhole-plus-star system, we find the corresponding mass-radius relations and show that it is possible to get characteristics comparable to those of ordinary neutron stars. For the wormhole inside the black hole, we find an extremal limit where the radius of the throat coincides with the radius of the event horizon and demonstrate that the Hawking temperature vanishes in this limit.

Abstract The $$H_{0}$$ H 0 tension problem is studied in the light of a matter creation mechanism (an effective approach to replacing dark energy), the way to define the matter creation rate being of pure phenomenological nature. Bayesian (probabilistic) Machine Learning is used to learn the constraints on the free parameters of the models, with the learning being based on the generated expansion rate, H(z). Taking advantage of the method, the constraints for three redshift ranges are learned. Namely, for the two redshift ranges: $$z\in [0,2]$$ z ∈ [ 0 , 2 ] (cosmic chronometers) and $$z\in [0,2.5]$$ z ∈ [ 0 , 2.5 ] (cosmic chronometers + BAO), covering already available H(z) data, to validate the learned results; and for a third redshift interval, $$z\in [0,5]$$ z ∈ [ 0 , 5 ] , for forecasting purposes. It is learned that the $$3\alpha H_{0}$$ 3 α H 0 term in the creation rate provides options that have the potential to solve the $$H_{0}$$ H 0 tension problem.