arXiv subjects

L. Perivolaropoulos

Publications and source records attributed to L. Perivolaropoulos.

At least 19 recordsLinked to original sources

arXiv2026

Cosmographic Reconstruction of the Quintessence Potential in Scalar-Tensor Gravity

We generalise the cosmographic reconstruction programme of Chakraborty, Dunsby & Scherrer to scalar-tensor gravity. Working in the Jordan frame with a general non-minimal coupling $F(\Phi)$, we derive exact closed-form expressions for the potential slope $\lambda_U$, the coupling slope $\lambda_F$, and their curvature parameters $\Gamma_U$ and $\Gamma_F$ in terms of the cosmographic parameters $(q,j,s)$, the Planck-mass running $\alpha_M = d\ln F/d\ln a$ and its derivatives. We express $\alpha_M$ and its derivatives in terms of a set of coefficients $g_n$ describing the time variation of the gravitational constant $G\propto F^{-1}$, casting all four quantities in fully observable form. We then evaluate the reconstruction against current data, including DESI~DR2 baryon acoustic oscillation measurements and Lunar Laser Ranging constraints on $\dot G/G$, propagating the cosmographic uncertainties through to the reconstructed potential. All expressions reduce analytically to those of Chakraborty, Dunsby & Scherrer in the minimally-coupled limit, which we verify symbolically. We find that the potential slope $\lambda_U$ is recovered at the few-tenths level while the curvature $\Gamma_U$ is essentially unconstrained. We further show that the positivity of the scalar kinetic term is equivalent to $w_{\rm eff,0}\ge-1$, so that the region of cosmographic parameter space closed to minimally-coupled quintessence is exactly the phantom region, and that the non-minimal coupling reopens it through a single coefficient $g_2$ of the gravitational tower. Because Lunar Laser Ranging forces $|g_1|\lesssim2\times10^{-4}$ while the reconstruction is sensitive to $g_2\sim O(0.1)$, the framework presupposes that $\alpha_M$ is passing through zero at the present epoch, as expected on the Damour--Nordtvedt least-coupling attractor.

astro-ph.CO↗

arXiv2023

Probing dark fluids and modified gravity with gravitational lensing

We generalize the Rindler-Ishak (2007) result for the lensing deflection angle in a SdS spacetime, to the case of a general spherically symmetric fluid beyond the cosmological constant. We thus derive an analytic expression to first post-Newtonian order for the lensing deflection angle in a general static spherically symmetric metric of the form $ ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(dθ^2 +\sin ^2 θdϕ^2)$ with $f(r) = 1 - \frac{2m}{r}-\sum_{i} b_i\; r_0^{-q_i}\; \left( \frac{r_0}{r}\right)^{q_i}$ where $r_0$ is the lensing impact parameter, $b_i\ll r_0^{q_i}$, $m$ is the mass of the lens and $q_i$ are real arbitrary constants related to the properties of the fluid that surrounds the lens or to modified gravity. This is a generalization of the well known Kiselev black hole metric. The approximate analytic expression of the deflection angle is verified by an exact numerical derivation and in special cases it reduces to results of previous studies. The density and pressure of the spherically symmetric fluid that induces this metric is derived in terms of the constants $b_i$. The Kiselev case of a Schwarzschild metric perturbed by a general spherically symmetric dark fluid (eg vacuum energy) is studied in some detail and consistency with the special case of Rindler Ishak result is found for the case of a cosmological constant background. Observational data of the Einstein radii from distant clusters of galaxies lead to observational constraints on the constants $b_i$ and through them on the density and pressure of dark fluids, field theories or modified gravity theories that could induce this metric.

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arXiv2022

Constraining a late time transition of $G_{\rm eff}$ using low-z galaxy survey data

It has recently been pointed out that a gravitational transition taking place at a recent redshift $z_t$, reducing the effective gravitational constant $G_{\rm eff}$ by about $10\%$ for $z>z_t$, has the potential to lead to a resolution of the Hubble tension if $z_t\lesssim 0.01$. Since $H(z)^2\sim G_{\rm eff}$, such a transition would also lead to sharp change of the slope of the Hubble diagram at $z=z_t$ and a sharp decrease in the number of galaxies per redshift bin at $z_t$. Here we attempt to impose constraints on such a transition by using two robust low-z redshift survey datasets ($z<0.01$), taken from the Six-degree Field Galaxy Survey (6dFGS) as well as the 2MASS Redshift Survey (2MRS). In both surveys, we bin the data in redshift bins and focus on the number of galaxies in each bin ($ΔN(z_i)$). We observe a peak in the distribution of galaxies near a distance of approximately 20 Mpc in both datasets. This feature could be attributed to galactic density fluctuations, to coherent peculiar velocities of galaxies or to an ultra late-time gravitational transition in the same era. In the context of the later scenario we show that this feature could have been induced by a sharp change of $G_{\rm eff}$ by $ΔG_{\rm eff}/G_{\rm eff} \simeq 0.6$ at $z_t\simeq 0.005$. Thus, in a conservative approach, this method can be used to impose constraints on a possible abrupt change of the gravitational constant taking place at very low redshifts.

astro-ph.CO↗

arXiv2022

Stabilizing Spherical Energy Shells with Angular Momentum in Gravitational Backgrounds

Spherical energy shells in General Relativity tend to collapse due to gravitational effects and/or due to tension effects. Shell stabilization may be achieved by modifying the gravitational properties of the background spacetime. Thus, gravastars consist of stiff matter shells with an interior deSitter space and an exterior Schwarzshild spacetime whose attractive gravity balances the interior repulsive gravity of the interior deSitter spacetime leading to a stable stiff matter shell. Similar stabilization effects may be achieved by considering rotating shells. Here we study the stability of slowly rotating fluid shells. We show that the angular velocity of the shell has stabilizing properties analogous to the repulsive deSitter gravity of the interior of a gravastar. We thus use the Israel junction conditions and the fluid equation of state of the rotating shell to construct the dynamical equations that determine the evolution of the rotating shell radius. These dynamical equations depend on the parameters of the background spacetime and on the angular velocity of the shell. Assuming a rotating interior and a Schwarzschild exterior spacetime we show that the angular velocity of the shell has interesting stabilizing properties on the evolution of its radius R. Thus rotating matter (or vacuum) shells can imitate black holes while avoiding the presence of a singularity and without the presence of an interior deSitter space.

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arXiv2021

Late time approaches to the Hubble tension deforming $H(z)$, worsen the growth tension

Many late time approaches for the solution of the Hubble tension use late time smooth deformations of the Hubble expansion rate $H(z)$ of the Planck18/$Λ$CDM best fit to match the locally measured value of $H_0$ while effectively keeping the comoving distance to the last scattering surface and $Ω_{0m} h^2$ fixed to maintain consistency with Planck CMB measurements. A well known problem of these approaches is that they worsen the fit to low $z$ distance probes. Here we show that another problem of these approaches is that they worsen the level of the $Ω_{0m}-σ_8$ growth tension. We use the generic class of CPL parametrizations corresponding to evolving dark energy equation of state parameter $w(z)=w_0+w_1\frac{z}{1+z}$ with local measurements $H_0$ prior and identify the pairs $(w_0, w_1)$ that satisfy this condition. This is a generic class of smooth deformations of $H(z)$ that are designed to address the Hubble tension. We show that for these models the growth tension between dynamical probe data and CMB constraints is worse than the corresponding tension of the standard Planck18/$Λ$CDM model. We justify this feature using a full numerical solution of the growth equation and fit to the data, as well as by using an approximate analytic approach. The problem does not affect recent proposed solutions of the Hubble crisis involving a SnIa intrinsic luminosity transition at $z_t\simeq 0.01$.

astro-ph.CO↗

arXiv2021

Hints for possible low redshift oscillation around the best fit $Λ$CDM model in the expansion history of the Universe

We search for possible deviations from the expectations of the concordance $Λ$CDM model in the expansion history of the Universe by analysing the Pantheon Type Ia Supernovae (SnIa) compilation along with its Monte Carlo simulations using redshift binning. We demonstrate that the redshift binned best fit $Λ$CDM matter density parameter $Ω_{0m}$ and the best fit effective absolute magnitude $\cal M$ oscillate about their full dataset best fit values with considerably large amplitudes. Using the full covariance matrix of the data taking into account systematic and statistical errors, we show that at the redshifts below $z\approx0.5$ such oscillations can only occur in 4 to 5$\%$ of the Monte Carlo simulations. While statistical fluctuations can be responsible for this apparent oscillation, we might have observed a hint for some behaviour beyond the expectations of the concordance model or a possible additional systematic in the data. If this apparent oscillation is not due to statistical or systematic effects, it could be due to either the presence of coherent inhomogeneities at low $z$ or due to oscillations of a quintessence scalar field.

astro-ph.CO↗

arXiv2020

Existence and Stability of Static Spherical Fluid Shells in a Schwarzschild-Rindler-anti-de Sitter Metric

We demonstrate the existence of static stable spherical fluid shells in the Schwarzschild-Rindler-anti-de Sitter (SRAdS) spacetime where $ds^2 = f(r)dt^{2} -\frac{dr^{2}}{f(r)}-r^{2}(dθ^2 +\sin ^2 θdϕ^2)$ with $f(r) = 1 -\frac{2Gm}{r} + 2 b r -\fracΛ{3}r^2$. This is an alternative to the well known gravastar geometry where the stability emerges due to the combination of the repulsive forces of the interior de Sitter space with the attractive forces of the exterior Schwarzschild spacetime. In the SRAdS spacetime the repulsion that leads to stability of the shell comes from a negative Rindler term while the Schwarzschild and anti-de Sitter terms are attractive. We demonstrate the existence of such stable spherical shells for three shell fluid equations of state: vacuum shell ($p=-σ$), stiff matter shell ($p=σ$) and dust shell ($p=0$) where $p$ is the shell pressure and $σ$ is the shell surface density. We also identify the metric parameter conditions that need to be satisfied for shell stability in each case. The vacuum stable shell solution in the SRAdS spacetime is consistent with previous studies by two of the authors that demonstrated the existence sf stable spherical scalar field domain walls in the SRAdS spacetime.

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arXiv2020

Scalar tachyonic instabilities in gravitational backgrounds: Existence and growth rate

It is well known that the Klein Gordon (KG) equation $\Box Φ+ m^2Φ=0$ has tachyonic unstable modes on large scales ($k^2<\vert m \vert^2$) for $m^2 0$ and multiple horizons. By solving the KG equation in the range between the event and cosmological horizons, using tortoise coordinates $r_*$, we identify the bound states of the emerging Schrodinger-like Regge-Wheeler equation corresponding to instabilities. We find that the critical value $m_{cr}$ such that for $m^2<m_{cr}^2$ bound states and instabilities appear, remains equal to the flat space value $m_{cr}=0$ for all values of background metric parameters despite the locally negative nature of the Regge-Wheeler potential for $m=0$. However, the growth rate $Ω$ of tachyonic instabilities for $m^2<0$ gets significantly reduced compared to the flat case for all parameter values of the background metric ($Ω(Q/M,M^2 Λ, mM)< \vert m \vert$). This increased lifetime of tachyonic instabilities is maximal in the case of a near extreme Schwarzschild-deSitter (SdS) black hole where $Q=0$ and the cosmological horizon is nearly equal to the event horizon ($ξ\equiv 9M^2 Λ\simeq 1$). The physical reason for this delay of instability growth appears to be the existence of a cosmological horizon that tends to narrow the negative range of the Regge-Wheeler potential in tortoise coordinates.

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arXiv2020

Hints of a Local Matter Underdensity or Modified Gravity in the Low $z$ Pantheon data

A redshift tomography of the Pantheon type Ia supernovae (SnIa) data focusing on the best fit value of the absolute magnitude $M$ and/or Hubble constant $H_0$ in the context of $Λ$CDM indicates a local variation ($z\lesssim 0.2$) at $2σ$ level, with respect to the best fit of the full dataset. If this variation is physical, it can be interpreted either as a locally higher value of $H_0$, corresponding to a local matter underdensity $δρ_0/ρ_0 \simeq -0.10 \pm 0.04$ or as a time variation of Newton's constant which implies an evolving Chandrasekhar mass and thus an evolving absolute magnitude $M$ of SnIa. The local void scenario would predict an anisotropy in the best fit value of $H_0$ since it is unlikely that we are located at the center of a local spherical underdensity. Using a hemisphere comparison method we find an anisotropy level consistent with simulated isotropic datasets. We show however, that the anisotropic sky distribution of the Pantheon SnIa data induces a preferred range of directions even in simulated Pantheon data obtained in the context of isotropic $Λ$CDM. We thus construct a more isotropically distributed subset of the Pantheon SnIa and show that the preferred range of directions disappears. Using this subset we again find no evidence for anisotropy using either the hemisphere comparison method or the dipole fit method. In the context of the modified gravity scenario, we allow for an evolving normalized Newton's constant consistent with General Relativity (GR) at early and late times $μ(z)=1+g_a z^2/(1+z)^2-g_a z^4/(1+z)^4$ and fit for $g_a$ assuming $L\sim G_{\rm{eff}}^b$. For $b=-3/2$ indicated by previous studies we find $g_a=-0.47 \pm 0.36$ which is more than $1.5σ$ away from the GR value of $g_a=0$. This weak hint for weaker gravity at low $z$ is consistent with similar evidence from growth and weak lensing data.

astro-ph.CO↗

arXiv2020

$H_0$ Tension, Phantom Dark Energy and Cosmological Parameter Degeneracies

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 $Ω_{0 \rm m}h^2$ and $d_A=\int_0^{z_{rec}}\frac{dz}{H(z)}$ remain constant (for invariant CMB spectrum) and equal to their best fit Planck/$Λ$CDM values as $H_0$, $Ω_{0 \rm m}$ 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 $Ω_{0 \rm m}h^2$ 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 ($χ^2$) is similar to that of $Λ$CDM. However, when including SnIa, BAO or growth data the quality of fit becomes worse than $Λ$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.

astro-ph.CO↗

arXiv2020

Tension of the $E_G$ statistic and RSD data with Planck/$Λ$CDM and implications for weakening gravity

The $E_G$ statistic is a powerful probe for detecting deviations from GR by combining weak lensing (WL), real-space clustering and redshift space distortion (RSD) measurements thus probing both the lensing and the growth effective Newton constants ($G_L$ and $G_{eff}$). We construct an up to date compilation of $E_G$ statistic data including both redshift and scale dependence ($E_G(R,z)$). We combine this $E_G$ data compilation with an up to date compilation of $fσ_8$ data from RSD observations to identify the current level of tension between the Planck/$Λ$CDM standard model based on general relativity and a general model independent redshift evolution parametrization of $G_L$ and $G_{eff}$. Each $fσ_8$ datapoint considered has been published separately in the context of independent analyses of distinct galaxy samples. However, there are correlations among the datapoints considered due to overlap of the analyzed galaxy samples. Due to these correlations the derived levels of tension of the best fit parameters with Planck/$Λ$CDM are somewhat overestimated but this is the price to pay for maximizing the information encoded in the compilation considered. We find that the level of tension increases from about $3.5σ$ for the $fσ_8$ data compilation alone to about $6σ$ when the $E_G$ data are also included in the analysis. The direction of the tension is the same as implied by the $fσ_8$ RSD growth data alone (lower $Ω_m$ and/or weaker effective Newton constant at low redshifts for both the lensing and the growth effective Newton constants ($G_L$ and $G_{eff}$)). These results further amplify the hints for weakening modified gravity discussed in other recent analyses.

astro-ph.CO↗

arXiv2019

Primordial Power Spectra of Cosmological Fluctuations with Generalized Uncertainty Principle and Maximum Length Quantum Mechanics

The existence of the cosmological particle horizon as the maximum measurable length $l_{max}$ in the universe leads to a generalization of the quantum uncertainty principle (GUP) to the form $Δx Δp \geq \frac{\hbar}{2}\frac{1}{1-αΔx^2} $, where $α\equiv l_{max}^{-2}$. The effects of this GUP on simple quantum mechanical systems has been shown recently by one of the authors\cite{Perivolaropoulos:2017rgq} to be extremely small (beyond current measurements) due to the extremely large scale of the current particle horizon. This is not the case in the Early Universe during the quantum generation of the inflationary primordial fluctuation spectrum. We estimate the effects of such GUP on the primordial fluctuation spectrum and on the corresponding spectral index. We generalize the field commutation (GFC) relation to $[φ(k),π_φ(k')]$=$iδ(k-k')\frac{1}{1-μφ^2(k)}$, where $μ\sim α^2\equiv l_{max}^{-4}$ is a GFC parameter, $φ$ denotes a scalar field and $π_φ$ denotes its canonical conjugate momentum. We obtain the predicted primordial perturbation spectrum as $P_S(k)=P_S^{(0)}(k)\left(1+\frac{\barμ}{k}\right)$ where $\barμ\equivμV_* \simeq \sqrtα= l_{max}^{-1}$ (here $V_*\simeq l_{max}^3$ is the volume corresponding to $l_{max}$) and $P_S^{(0)}(k)$ is the standard primordial spectrum obtained in the context of the Heisenberg uncertainty principle ($μ=0$). We show that the predicted scalar spectral index is $n_s=1-λ-\frac{\barμ}{k}$ where $λ$ is a slow-roll parameter. Using observational constraints on the scale dependence of the spectral index $n_s$ we show that the $2σ$ range of $α$ corresponds to $l_{max}\gtrsim 10^{26} m $ which is of the same order as the current particle horizon.

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arXiv2019

Constraining power of cosmological observables: blind redshift spots and optimal ranges

A cosmological observable measured in a range of redshifts can be used as a probe of a set of cosmological parameters. Given the cosmological observable and the cosmological parameter, there is an optimum range of redshifts where the observable can constrain the parameter in the most effective manner. For other redshift ranges the observable values may be degenerate with respect to the cosmological parameter values and thus inefficient in constraining the given parameter. These are blind redshift ranges. We determine the optimum and the blind redshift ranges of cosmological observables with respect to the cosmological parameters: matter density parameter $Ω_m$, equation of state parameter $w$ and a modified gravity parameter $g_a$ which parametrizes the evolution of an effective Newton's constant. We consider the observables: growth rate of matter density perturbations expressed through $f(z)$ and $fσ_8$, the distance modulus $μ(z)$, Baryon Acoustic Oscillation observables $D_V(z) \times \frac{r_s^{fid}}{r_s}$, $H \times \frac{r_s}{r_s^{fid}}$ and $D_A \times \frac{r_s^{fid}}{r_s}$, $H(z)$ measurements and the gravitational wave luminosity distance. We introduce a new statistic $S_P^O(z)\equiv \frac{ΔO}{ΔP}(z) \cdot V_{eff}^{1/2}$, including the effective survey volume $V_{eff}$, as a measure of the constraining power of a given observable $O$ with respect to a cosmological parameter $P$ as a function of redshift $z$. We find blind redshift spots $z_b$ ($S_P^O(z_b)\simeq 0$) and optimal redshift spots $z_s$ ($S_P^O(z_s)\simeq max$) for these observables with respect to the parameters $Ω_m$, $w$ and $g_a$. For $O=fσ_8$ and $P=(Ω_{m},w,g_a)$ we find blind spots at $z_b\simeq(1,2,2.7)$ respectively and optimal (sweet) spots at $z_s=(0.5,0.8,1.2)$. Thus probing higher redshifts may be less effective than probing lower redshifts with higher accuracy.

astro-ph.CO↗

arXiv2019

Reconstructing a Model for Gravity at Large Distances from Dark Matter Density Profiles

Using the Navarro-Frenk-White (NFW) dark matter density profile we reconstruct an effective field theory model for gravity at large distances from a central object by demanding that the vacuum solution has the same gravitational properties as the NFW density profile has in the context of General Relativity (GR). The dimensionally reduced reconstructed action for gravity leads to a vacuum metric that includes a modified Rindler acceleration term in addition to the Schwarzschild and cosmological constant terms. The new term is free from infrared curvature singularities and leads to a much better fit of observed galaxy velocity rotation curves than the corresponding simple Rindler term of the Grumiller metric, at the expense of one additional parameter. When the new parameter is set to zero the new metric term reduces to a Rindler constant acceleration term. We use galactic velocity rotation data to find the best fit values of the parameters of the reconstructed geometric potential and discuss possible cosmological implications.

gr-qc↗

arXiv2019

Spinning particle orbits around a black hole in an expanding background

We investigate analytically and numerically the orbits of spinning particles around black holes in the post Newtonian limit and in the presence of cosmic expansion. We show that orbits that are circular in the absence of spin, get deformed when the orbiting particle has spin. We show that the origin of this deformation is twofold: a. the background expansion rate which induces an attractive (repulsive) interaction due to the cosmic background fluid when the expansion is decelerating (accelerating) and b. a spin-orbit interaction which can be attractive or repulsive depending on the relative orientation between spin and orbital angular momentum and on the expansion rate.

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arXiv2019

Evading Derrick's theorem in curved space: Static metastable spherical domain wall

A recent analysis by one of the authors\cite{Perivolaropoulos:2018cgr} has pointed out that Derrick's theorem can be evaded in curved space. Here we extend that analysis by demonstrating the existence of a static metastable solution in a wide class of metrics that include a Schwarzschild-Rindler-AntideSitter spacetime (Grumiller metric) defined as $ds^2= f(r) dt^2 - f(r)^{-1} dr^2 - r^2 (dθ^2 +\sin^2θdϕ^2)$ with $f(r)=1-\frac{2Gm}{r}+2br-\fracΛ{3} r^2$ ($Λ<0\; b<0$). This metric emerges generically as a spherically symmetric vacuum solution in a class of scalar-tensor theories\cite{Grumiller:2010bz} as well as in Weyl conformal gravity\cite{Mannheim:1988dj}. It also emerges in General Relativity (GR) in the presence of a cosmological constant and a proper spherically symmetric perfect fluid. We demonstrate that this metric supports a static spherically symmetric metastable soliton scalar field solution that corresponds to a spherical domain wall. We derive the static solution numerically and identify a range of parameters $m, b, Λ$ of the metric for which the spherical wall is metastable. Our result is supported by both a minimization of the scalar field energy functional with proper boundary conditions and by a numerical simulation of the scalar field evolution. The metastable solution is very well approximated as $ϕ(r) = Tanh\left[q (r-r_0)\right]$ where $r_0$ is the radius of the metastable wall that depends on the parameters of the metric and $q$ determines the width of the wall. We also find the gravitational effects of the thin spherical wall solution and its backreaction on the background metric that allows its formation. We show that this backreaction does not hinder the metastability of the solution even though it can change the range of parameters that correspond to metastability.

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arXiv2018

Gravitational Interactions of Finite Thickness Global Topological Defects with Black Holes

It is well known that global topological defects induce a repulsive gravitational potential for test particles. 'What is the gravitational potential induced by black holes with a cosmological constant (Schwarzschild-de Sitter (S-dS) metric) on finite thickness global topological defects?'. This is the main question addressed in the present analysis. We also discuss the validity of Derrick's theorem when scalar fields are embedded in non-trivial gravitational backgrounds. In the context of the above question, we consider three global defect configurations: a finite thickness spherical domain wall with a central S-dS black hole, a global string loop with a S-dS black hole in the center and a global monopole near a S-dS black hole. Using an analytical model and numerical simulations of the evolving spherical wall we show that the spherical wall experiences a repelling gravitational potential due to the mass of the central black hole. This potential is further amplified by the presence of a cosmological constant. For initial domain wall radius larger than a critical value, the repulsive potential dominates over the wall tension and the wall expands towards the cosmological horizon of the S-dS metric where it develops ghost instabilities. For smaller initial radius, tension dominates and the wall contracts towards the black hole horizon where it also develops ghost instabilities. We also show, using the same analytical model and energetic arguments that a global monopole is gravitationally attracted by a black hole while a cosmological constant induces a repulsive gravitational potential as in the case of test particles. Finally we show that a global string loop with finite thickness experiences gravitational repulsion due to the cosmological constant which dominates over its tension for a radius larger than a critical radius leading to an expanding rather than contracting loop.

gr-qc↗

arXiv2017

Sudden Future Singularities in Quintessence and Scalar-Tensor Quintessence Models

We demonstrate analytically and numerically the existence of geodesically complete singularities in quintessence and scalar tensor quintessence models with scalar field potential of the form $V(ϕ)\sim \vert ϕ\vert^n$ with $0<n<1$. In the case of quintessence, the singularity which occurs at $ϕ=0$, involves divergence of the third time derivative of the scale factor (Generalized Sudden Future Singularity (GSFS)), and of the second derivative of the scalar field. In the case of scalar-tensor quintessence with the same potential and with a linear minimal coupling ($F(ϕ)=1-λϕ$), the singularity is stronger and involves divergence of the second derivative of the scale factor (Sudden Future Singularity (SFS)). We show that the scale factor close to the singularity is of the form $a(t)=a_s+b(t_{s}-t) + c(t_{s}-t)^2 +d(t_{s}-t)^q$ where $a_s,b,c,d$ are constants obtained from the dynamical equations and $t_s$ is the time of the singularity. In the case of quintessence we find $q=n+2$ (ie $2<q<3$), while for the case of scalar-tensor quintessence $q=n+1$ ($1<q<2$). We verify these analytical results numerically and extend them to the case where a perfect fluid is present. The linear and quadratic terms in $(t_{s}-t)$ that appear in the expansion of the scale factor around $t_s$ are subdominant for the diverging derivatives close to the singularity, but can play an important role in the estimation of the Hubble parameter. Using the analytically derived relations between these terms, we derive relations involving the Hubble parameter close to the singularity, which may be used as observational signatures of such singularities in this class of models. For quintessence with matter fluid, we find that close to the singularity $\dot H=\frac{3}{2}Ω_{0m} (1+z_{s})^{3}-3H^{2}$.

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