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We investigate the validity of the generalized second law of thermodynamics, applying Barrow entropy for the horizon entropy. The former arises from the fact that the black-hole surface may be deformed due to quantum-gravitational effects, quantified by a new exponent Δ. We calculate the entropy time-variation in a universe filled with the matter and dark energy fluids, as well as the corresponding quantity for the apparent horizon. We show that although in the case Δ=0, which corresponds to usual entropy, the sum of the entropy enclosed by the apparent horizon plus the entropy of the horizon itself is always a non-decreasing function of time and thus the generalized second law of thermodynamics is valid, in the case of Barrow entropy this is not true anymore, and the generalized second law of thermodynamics may be violated, depending on the universe evolution. Hence, in order not to have violation, the deformation from standard Bekenstein–Hawking expression should be small as expected.

We use observational data from Supernovae (SNIa) Pantheon sample, as well as from direct measurements of the Hubble parameter from the cosmic chronometers (CC) sample, in order to extract constraints on the scenario of Barrow holographic dark energy. The latter is a holographic dark energy model based on the recently proposed Barrow entropy, which arises from the modification of the black-hole surface due to quantum-gravitational effects. We first consider the case where the new deformation exponent Δ is the sole model parameter, and we show that although the standard value Δ = 0 , which corresponds to zero deformation, lies within the 1 σ region, a deviation is favored. In the case where we let both Δ and the second model parameter to be free we find that a deviation from standard holographic dark energy is preferred. Additionally, applying the Akaike, Bayesian and Deviance Information Criteria, we conclude that the one-parameter model is statistically compatible with Λ CDM paradigm, and preferred comparing to the two-parameter one. Finally, concerning the present value of the Hubble parameter we find that it is close to the Planck value.

In this article, we elaborate further on the Λ CDM “tension”, suggested recently by the authors Lusso et al. (Astron Astrophys 628:L4, 2019) and Risaliti and Lusso (Nat Astron 3(3):272, 2019). We combine Supernovae type Ia (SNIa) with quasars (QSO) and Gamma Ray Bursts (GRB) data in order to reconstruct in a model independent way the Hubble relation to as high redshifts as possible. Specifically, in the case of either SNIa or SNIa/QSO data we find that the current values of the cosmokinetic parameters extracted from the Gaussian process are consistent with those of Λ CDM. Including GRBs in the analysis we find a tension, which lies between 2 σ and 3 σ levels respectively. Finally, we find that at high redshifts ( z > 1 ) the corresponding cosmokinetic parameters significantly deviate from those of Λ CDM, hence the possibility of new Physics is not precluded by the present analysis.

We apply the gravity-thermodynamics conjecture, namely the first law of thermodynamics on the Universe horizon, but using the generalized Kaniadakis entropy instead of the standard Bekenstein–Hawking one. The former is a one-parameter generalization of the classical Boltzmann–Gibbs–Shannon entropy, arising from a coherent and self-consistent relativistic statistical theory. We obtain new modified cosmological scenarios, namely modified Friedmann equations, which contain new extra terms that constitute an effective dark energy sector depending on the single model Kaniadakis parameter K. We investigate the cosmological evolution, by extracting analytical expressions for the dark energy density and equation-of-state parameters and we show that the Universe exhibits the usual thermal history, with a transition redshift from deceleration to acceleration at around 0.6. Furthermore, depending on the value of K, the dark energy equation-of-state parameter deviates from ΛCDM cosmology at small redshifts, while lying always in the phantom regime, and at asymptotically large times the Universe always results in a dark-energy dominated, de Sitter phase. Finally, even in the case where we do not consider an explicit cosmological constant the resulting cosmology is very interesting and in agreement with the observed behavior.

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 in comparison to that of the standard Λ CDM evolution, and then we impose the observational bound on δ T f T f 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.

We study how the cosmological constraints from growth data are improved by including the measurements of bias from Dark Energy Survey (DES). In particular, we utilize the biasing properties of the DES Luminous Red Galaxies (LRGs) and the growth data provided by the various galaxy surveys in order to constrain the growth index ( γ ) of the linear matter perturbations. Considering a constant growth index we can put tight constraints, up to ∼ 10 % accuracy, on γ . Specifically, using the priors of the Dark Energy Survey and implementing a joint likelihood procedure between theoretical expectations and data we find that the best fit value is in between γ = 0.64 ± 0.075 and 0.65 ± 0.063 . On the other hand utilizing the Planck priors we obtain γ = 0.680 ± 0.089 and 0.690 ± 0.071 . This shows a small but non-zero deviation from General Relativity ( γ GR ≈ 6 / 11 ), nevertheless the confidence level is in the range ∼ 1.3 - 2 σ . Moreover, we find that the estimated mass of the dark-matter halo in which LRGs survive lies in the interval ∼ 6.2 × 10 12 h - 1 M ⊙ and 1.2 × 10 13 h - 1 M ⊙ , for the different bias models. Finally, allowing γ to evolve with redshift [Taylor expansion: γ ( z ) = γ 0 + γ 1 z / ( 1 + z ) ] we find that the ( γ 0 , γ 1 ) parameter solution space accommodates the GR prediction at ∼ 1.7 - 2.9 σ levels.

Primordial black hole (PBH) fluctuations can induce a stochastic gravitational wave background at second order, and since this procedure is sensitive to the underlying gravitational theory it can be used as a novel tool to test general relativity and extract constraints on possible modified gravity deviations. We apply this formalism in the framework of f ( T ) gravity, considering three viable mono-parametric models. In particular, we investigate the induced modifications at the level of the gravitational-wave source, which is encoded in terms of the power spectrum of the PBH gravitational potential, as well as at the level of their propagation, described in terms of the Green function which quantifies the propagator of the tensor perturbations. We find that, within the observationally allowed range of the f ( T ) model-parameters, the obtained deviations from general relativity, both at the levels of source and propagation, are practically negligible. Hence, we conclude that realistic and viable f ( T ) theories can safely pass the primordial black hole constraints, which may offer an additional argument in their favor.

We study the dynamical properties of a large body of varying vacuum cosmologies for which dark matter interacts with vacuum. In particular, performing the critical point analysis we investigate the existence and the stability of cosmological solutions which describe de-Sitter, radiation and matter dominated eras. We find several cases of varying vacuum models that admit stable critical points, hence they can be used in describing the cosmic history.

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 γ , 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 β .

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.