Schwarzschild black hole and generalized second law in phantom-dominated universe

The scalar perturbation induced gravitational waves are a probe of the primordial density perturbation spectrum on small scales. In this paper, we show that they can also probe the thermal history of the universe. We assume the universe underwent a stage with a constant equation of state parameter w, followed by the radiation-dominated stage of the conventional big bang universe. We find that the infrared slope of the power spectrum of the induced stochastic gravitational wave background for decelerating cosmologies is related to the equation of state of the universe. Furthermore, the induced gravitational wave spectrum has in general a broken power-law shape around the scale of reheating. Interestingly, below the threshold 0w= of the equation of state parameter, the broken power-law presents a peak for a Dirac delta peak in the scalar spectrum. For a finite width peak, the threshold changes to w=−1/15 depending on the value of the width. In some cases, such a broken power-law gravitational wave spectrum may degenerate to the spectrum from other sources like phase transitions or global cosmic strings.

A possible candidate for the late time accelerated expanding universe is phantom energy, which possesses rather bizarre properties, such as the prediction of a Big Rip singularity and the violation of the null energy condition. The latter is a fundamental ingredient of traversable wormholes, and it has been shown that phantom energy may indeed sustain these exotic geometries. Inspired by the evolving dark energy parameter crossing the phantom divide, we consider in this work a varying equation of state parameter dependent on the radial coordinate, i.e., ω(r) = p(r)/ρ(r). We shall impose that phantom energy is concentrated in the neighbourhood of the throat, to ensure the flaring out condition, and several models are analysed. We shall also consider the possibility that these phantom wormholes be sustained by their own quantum fluctuations. The energy density of the graviton one-loop contribution to a classical energy in a phantom wormhole background and the finite one-loop energy density are considered as a self-consistent source for these wormhole geometries. The latter semi-classical approach prohibits solutions with a constant equation of state parameter, which further motivates the imposition of a radial dependent parameter, ω(r), and only permits solutions with a steep positive slope proportional to the radial derivative of the equation of state parameter, evaluated at the throat. The size of the wormhole throat as a function of the relevant parameters is also explored.

We provide exact solutions to the cosmological matter perturbation equation in a homogeneous FLRW universe with a vacuum energy that can be parametrized by a constant equation of state parameter w and a very accurate approximation for the Ansatz w(a) = w0+wa(1−a). We compute the growth index γ = log f(a)/log Ωm(a), and its redshift dependence, using the exact and approximate solutions in terms of Legendre polynomials and show that it can be parametrized as γ(a) = γ0+γa(1−a) in most cases. We then compare four different types of dark energy (DE) models: wΛCDM, DGP, f(R) and a LTB-large-void model, which have very different behaviors at z≳1. This allows us to study the possibility to differentiate between different DE alternatives using wide and deep surveys like Euclid, which will measure both photometric and spectroscopic redshifts for several hundreds of millions of galaxies up to redshift z ≃ 2. We do a Fisher matrix analysis for the prospects of differentiating among the different DE models in terms of the growth index, taken as a given function of redshift or with a principal component analysis, with a value for each redshift bin for a Euclid-like survey. We use as observables the complete and marginalized power spectrum of galaxies P(k) and the Weak Lensing (WL) power spectrum. We find that, using P(k), one can reach (2%, 5%) errors in (w0,wa), and (4%, 12%) errors in (γ0,γa), while using WL we get errors at least twice as large. These estimates allow us to differentiate easily between DGP, f(R) models and ΛCDM, while it would be more difficult to distinguish the latter from a variable equation of state parameter or LTB models using only the growth index.

In this paper we have studied the dynamics of accelerating scenario within the framework of scalar field models possessing a non-canonical kinetic term. In this toy model, the scalar field is allowed to interact with the dark matter component through a source term. We have assumed a specific form for the coupling term and then have studied the dynamics of the scalar field having a constant equation of state parameter. We have also carried out the dynamical system study of such interacting non-canonical scalar field models for power law potentials for some physically relevant specific values of the model parameters. It has been found that the only for two particular stable fixed points of the system, an accelerating solution is possible and the universe will settle down to a $\Lambda$CDM universe in future and thus there is no future singularity in this model.

Observational Constraints on Phenomenological Emergent Dark Energy and Barotropic Dark Matter Characterized by a Constant Equation of State Parameter

Holographic principle inspired dark energy description of unified early and late universe in viscous mimetic gravity

The existence and stability conditions of Einstein static universe against homogeneous scalar perturbations in the context of Lyra geometry is investigated. The stability condition is obtained in terms of the constant equation of state parameter ω = p/ρ depending on energy density ρ0 and scale factor a0 of the initial Einstein static universe. Also, the stability against vector and tensor perturbations is studied. It is shown that a stable Einstein static universe can be found in the context of Lyra geometry against scalar, vector, and tensor perturbations for suitable range and values of physical parameters.

As a deformed matter bounce scenario with a dark energy component, we propose a deformed one with running vacuum model (RVM) in which the dark energy density rho _{Lambda } is written as a power series of H^2 and dot{H} with a constant equation of state parameter, same as the cosmological constant, w=-1. Our results in analytical and numerical point of views show that in some cases same as Lambda CDM bounce scenario, although the spectral index may achieve a good consistency with observations, a positive value of running of spectral index (alpha _s) is obtained which is not compatible with inflationary paradigm where it predicts a small negative value for alpha _s. However, by extending the power series up to H^4, rho _{Lambda }=n_0+n_2 H^2+n_4 H^4, and estimating a set of consistent parameters, we obtain the spectral index n_s, a small negative value of running alpha _s and tensor to scalar ratio r, which these reveal a degeneracy between deformed matter bounce scenario with RVM-DE and inflationary cosmology.

The reconstruction of an inflationary universe considering the parametrization of the scalar spectral index as a function of the number of e − folds in the framework of a modified Friedmann equation is analyzed. In this context, we examine the possibility of reconstructing the Hubble parameter together with the effective potential considering a modified Friedmann equation specified by F ( H ) ∝ ρ , where F ( H ) corresponds to an arbitrary function of the Hubble parameter H and ρ denotes the energy density associated with the matter in the Universe. To reconstruct the background variables during the inflationary scenario, we develop a new methodology by expressing the spectral index in terms of the Hubble parameter and its derivatives. Thus, we derive a general formalism for the reconstruction of inflation, employing the slow-roll approximation in conjunction with the parametrization of the scalar spectral index as a function of the number of e-folds, N. As specific examples, we consider the simplest attractor n s − 1 = − 2/N together with different functions F ( H ) , associated to the modified Friedmann equation, to rebuild the Hubble parameter and the effective potential in terms of the scalar field ϕ. Additionally, we analyze the reheating epoch by assuming a constant equation of state parameter, determining the temperature and the number of e-folds during this period. This is done using the background variables obtained from the reconstruction of the various F ( H ) -models studied. In addition, we restrict several parameters related to the reconstructed inflationary models F ( H ) − during the inflation and reheating epochs, utilizing current astronomical data from Planck and BICEP/Keck results.

The importance of local measurements for cosmology

Phantom dark energy can produce amplified cosmic acceleration at late times, thus increasing the value of $H_0$ favored by CMB data and releasing the tension with local measurements of $H_0$. We show that the best fit value of $H_0$ in the context of the CMB power spectrum is degenerate with a constant equation of state parameter $w$, in accordance with the approximate effective linear equation $H_0 + 30.93\; w - 36.47 = 0$ ($H_0$ in $km \; sec^{-1} \; Mpc^{-1}$). This equation is derived by assuming that both $\Omega_{0 \rm m}h^2$ and $d_A=\int_0^{z_{rec}}\frac{dz}{H(z)}$ remain constant (for invariant CMB spectrum) and equal to their best fit Planck/$\Lambda$CDM values as $H_0$, $\Omega_{0 \rm m}$ and $w$ vary. For $w=-1$, this linear degeneracy equation leads to the best fit $H_0=67.4 \; km \; sec^{-1} \; Mpc^{-1}$ as expected. For $w=-1.22$ the corresponding predicted CMB best fit Hubble constant is $H_0=74 \; km \; sec^{-1} \; Mpc^{-1}$ which is identical with the value obtained by local distance ladder measurements while the best fit matter density parameter is predicted to decrease since $\Omega_{0 \rm m}h^2$ is fixed. We verify the above $H_0-w$ degeneracy equation by fitting a $w$CDM model with fixed values of $w$ to the Planck TT spectrum showing also that the quality of fit ($\chi^2$) is similar to that of $\Lambda$CDM. However, when including SnIa, BAO or growth data the quality of fit becomes worse than $\Lambda$CDM when $w< -1$. Finally, we generalize the $H_0-w(z)$ degeneracy equation for $w(z)=w_0+w_1\; z/(1+z)$ and identify analytically the full $w_0-w_1$ parameter region that leads to a best fit $H_0=74\; km \; sec^{-1} \; Mpc^{-1}$ in the context of the Planck CMB spectrum. This exploitation of $H_0-w(z)$ degeneracy can lead to immediate identification of all parameter values of a given $w(z)$ parametrization that can potentially resolve the $H_0$ tension.

We regardfTtheory as an efficient tool to explain the current cosmic acceleration and associate its evolution with the known dark energy models. The numerical scheme is applied to reconstructfTtheory from dark energy model with constant equation of state parameter and holographic dark energy model. We set the model parametersωϑandcas describing the different evolution eras and show the distinctive behavior of each case realized infTtheory. We also present the future evolution of reconstructedfTand find that it is consistent with the recent observations.

If the linear polarization of the optical emission of active galactic nuclei (AGNs) arises in magnetized accretion disk (the Milne problem), the degree of polarization should depend strongly on the spin of the central black hole. For the same black hole luminosities and masses, the polarization is substantially higher for rotating Kerr than for non-rotating Schwarzschild black holes. Statistically, this means that the majority of AGNs displaying appreciable linear polarization should have Kerr black holes. The spin dependence of the polarization is due to the fact that the radius of the innermost stable circular orbit risco depends on the spin—this radius is three gravitational radii for a Schwarzschild black hole, and a factor of six smaller for a rapidly rotating black hole. This means that the magnetic field in the region of emergence of the optical emission, which decreases with distance from risco, is higher for a non-rotating than for a rapidly rotating black hole. This higher magnetic field gives rise to strong Faraday depolarization, explaining the effect considered here.

We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this field theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Afterwards, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and extreme Reissner-Nordstrom black holes in arbitrary dimensions higher than three.

We show that rotating dyonic black holes with static and counterrotating\nhorizon exist in Einstein-Maxwell-dilaton theory when the dilaton coupling\nconstant exceeds the Kaluza-Klein value. The black holes with static horizon\nbifurcate from the static black holes. Their mass decreases with increasing\nangular momentum, their horizons are prolate.\n