We investigate how deviations from the Bekenstein–Hawking entropy modify black-hole spacetimes through the recently proposed entropy-geometry correspondence. For four representative modified entropies, namely Barrow, Rényi, Kaniadakis, and logarithmic, we derive the corresponding effective metrics and analyze their thermodynamic and topological classification using the off-shell free energy and winding numbers. We show that Barrow and Rényi entropies yield a single unstable sector with global charge $$W=-1$$ , while logarithmic and Kaniadakis corrections produce canceling defects with $$W=0$$ , revealing topological structures absent in the Schwarzschild case. Using the modified metrics, we further calculate the photon-sphere radius and shadow size, showing that each modified entropy relation induces characteristic optical shifts. Thus, by comparing with Event Horizon Telescope observations of Sgr A $$^*$$ , we extract new bounds on all entropy-deformation parameters. Our results demonstrate that thermodynamic topology, together with photon-sphere phenomenology, offers a viable way to test generalized entropy frameworks and probe departures from the Bekenstein-Hawking area law.

India

Ankit Anand

North Macedonia

Kimet Jusufi

Greece

Cyprus

Spyros Basilakos

Chile

China

Emmanuel Saridakis

Topological and optical signatures of modified black-hole entropies

In this work we apply the gravity-thermodynamics approach for the case of generalized mass-to-horizon entropy, which is a two-parameter extension of Bekenstein–Hawking entropy that arises from the extended mass-to-horizon relation, that is in turn required in order to have consistency with the Clausius relation. We extract the modified Friedmann equations and we obtain an effective dark energy sector arising from the novel terms. We derive analytical solutions for the dark energy density parameter, the dark energy equation-of-state parameter, and the deceleration parameter, and we show that the Universe exhibits the usual thermal history with the succession of matter and dark energy epochs. Additionally, depending on the value of the entropy parameters, the dark energy equation-of-state parameter can either lie in the phantom regime at high redshifts entering into the quintessence regime at small redshifts, or it can lie in the quintessence regime at high redshifts and experience the phantom-divide crossing at small redshifts, while in the far future in all cases it asymptotically obtains the cosmological constant value $$-1$$ . Finally, we perform observational confrontation with Supernova Type Ia (SNIa), Cosmic Chronometers (CC) and Baryonic Acoustic Oscillations (BAO) datasets, showing that the scenario is in agreement with observations.

Andreas Lymperis

Maria Petronikolou

Modified cosmology through spacetime thermodynamics and generalized mass-to-horizon entropy

We show that <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> cosmology with a non-trivial connection, namely the Connection II of the literature, is dynamically equivalent with a quintom-like model. In particular, we show that the scalar field arising from the non-linear <math altimg='si1.svg'><mi>f</mi><mo stretchy='false'>(</mo><mi>Q</mi><mo stretchy='false'>)</mo></math> form, and the scalar field associated to the non-trivial connection, are combined to provide one canonical and one phantom field in the minisuperspace Lagrangian. Hence, the combination of two well-behaved fields appears effectively as a phantom field. This is fundamentally different from the usual approach in phantom and quintom cosmology, in which the phantom field is introduced ad hoc, and thus it may open a new way to handle the phantom fields, namely as effective realizations of the connection-related canonical fields.

South Africa

Andronikos Paliathanasis

Emmanuel N. Saridakis

Equivalence of <italic>f</italic>( <italic>Q</italic>) cosmology with quintom-like scenario: The phantom field as effective realization of the non-trivial connection

We construct Barrow holographic dark energy with varying exponent. Such an energy-scale-dependent behavior is typical in quantum field theory and quantum gravity under renormalization group considerations, however in the present scenario it has an additional justification, since in realistic cases one expects that Barrow entropy quantum-gravitational effects to be stronger at early times and to smooth out and disappear at late times. We impose specific, redshift-dependent ansätze for the Barrow running exponent, such as the linear, CPL-like, exponential, and trigonometric ones, and we investigate their cosmological behavior. We show that we can recover the standard thermal history of the universe, with the sequence of matter and dark energy epochs, in which the transition from deceleration to acceleration happens at <math altimg='si1.svg'><mi>z</mi><mo>&#8776;</mo><mn>0.65</mn></math>, in agreement with observations. In the most realistic case of hyperbolic tangent ansatz, in which we can easily bound Barrow exponent inside its theoretically determined bounds 0 and 1 for all redshifts, we see that the dark-energy equation-of-state parameter can be quintessence like, or experience the phantom-divide crossing, while in the future it can either tend to the cosmological constant value or start increasing again. All these features reveal that Barrow holographic dark energy with varying exponent is not only theoretically more justified than the standard, constant-exponent case, but it leads to richer cosmological behavior too.

Barrow holographic dark energy with varying exponent

We present how Tsallis cosmology can alleviate both  $$H_0$$  <math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math>   and  $$\sigma _8$$  <math> <msub> <mi>σ</mi> <mn>8</mn> </msub> </math>   tensions simultaneously. Such a modified cosmological scenario is obtained by the application of the gravity-thermodynamics conjecture, but using the non-additive Tsallis entropy, instead of the standard Bekenstein–Hawking one. Hence, one obtains modified Friedmann equations, with extra terms that depend on the new Tsallis exponent  $$\delta $$  <math> <mi>δ</mi> </math>   that quantifies the departure from standard entropy. We show that for particular  $$\delta $$  <math> <mi>δ</mi> </math>   choices we can obtain a phantom effective dark energy, which is known to be one of the sufficient mechanisms that can alleviate  $$H_0$$  <math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math>   tension. Additionally, for the same parameter choice we obtain an increased friction term and an effective Newton’s constant smaller than the usual one, and thus the  $$\sigma _8$$  <math> <msub> <mi>σ</mi> <mn>8</mn> </msub> </math>   tension is also solved. These features act as a significant advantage of Tsallis modified cosmology.

Alleviating both  $$H_0$$  <math> <msub> <mi>H</mi> <mn>0</mn> </msub> </math>   and  $$\sigma _8$$  <math> <msub> <mi>σ</mi> <mn>8</mn> </msub> </math>   tensions in Tsallis cosmology

We investigate sufficient conditions under which cubic gravity is healthy and viable at the perturbation level. We perform a detailed analysis of the scalar and tensor perturbations. We impose the requirement that the two scalar potentials, whose ratio is the post-Newtonian parameter  $$\gamma $$  <math> <mi>γ</mi> </math>  , should deviate only minimally form general relativity. Additionally, concerning tensor perturbations we impose satisfaction of the LIGO-VIRGO and Fermi Gamma-ray Burst observations, and thus we result to a gravitational-wave equation with gravitational-wave speed equal to the speed of light, and where the only deviation from general relativity appears in the dispersion relation. Furthermore, we show that cubic gravity exhibits an effective Newton’s constant that depends on the model parameter, on the background evolution, and on the wavenumber scale. Hence, by requiring its deviation from the standard Newton’s constant to be within observational bounds we extract the constraints on the single coupling parameter  $$\beta $$  <math> <mi>β</mi> </math>  .

Petros Asimakis

Building cubic gravity with healthy and viable scalar and tensor perturbations

In this Letter, we derive for the first time a characteristic three-peaked GW signal within the framework of no-scale Supergravity, being the low-energy limit of Superstring theory. We concentrate on the primordial gravitational wave (GW) spectrum induced due to second-order gravitational interactions by inflationary curvature perturbations as well as by isocurvature energy density perturbations of primordial black holes (PBHs) both amplified due to the presence of an early matter-dominated era (eMD) era before Big Bang Nucleosythesis (BBN). In particular, we work with inflection-point inflationary potentials naturally-realised within Wess-Zumino type no-scale Supergravity and giving rise to the formation of microscopic PBHs triggering an eMD era and evaporating before BBN. Remarkably, we obtain an abundant production of gravitational waves at the frequency ranges of nHz, Hz and kHz and in strong agreement with Pulsar Time Array (PTA) GW data. Interestingly enough, a simultaneous detection of all three nHz, Hz and kHz GW peaks can constitute a potential observational signature for no-scale Supergravity.

United States

Dimitri V. Nanopoulos

Italy

Theodoros Papanikolaou

Charalampos Tzerefos

Gravitational wave signatures of no-scale supergravity in NANOGrav and beyond

The no-scale flipped SU(5) superstring framework constitutes a very promising paradigm for physics below the Planck scale providing us with a very rich cosmological phenomenology in accordance with observations. In particular, it can accommodate Starobinsky-like inflation, followed by a reheating phase, which is driven by a light “flaton” field, and during which the GUT phase transition occurs. In this Letter, we extract for the first time a gravitational-wave (GW) signal which naturally arises in the context of the flipped SU(5) cosmological phenomenology and is related to the existence of an early matter era (eMD) driven by the flaton field. Specifically, we study GWs non-linearly induced by inflationary perturbations and which are abundantly produced during a sudden transition from the flaton-driven eMD era to the late-time radiation-dominated era. Remarkably, we find a GW signal with a characteristic peak frequency <math><msub><mrow><mi>f</mi></mrow><mrow><mi>GW</mi><mo>,</mo><mi>peak</mi></mrow></msub></math> depending only on the string slope <math><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup></math> and reading as <math><msub><mrow><mi>f</mi></mrow><mrow><mi>GW</mi><mo>,</mo><mi>peak</mi></mrow></msub><mo>∝</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>9</mn></mrow></msup><msup><mrow><mo>(</mo><mfrac><mrow><msup><mrow><mi>α</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow><mrow><msubsup><mrow><mi>α</mi></mrow><mrow><mo>⁎</mo></mrow><mrow><mo>′</mo></mrow></msubsup></mrow></mfrac><mo>)</mo></mrow><mrow><mn>4</mn></mrow></msup><mspace width="0.25em"></mspace><mrow><mi>Hz</mi></mrow></math>, where <math><msubsup><mrow><mi>α</mi></mrow><mrow><mo>⁎</mo></mrow><mrow><mo>′</mo></mrow></msubsup></math> is the fiducial string slope being related directly to the reduced Planck scale <math><msub><mrow><mi>M</mi></mrow><mrow><mi>Pl</mi></mrow></msub></math> as <math><msubsup><mrow><mi>α</mi></mrow><mrow><mo>⁎</mo></mrow><mrow><mo>′</mo></mrow></msubsup><mo>=</mo><mn>8</mn><mo>/</mo><msubsup><mrow><mi>M</mi></mrow><mrow><mi>Pl</mi></mrow><mrow><mn>2</mn></mrow></msubsup></math>. Interestingly enough, <math><msub><mrow><mi>f</mi></mrow><mrow><mi>GW</mi><mo>,</mo><mi>peak</mi></mrow></msub></math> lies within the nHz frequency range; hence rendering this primordial GW signal potentially detectable by SKA, NANOGrav and PTA probes at their very low frequency region of their detection bands.

Induced gravitational waves from flipped SU(5) superstring theory at nHz

Soft cosmology is an extension of standard cosmology allowing for a scale-dependent equation-of-state (EoS) parameter in the dark sectors, which is one of the properties of soft materials in condensed-matter physics, that may arise either intrinsically or effectively. We use data from Cosmic Microwave Background (CMB), Baryonic Acoustic Oscillations (BAO), Supernovae Type Ia (SNIa), and Redshift space distortion (RSD) probes, in order to impose observational constraints on soft dark energy and soft dark matter. We examine three simple models, corresponding to the minimum extensions of ΛCDM scenario, namely we consider that at large scales the dark sectors have the EoS's of ΛCDM model (dust dark matter and cosmological constant respectively), while at intermediate scales either dark energy or dark matter or both, may have a different EoS according to constant “softness” parameters <math><msub><mrow><mi>s</mi></mrow><mrow><mi>d</mi><mi>e</mi></mrow></msub></math> and <math><msub><mrow><mi>s</mi></mrow><mrow><mi>d</mi><mi>m</mi></mrow></msub></math>. The observational confrontation shows that for almost all datasets the softness parameters deviate from their ΛCDM values, in a prominent way for soft dark energy and mildly for soft dark matter, and thus the data favor soft cosmology. Finally, performing a Bayesian evidence analysis we find that the examined models are certainly preferred over ΛCDM cosmology.

Weiqiang Yang

Supriya Pan

Fotios K. Anagnostopoulos

Observational constraints on soft dark energy and soft dark matter: Challenging ΛCDM cosmology

The f(Q) theories of modified gravity arise from the consideration of non-metricity as the basic geometric quantity, and have been proven to be very efficient in describing the late-time Universe. We use the Big Bang Nucleosynthesis (BBN) formalism and observations in order to extract constraints on various classes of f(Q) models. In particular, we calculate the deviations that f(Q) terms bring on the freeze-out temperature  $$T_f$$  <math> <msub> <mi>T</mi> <mi>f</mi> </msub> </math>   in comparison to that of the standard  $$\Lambda $$  <math> <mi>Λ</mi> </math>  CDM evolution, and then we impose the observational bound on  $$ \left| \frac{\delta {T}_f}{{T}_f}\right| $$  <math> <mfenced> <mfrac> <mrow> <mi>δ</mi> <msub> <mi>T</mi> <mi>f</mi> </msub> </mrow> <msub> <mi>T</mi> <mi>f</mi> </msub> </mfrac> </mfenced> </math>   to extract constraints on the involved parameters of the considered models. Concerning the polynomial model, we show that the exponent parameter should be negative, while for the power-exponential model and the new hyperbolic tangent-power model we find that they pass the BBN constraints trivially. Finally, we examine two DGP-like f(Q) models, and we extract the bounds on their model parameters. Since many gravitational modifications, although able to describe the late-time evolution of the Universe, produce too-much modification at early times and thus fall to pass the BBN confrontation, the fact that f(Q) gravity can safely pass the BBN constraints is an important advantage of this modified gravity class.